Directions for the following 5 (five) item:

Read the following three passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.

Passage – 1

In India, the segregation of municipal waste at source is rare. Recycling is mostly with the informal sector. More than three-fourths of the municipal budget goes into collection and transportation, which leaves very little for processing/resource recovery and disposal. Where does waste-to-energy fit into all this? Ideally it fits in the chain after segregation (between wet waste and rest), collection, recycling, and before getting to the landfill. Which technology is most appropriate in converting waste to energy depends on what is in the waste (that is biodegradable versus non-biodegradable component) and its calorific value. The biodegradable component of India’s municipal solid waste is a little over 50 per cent, and biomethanation offers a major solution for processing this.

1. Based on the above passage, the following assumptions have been made:

1. Collection, processing and segregation of municipal waste should be with government agencies.

2. Resource recovery and recycling require technological inputs that can be best handled by private sector enterprises.

Which of the assumptions given above is/are correct ?

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

Soln: Statement 1 is an incorrect assumption. We can apply negation test to see that the negated statement does not challenge the premise of the passage at all. So, this is an incorrect assumption. Another way of solving – The assumption is the missing link between the premise and conclusion. Think of it like the linchpin holding the whole thing together. Now, the passage is not about comparison of Private and Government sector, so we can rule out both these statements as valid assumptions. 

Hence, Statement 2 is an incorrect assumption. We can also apply negation test to verify this.

2. Which one of the following statements best reflects the crux of the passage?

(a) Generation of energy from municipal solid waste is inexpensive.

(b) Biomethanation is the most ideal way of generating energy from municipal solid waste.

(c) Segregation of municipal solid waste is the first step in ensuring the success of waste-to- energy plants.

(d) The biodegradable component of India’s municipal solid waste is not adequate to provide energy from waste efficiently/effectively.

Soln: Crux is the most important or difficult part of a problem i.e. main point of the passage that is explicitly stated by the author. Option (a) is incorrect as it beyond the scope of the passage, expenses are not discussed. 

Option (b) is incorrect: The usage of “most ideal” is a red flag and so we check whether author puts it so explicitly and also if this is the main point. As the passage mentions “major” solution and not “most ideal”, we can rule this out. 

Option (c) is correct: The passage begins with premise that “In India, the segregation of municipal waste at source is rare.” Further, the conclusion which advocates biomethanation necessitates segregation. Hence we see that this given statement ties the passage together and captures the main idea.

Option (d) is incorrect as again, this statement is beyond the scope of the passage. 

Passage – 2

There is a claim that organic farming is inherently safer and healthier. The reality is that because the organic farming industry is still young and not well-regulated in India, farmers and consumers, alike, are not only confused about what products are best for them, but sometimes use products in ways that could harm them as well. For example, since organic fertilizers are difficult to obtain on a large scale in India, farmers often use farmyard manure, which may contain toxic chemicals and heavy metals. Certain plant sprays, such as Datura flower and leaf spray, have an element called atropine. If it is not applied in the right dose, it can act on the nervous system of the consumer. Unfortunately, how much and when to use it are not well-researched or regulated issues.

3. Based on the above passage, the following assumptions have been made:

1. Organic farming is inherently unsafe for both farmers and consumers.

2. Farmers and consumers need to be educated about eco-friendly food. 

Which of the assumptions given above is/are correct?

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

Soln: Statement 1 is an incorrect assumption: The premise of the passage is that organic farming is new & unregulated. Conclusion is that due to this it is not necessary that organic is definitely better in all cases. Therefore, by both Negation & general test as seen in question 1, we can see that it is not a valid assumption. 

Statement 2 is correct as we know that assumptions are most often general statements, not specific statements. Further, valid assumptions strengthen or support the conclusion, which we can see by author’s concern in the passage “…farmers and consumers, alike, are not only confused about what products are best for them, but sometimes use products in ways that could harm them as well..” 

4. Which one of the following statements best reflects the most logical, rational and practical message conveyed by the author of the passage ?

(a) In India, organic farming should not be promoted as a substitute for conventional farming.

(b) There are no safe organic alternatives to chemical fertilizers.

(c) In India, farmers need to be guided and helped to make their organic farming sustainable.

(d) The aim of organic farming should not be to generate huge profits as there is still no global market for its products.

Soln: Option (a) is incorrect as conventional farming is not being promoted by the author or being compared to organic farming. So, it can be ruled out as most logical & rational message. 

Option (b) is incorrect as it is an extreme statement. Passage mentions only a few issues with organic alternatives like datura spray which cannot be extrapolated to say that no safe organic alternatives to chemical fertilizers.

Option (c) is correct: The conclusion of the passage mentions, “The reality is that because the organic farming industry is still young and not well-regulated in India, farmers and consumers, alike, are not only confused about what products are best for them, but sometimes use products in ways that could harm them as well.” The passage explains this through example as well. Therefore, we can infer that In India, farmers need to be guided and helped to make their organic farming sustainable. (Conclusion is more specific statement, while an inference is a more generic statement drawn from the given statement/s.)

Option (d) is incorrect as this is beyond the scope of the passage. 

Passage – 3

Food consumption patterns have changed substantially in India over the past few decades. This has resulted in the disappearance of many nutritious foods such as millets. While food grain production has increased over five times since independence, it has not sufficiently addressed the issue of malnutrition. For long, the agriculture sector focused on increasing food production particularly staples, which led to lower production and consumption of indigenous traditional corps/grains, fruits and other vegetables, impacting food and nutrition security in the process. Further, intensive, monoculture agriculture practices can perpetuate the food and nutrition security problem by degrading the quality of land, water and food derived through them.

5. Based on the above passage, the following assumptions have been made:

1. To implement the Sustainable Development Goals and to achieve zero-hunger goal, monoculture agriculture practices are inevitable even if they do not address malnutrition.

2. Dependence on a few crops has negative consequences for human health and the ecosystem.

3. Government policies regarding food planning need to incorporate nutritional security.

4. For the present monoculture agriculture practices, farmers receive subsidies in various ways and government offers remunerative prices for grains and therefore they do not tend to consider crop diversity.

Which of the above assumptions are valid?

(a) 1, 2 and 4 only

(b) 2 and 3 only

(c) 3 and 4 only

(d) 1, 2, 3 and 4

Soln: The premise of the passage is “malnutrition due to changed consumption pattern” while conclusion “monoculture has led to changed consumption pattern and malnutrition”. Now, any statement that links these two and strengthens the conclusion can be taken as a vallid assumption. Also, you can test using “Negation Test”.

Statement 1 is an incorrect assumption: The passage does not make any reference to Sustainable Development Goals or zero-hunger goal. It only mentions how the change in consumption patterns and focus on stable crops have affected nutrition security. Therefore, this option is beyond the scope of this passage.

Statement 2 is a correct assumption: this statement effectively links the premise and conclusion.

Statement 3 is a correct assumption: The passage mentions, “disappearance of many nutritious foods such as millets”, “food grain production has increased over five times since independence, it has not sufficiently addressed the issue of malnutrition”.

Statement 4 is an incorrect assumption: It fails the negation test and also beyond the scope of the passage.

6. A box contains 14 black balls, 20 blue balls, 26 green balls, 28 yellow balls, 38 red balls and 54 white balls. Consider the following statements :

1. The smallest number n such that any n balls drawn from the box randomly must contain one full group of at least one colour is 175.

2. The smallest number m such that any m balls drawn from the box randomly must contain at least one ball of each colour is 167.

Which of the above statements is/are correct?

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

Soln: To find out the minimum possible number of balls that should be drawn from the box such that the balls drawn must contain one full group of at least one colour, find the maximum number of balls that we can draw without selecting a full group of any colour.

i.e. we draw one less from each colour, 13 black balls + 19 blue balls + 25 green balls + 27 yellow balls + 37 red balls + 53 white balls = 174 balls in total.

Now, if we pick any one more ball (of any colour) that group will be complete. So, the value of n = 174 + 1 = 175.

To find out the minimum possible number of balls that should be drawn from the box such that the balls drawn must contain at least one ball of each colour, we must maximise number of balls without any balls of a particular colour. 

As the number of black balls is the least, we can maximise possible number of balls without selecting a black ball. So, we have 20 blue balls + 26 green balls + 28 yellow balls + 38 red balls + 54 white balls = 166 balls in total.

Since now only black balls are left, adding any black ball fulfils our need = 166 + 1 = 167

7. If ‘ZERO’ is written as ‘CHUR’, then how is ‘PLAYER’ written?

(a) SOCAGT

(b) SODBGT

(c) SODBHT

(d) SODBHU’

Soln: ZERO is written as CHUR. 

Z + 3 = C

E + 3 = H 

R + 3 = U 

O + 3 = R

Therefore, for PLAYER –

P + 3 = S

L + 3 = O 

A + 3 = D 

Y + 3 = B 

E + 3 = H 

R + 3 = U

Hence, option (d) is correct.

Easier way to solve – in ZERO, R = U. In PLAYER, Last letter is also R, therefore last letter of answer = U, hence only option (d) can be correct.

8. Consider the following statements:

1. A is older than B.

2. C and D are of the same age.

3. E is the youngest.

4. F is younger than D.

5. F is older than A.

How many statements given above are required to determine the oldest person/persons?

(a) Only two

(b) Only three

(c) Only four

(d) All five

Soln: We need to find relationship between all 6 persons with respect to each other. Statement 1 and 2 , give us relationship between A & B and C & D respectively. Statement 4 and 5 are needed to establish relationship between these two groups and F. Including statement 3, we have complete information. Hence, all statements are needed and option (d) is correct.

9. Consider the following including the Question and the Statements: 

There are 5 members A, B, C, D, E in a family.

Question: What is the relation of E to B? 

Statement-1: A and B are a married couple. 

Statement-2: D is the father of C. 

Statement-3: E is D’s son.

Statement-4: A and C are sisters.

Which one of the following is correct in respect of the above Questions and Statements?

(a) Statement-1, Statement-2 and Statement-3 are sufficient to answer the Question.

(b) Statement-1, Statement-3 and Statement-4 are sufficient to answer the Question.

(c) All four statement together are sufficient to answer the Question.

(d) All four statements are not sufficient to answer the Question.

Soln: Statements 1, 2 and 3 alone are not sufficient, as we cannot find a link between B and E in these statements.

Statements 1, 3 and 4 alone are not sufficient, as we cannot find a link between B and E in these statements.

Now we are left with 2 choices, we try to find a solution, if we can, (c) is correct.

By statement 2 and 4, we know D is male and father of two females A & C.

By statement 3, we know D also has a son E

By statement 1, we know relationship of B with all members of this known family ie E is the brother-in-law of B. Hence, option (c) is correct.

10. Choose the group which is different from the others: 

(a) 17, 37, 47, 97

(b) 31, 41, 53, 67

(c) 71, 73, 79, 83

(d) 83, 89, 91, 97

Soln: All numbers except 91 in above options are prime number. So, this group is different from the others.

Hence, option (d) is correct.

Directions for the following 3 (three) item:

Read the following three passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.

Passage – 1

To tackle the problem of pollution in cities, policy makers think that drastic actions like temporary use of odd-even number scheme for vehicles, closing schools, factories, construction activities, and banning the use of certain type of vehicles are a way forward. Even then the air is not clean. Vehicles more than 15 years old comprise one percent of the total; and taking them off the road will not make any difference. Banning certain fuels and car types arbitrarily is not proper. Diesel engines produce more PM 2.5 and less CO2 than petrol or CNG engines. On the other hand, both diesel and CNG engines produce more NOx than petrol engines. No one has measured the amount of NOx that CNG engines are emitting. Arbitrary bans on vehicles that have passed mandated fitness tests and periodic pollution tests are unfair. What is needed is the scientific and reliable information about the source of pollutants on a continuing basis and the technologies that will work to reduce pollution from them.

11. Which one of the following statements best reflects the most logical and rational implication conveyed by the passage?

(a) Arbitrary curbs on vehicles to reduce pollution are difficult to implement.

(b) Knee-jerk reactions cannot but an evidence-based approach will be more effective.

(c) A heavy penalty should be enforced on those driving without periodic pollution tests.

(d) In the absence of laws to deal with the problem of pollution, the administration tends to make arbitrary decisions.

Soln: Imply means to “to indicate or suggest something without actually stating it,”. Imply and infer are opposites, like a throw and a catch. To imply is to hint at something, but to infer is to make an educated guess. The speaker does the implying, and the listener does the inferring.

Option (a) is incorrect as author does not hint at implementation difficulty.

Option (b) is correct: Author mentions “arbitrariness” and gives several examples hinting at the “knee-jerk” reactions and the last line of passage (which is also conclusion) makes this implication amply clear from the author. 

Option (c) is incorrect as the author leaves no hint to suggest heavy fines etc.

Option (d) is incorrect as the author is not hinting at absence of laws. 

Passage – 2

Good corporate governance structures encourage companies to provide accountability and control. A fundamental reason why corporate governance has moved onto the economic and political agenda worldwide has been the rapid growth in international capital markets. Effective corporate governance enhance access to external financing by firms, leading to greater investment, higher growth and employment. Investors look to place their funds where the standards of disclosure, of timely and accurate financial reporting, and of equal treatment to all stakeholders are met.

12. Which of the following statements best reflects the logical inference from the passage given above?

(a) It is an important agenda of the countries around the world to ensure access to good external financing.

(b) Good corporate governance improves the credibility of the firms.

(c) International capital markets ensure that the firms maintain good corporate governance.

(d) Good corporate governance paves the way for robust supply chains.

Soln: Option (a) is incorrect as this is too far-fetched. Passage merely hints at this.

Option (b) is incorrect: The passage mentions “Investors look to place their funds where the standards of disclosure, of timely and accurate financial reporting” i.e. credibility. Therefore, this line is mere restatement of the passage and An inference is not a restatement of any of the information/statements. So, this is not a suitable choice.

Option (c) is correct: This line can be inferred from the passage’s line “why corporate governance has moved onto the economic and political agenda worldwide has been the rapid growth in international capital markets”.

Option (d) is incorrect: There is no direct mention of supply chains in the passage ie outside the scope of the passage. 

Passage – 3

Elephants are landscape architects, creating clearings in the forest, preventing overgrowth of certain plant species and allowing space for the regeneration of others, which in turn provide sustenance to others, which in turn provide sustenance to other herbivorous animals. Elephants eat plants, fruits and seeds, propagating the seeds when they defecate in other places as they travel. Elephant dung provides nourishment to plants and animals and acts as a breeding ground for insects. In times of drought, they access water by digging holes which benefits other wildlife.

13. Which one of the following statements best reflects the most logical and rational inference that can be drawn from the passage?

(a) The home range of elephants needs to be a vast area of rich biodiversity.

(b) Elephants are the keystone species and they benefit the biodiversity.

(c) Rich biodiversity cannot be maintained in the forests without the presence of elephants.

(d) Elephants are capable of regenerating forests with species as per their requirement.

Soln: Option (a) is incorrect as this statement is beyond the scope of the passage.

Option (b) is correct as this line can be inferred from the passage and represents the crux of the passage as well.

Option (c) is incorrect as the statement is framed like a definitive statement and we cannot be sure whether rich biodiversity is not possible at all without elephants. It can be ruled out as extreme statement.

Option (d) is incorrect because of the mention of “as per their requirement” which cannot be deduced from the passage.

14. If 7 ⨁ + 9 ⨁ 10 = 8, 9 ⨁ 11 ⨁ 30 = 5, 11 ⨁ 17 ⨁ 21 = 13, what is the value of 23 ⨁ 4 ⨁ 15 ?

(a) 6

(b) 8

(c) 13

(d) 15

Soln: 7 + 9 + 10 = 26 | Sum of digits 2 + 6 = 8

9 + 11 + 30 = 50 | Sum of digits 5 + 0 = 5

11 + 17 + 21 = 49 | Sum of digits 4 + 9 = 13

23 + 4 + 15 = 42 | Sum of digits 4 + 2 = 6

Hence (a) is correct.

15. Let x be a positive integer such that 7x + 96 is divisible by x. How many values of x are possible?

(a) 10

(b) 11

(c) 12

(d) Infinitely many

Soln: If 7x + 96 is divisible by x, It means that 96/x is a whole number

So, x is a factor of 96 ie 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96 = 12 possible values. Hence (c) is correct.

16.If p, q, r and s are distinct single digit positive numbers, then what is the greatest value of  (p + q) (r + s) ?

(a) 230

(b) 225

(c) 224

(d) 221

Soln: To maximize the value of (p + q) (r + s), we pick 4 biggest digits – 6, 7, 8, and 9.

Now either try all combinations or directly pick combination where two numbers are most similar/closest. So, the required answer = (6 + 9) (7 + 8) = 15 × 15 = 225. Hence, answer is (b).

17. A number N is formed by writing 9 for 99 times. What is the remainder if N is divided by 13?

(a) 11

(b) 9

(c) 7

(d) 1 

Soln: In remainder questions, we can check the pattern of remainders to arrive at required answer.

Remainder 1 (9/13) = 9 

Remainder 2 (99/13) = 8 

Remainder 3 (999/13) = 11 

Remainder 4 (9999/13) = 2 

Remainder 5 (99999/13) = 3 

Remainder 6 (999999/13) = 0

Remainder 7 (9999999/13) = 9
Therefore, after this, the pattern repeats. 

Remainder 99 = 11 (as per pattern)

Hence, answer is option (a).

18. Each digit of a 9-digit number is 1. It is multiplied by itself. What is the sum of the digits of the resulting number?

(a) 64

(b) 80

(c) 81

(d) 100

Soln: The Number is 111111111 – It is divisible by 9 (by divisibility rule)

Sum of digits of 111111111×111111111 will also be divisible by 9, therefore, answer will be the option which is a multiple of 9, i.e., 81. So, answer is option (c).

19. What is the sum of all digits which appear in all the integers from 10 to 100?

(a) 855

(b) 856

(c) 910

(d) 911

Soln: There are total 91 numbers and 9 groups of 0 to 9 (in singles digits) and 10 groups of 1 to 9 each (in doubles digits) and 100.

We know that sum of first n natural numbers = n (n + 1) / 2

So, sum of 1 to 9 = 9 × 10/2 = 45

Sum = 19 × 45 = 855

Adding 1 from 100, we get answer as 856.

20. ABCD is a square. One point on each of AB and CD; and two distinct points on each of BC and DA are chosen. How many distinct triangles can be drawn using any three points as vertices out of these six points ?

(a) 16

(b) 18

(c) 20

(d) 24

Soln: As none of the 3 points are collinear, the number of distinct triangles can be found using the formula = 6C3 = (6 × 5 × 4) / (3 × 2 × 1) = 20

Directions for the following 3 (three) item:

Read the following three passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.

Passage – 1

The emissions humans put into the atmosphere now will affect the climate in the middle of the century and onwards. Technological change, meanwhile, could make a future transition away from fossil fuels cheap or it might not, leaving the world with a terrible choice between sharply reducing emissions at huge cost or suffering through the effects of unabated warming. Businesses that do not hedge against the threat of uncertain outcomes fail. The world cannot afford such recklessness on climate change.

21. Which one of the following statements best reflects the crucial message conveyed by the author of the passage ?

(a) Businesses that cause emissions may need to close down or pay for pollution in future.

(b) The only solution is technological development related to the issues of climate change.

(c) Waiting to deal with carbon emissions until technology improves is not a wise strategy.

(d) Since future technological change is uncertain, new industries should be based on renewable energy sources.

Soln: Option (a) is incorrect. Passage says “Businesses that do not hedge against the threat of uncertain outcomes fail.” This line cannot be extrapolated to say that businesses would need to close down or pay for pollution in future.

Option (b) is incorrect: the statement is using extreme terms (“only solution”) which cannot be inferred from the passage.

Option (c) is correct: The passage says, “Technological change, meanwhile, could make a future transition away from fossil fuels cheap or it might not…” This is the main message of the author wherein he prods us to act faster and not wait.

Option (d) is incorrect: This statement is too specific and we know that inference is a more generic statement drawn from the given statement/s.

Passage – 2

Environmental problems cause health problems. Substantial changes in lifestyle can reduce environmental or health problems, but this idea appears almost impossible to adopt. With environmental problems, individual efforts can be perceived as having a negligible effect and therefore lead to inertia. With health, on the other hand, individual choices can make the difference between life and death, literally. And yet, barring a few, there seems to be the same collective lethargy towards making their choices.

22. Which one of the following statements best implies the most rational assumption that can be made from the passage?

(a) We are likely to spend more money on cure than prevention.

(b) It is the job of the government to solve our environmental and public health problems.

(c) Health can be protected even if environmental problems go on unattended.

(d) Loss of traditional lifestyle and the influence of western values led to some unhealthy way of living.

Soln: As mentioned earlier in this doc, imply means to “to indicate or suggest something without actually stating it,” and infer commonly means “to guess or use reasoning to come to a conclusion based on what has been suggested.

Option (a) is correct. This option is not directly addressed but hinted in the passage. The passage discusses the difficulty in adopting substantial changes in lifestyle to reduce environmental or health problems, ie people avoiding prevention.

Option (b) is incorrect as government job or role is not hinted in the passage.

Statement (c) is incorrect. Author hints that going after health should be logical than environmental problems but the given statement means entirely different thing which is not hinted/suggested.

Statement (d) is incorrect as too far-fetched.

Passage – 3

Many people are not eating the right food. For some, it is simply a decision to stick with food they enjoy but which is not too healthy. This is leading to an increase in non-communicable disease. This is turn leads to major burden on our health-care systems that have the potential to derail the economic progress which is essential for the poor to improve their lives. For others, it is about limited access to nutritious food or a lack of affordability, leading to monotonous diets that to not provide the daily nutrients for them to develop fully. Part of the reason nutrition is under threat worldwide is that our food systems are not properly responding to nutritional needs. Somewhere along that long road from farm to fork, there are serious detours taking place.

23. Which one of the following statements best reflects the crux of the passage ?

(a) The scheme of Universal Basic Income should be implemented worldwide as a way of poverty alleviation.

(b) We must place food-based nutrition at the centre of our policy debate.

(c) Nutritional status of food should be improved by creating appropriate genetically modified crops.

(d) Using modern food processing technologies, we must fortify food items with required nutrient elements.

Soln: Crux is the most important or difficult part of a problem i.e. main point of the passage that is explicitly stated by the author. 

Option (a) is incorrect. Although this can be inferred from the passage, it is not explicitly stated by the author. Hence, we can rule this option out.

Option (b) is correct as passage discusses lack of nutrition and various reasons surrounding it. When author talks about farm to fork, he is suggesting policy level course correction.

Option (c) and Option (d) are incorrect as they discuss ideas which are beyond the scope of the passage

24. Three of the five positive integers p, q, r, s, t is even and two of them are odd (not necessarily in order). Consider the following:

1. p + q + r – s – t is definitely even.

2. 2p + q + 2r – 2s + t is definitely odd. 

Which of the above statements is/are correct?

(a) 1 Only

(b) 2 Only

(c) Both 1 and 2

(d) Neither 1 nor 2

Soln: When we add or subtract even number of odd numbers, (ex – 5-3 or 3+7) we always get even number as answer. Also, doing addition & subtraction on even numbers always yields even number, so p + q + r – s – t will always be even.

Now, the problem with Statement 2 (2p + q + 2r – 2s + t) is that we don’t know how many of the two odd numbers are converted to even numbers by multiplying with 2. So, the resulting expression can be odd if there is only 1 odd number left. 

(You can put values to verify this and check)

So, statement 2 is incorrect. Hence, option (a) is the correct answer.

25. Consider the following in respect of prime number p and composite number c.

1. 𝑝+𝑐/𝑝−𝑐 can be even.

2. 2p+c can be odd.

3. pc can be odd.

Which of the statements given above are correct?

(a) 1 and 2 only

(b) 2 and 3 only

(c) 1 and 3 only

(d) 1, 2 and 3

Soln: Prime numbers are always odd (except 2) and here p could be 2. Composite number can be odd or even. 

In this question, “can be” is used, so even if one possibility exists, statements are true. So, one way is to find just one legit solution for each and mark the answer as (d).

1. p+c and p-c can both be even, so the answer can be odd

2. 2p is even c can be odd, so the answer can be odd

3. p and c can both be odd, so the answer can be odd

26. A 3-digit number ABC, on multiplication with D gives 37DD where A, B, C and D are different non-zero digits. What is the value of A+B+C?

(a) 18

(b) 16

(c) 15

(d) Cannot be determined due to insufficient data

Soln: 37DD can be written as 3700 + 10D + D = 3700 + 11D

Now, ABC x D = 3700 + 11D

or ABC = 3700/D + 11    …(i)

Now, 3700/D should be a whole number. So, possible values of D are 1, 2, 4, and 5.

Now put these 4 values and check ABC value.

If D = 4, ABC = 925 + 11 = 936. (Rest all are rejected as they violate conditions given)

So, A + B + C = 9 + 3 + 6 = 18

Hence, option (a) is correct.

27. For any choices of values of X,Y and Z, the 6 digit number of the form XYZXYZ is divisible by :

(a) 7 and 11 only

(b) 11 and 13 only

(c) 7 and 13 only

(d) 7, 11 and 13

Soln: XYZXYZ = XYZ*1000 + XYZ = XYZ (1000 + 1) = XYZ × 1001 

As, 1001 = 7 × 11 × 13

So, this must be divisible by 7, 11 and 13.

(Note – numbers like 101, 111, 1001, 1111, 10001, 11111 are exam favourites, practice these)

28. 125 identical cubes are arranged in the form of cubical block. How many cubes are surrounded by other cubes from each side?

(a) 27

(b) 25

(c) 21

(d) 18

Soln: Length, breadth and height all have 5 cubes. Now outer 2 cubes will be exposed to air, so the inner/protected cube has Length, breadth and height as 3 cubes. So, total number of cubes = 3 x 3 x 3 = 27

29. How many distinct 8-digit numbers can be formed by rearranging the digits of the number 11223344 such that odd digits occupy odd positions and even digits occupy even positions?

(a) 12

(b) 18

(c) 36

(d) 72

Soln: We have 4 odd and 4 even positions and there are 4 odd numbers (1, 1, 3, 3) and 4 even numbers (2, 2, 4, 4).

Number of ways these 4 odd numbers can be arranged in 4 positions = 4!/(2 × 2) = 6    (2 pairs of similar numbers hence extra 2 in denominator as permutations are halved)

Therefore, Number of ways 4 even numbers (2, 2, 4, 4) can be arranged is also 6

So, total ways = 6 × 6 = 36 

Hence, option (c) is the correct answer.

30. A, B, C working independently can do a piece of work in 8, 16 and 12 days respectively. A alone works on Monday, B alone works on Tuesday, C alone works on Wednesday; A alone, again works on Thursday and so on. Consider the following statements:

1. The work will be finished on Thursday.

2. The work will be finished in 10 days. 

Which of the above statements is/are correct?

(a) 1 Only

(b) 2 Only

(c) Both 1 and 2

(d) Neither 1 nor 2

Soln: A, B, C working independently can do a piece of work in 8, 16 and 12 days respectively ie in 1 day, 1/8, 1/16 and 1/12 of total work.

Now, 1/8 + 1/16 + 1/12 = 13/48

So, in 9 days, 39/48 work done.

On 10th day, A works. so, 39/48 + 1/8 = 45/48

so, work not finished on 10th day and gets finished by 11th day which is a Thursday (Assuming First day is Monday and work started by A)

Hence, option (a) is the correct answer.

Directions for the following 3 (three) items:

Read the following three passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.

Passage – 1

We often hear about conflicts among different States in India over river waters. Of the 20 major river system, 14 are already water-stressed; 75% of the population lives in water-stressed regions, a third of whom live in water-scarce areas. Climate change, the demands of rising population and the need for agriculture to keep pace, and increased rate of urbanization and industralization will exacerbate water stress. According to the Constitution of India, water is a State subject and not that of the Union, except for regulation of inter-State rivers. Key to ensuring balance between competing demands of various stakeholders is a basin-based approach to allocate water amongst constituent regions and States. Allocating fair share of water to them requires assessments based on objective criteria, such as specificities of the river basin, size of dependent population, existing water use and demand, efficiency of use, projected future use, etc. while ensuring the environmental needs of the river and aquifers.

31. Which one of the following statements best reflects the most rational, practical and immediate action required to ensure fair and equitable allocation of water to different stakeholders?

(a) A national, pragmatic, legal and policy framework for water allocation should be made.

(b) All river systems of the country should be linked and huge aquifers created.

(c) Water channels between regions of water surplus and regions of water deficit should be created.

(d) To mitigate water crisis, water demand of sectors such as agriculture and industry should be reduced.

Soln: Option (a) is correct and best choice as passage mentions water being state subject, need for policy of basin based approach with assessment.

Options (b) and (c) are incorrect as interlinking etc are beyond the scope of passage.

Option (d) is incorrect as question is asking action required to ensure fair and equitable allocation of water specifically.

Passage – 2

More than half of Indian women and almost a quarter of Indian men of working age suffer from anaemia. According to studies, they are anywhere from 5-15% less productive than they could be, as a result thereof. India also has the largest tuberculosis burden in the world, costing 170 million workdays to the country annually. But what is just as important as lost productivity now is lost potential in the future. It is becoming increasingly clear that on many measures of cognitive ability, malnourished Indian children perform, two or three times worse than their adequately nourished peers. For an economy that will be more dependent on highly skilled workers, this poses a significant challenge. And it is one that really should be addressed given India’s demographic outlook.

32. Which one the following statements best reflects what is implied by the passage?

(a) Education system must be strengthened in rural areas.

(b) Large scale and effective implementation of skill development programme is the need of the hour.

(c) For economic development, health and nutrition of only skilled workers needs special attention.

(d) For rapid economic growth as envisaged by us, attention should be paid to health and nutrition of the people.

Soln: Options (a) and (b) are incorrect as the focus of the passage seems to be nutrition and not education or skills.

Option (c) is incorrect. The word “only” is a red flag and when we check the statement, it comes to be extreme and unfounded as per the passage.

Option (d) is correct as the author hints at the impact of health issues like anemia and tuberculosis on productivity, the effect of malnutrition on cognitive abilities in children, etc.

Passage-3

In India, a majority of farmers are marginal and small, less educated and possess low adaptive capabilities to climate change, perhaps because of credit and other constraints. So, one cannot expect autonomous adaptation to climate change. Even if it was possible, it would not be sufficient to offset losses from climate change. To deal with this, adaptation to climate change is paramount, alongside a fast mitigation response. Another solution is to have a planned or policy-driven adaptation, which would require the government to come up with policy recommendations. Perception is a necessary pre- requisite for adaptation. Whether farmers are adapting agricultural practices to climate change depends on whether they perceive it or not. However, this is not always enough for adaptation. It is important how a farmer perceives the risks associated with climate change.

33. Which one of the following statements best reflects the most logical and rational message conveyed by the author of the passage?

(a) Adaptation to climate change and mitigation response are basically the responsibilities of the government.

(b) Climate change causes a change in government policies regarding land use patters in the country.

(c) Risk perceptions of farmers are important for motivating them for taking adaptation decisions.

(d) Since mitigation is not possible, governments should come up with policies for quick response to climate change.

Soln: Option (a) is incorrect. While the passage suggests that government involvement could be beneficial, it does not state outright that these are exclusively the government’s responsibilities. The farmers’ perception and adaptation practices are also considered important.

Option (b) is incorrect. The passage doesn’t provide information regarding climate change causing changes in government policies specifically about land use patterns. The author’s focus is on the adaptation to climate change and potential policy intervention to support that adaptation.

Option (c) is correct This option aligns well with the passage. The author discusses that the farmers’ perception of the risks associated with climate change is important for adaptation. However, the author also states that perception alone is not enough for adaptation. However, it’s worth noting that the author emphasizes that perception alone is not sufficient for adaptation and suggests that there may be a need for planned or policy-driven adaptation strategies by the government.

Option (d) is incorrect. The passage does not state that mitigation is not possible. It talks about the necessity of adaptation alongside a fast mitigation response. Hence, this Option does not correctly reflect the author’s message.

34. Raj has ten pairs of red, nine pairs of white and eight pairs of black shoes in a box. If he randomly picks shoes one by one (without replacement) from the box to get a red pair of shoes to wear, what is the maximum number of attempts he has to make?

(a) 27

(b) 36

(c) 44

(d) 45

Soln: Raj has ten pairs of red, nine pairs of white and eight pairs of black shoes in a box. So, he has 20 red shoes, 18 white shoes, and 16 black shoes.

To find the maximum number of attempts we need to visualize the worst-case scenario. Let Raj draw all white and black shoes, which amounts to 18 + 16 = 34 shoes.

Now, if he picks any two shoes, they are certainly going to be red. However, we also need to ensure that the red shoes picked by him make a pair, i.e., there should be one red shoe for left foot and one red shoe for right foot. For this to happen we need to pick 11 red shoes.

So, maximum number of attempts to get a red pair of shoes = 34 + 11 = 45 Hence, option (d) is correct.

35. In how many ways can a batsman score exactly 25 runs by scoring single runs, fours and sixes only, irrespective of the sequence of scoring shots?

(a) 18

(b) 19

(c) 20

(d) 21

Soln: Let the singles taken and the fours and the sixes scored by the batsman be x, y and z respectively. So, as per the question:

x + 4y + 6z = 25, wherein x, y, z ≥ 0

If no six has been hit, i.e., z = 0 x + 4y = 25

So, the possible values of (x, y) may be (1, 6), (5, 5), (9, 4), (13, 3), (17, 2), (21, 1), (25, 0), i.e., 7 possible ways.

If one six has been hit, i.e., z = 1 x + 4y = 19

So, the possible values of (x, y) may be (3, 4), (7, 3), (11, 2), (15, 1), (19, 0), i.e., 5 possible ways.

If two sixes have been hit, i.e., z = 2 x + 4y = 13

So, the possible values of (x, y) may be (1, 3), (5, 2), (9, 1), (13, 0), i.e., 4 possible ways.

If three sixes have been hit, i.e., z = 3 x + 4y = 7

So, the possible values of (x, y) may be (3, 1), (7, 0), i.e., 2 possible ways.

If four sixes have been hit, i.e., z = 4 x + 4y = 1

So, the possible values of (x, y) may be (1, 0), i.e., 1 possible way.

So, total number of possible ways = 7 + 5 + 4 + 2 + 1 = 19 Hence, option (b) is correct.

36. There are four letters and four envelopes and exactly one letter is to be put in exactly one envelope with the correct address. If the letters are randomly inserted into the envelopes, then consider the following statements:

1. It is possible that exactly one letter goes into an incorrect envelope.

2. There are only six ways in which only two letters can go into the correct envelopes. Which of the statements given above is/are correct?

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

Soln: Statement 1:

If one letter is placed in an incorrect envelop, then the letter that belonged to that envelop must have also been placed in an incorrect envelop. So, it’s not possible that only one letter gets placed in an incorrect envelop. Either no letter will get misplaced, or at least two letters will get misplaced.

So, Statement 1 is incorrect.

Statement 2:

We need to place two letters in correct envelops and two in incorrect envelops.

We can choose the two letters to be placed in correct envelops in 4C2 ways, i.e. 6 ways. The remaining two letters will automatically get chosen to get placed in each other’s envelops (i.e. incorrect envelops).

So, Statement 2 is correct. Hence, option (b) is correct.

37. What is the remainder when 85 × 87 × 89 × 91 × 95 × 96 is divided by 100?

(a) 0

(b) 1

(c) 2

(d) 4

Soln: In 85 × 87 × 89 × 91 × 95 × 96 there are two 5’s (in 85 and 95) and a 4 (in 96).

We know that, 5 × 5 × 4 = 100

So, the given expression is completely divisible by 100. So, remainder will be zero. Hence, option (a) is correct.

38. What is the unit digit in the expansion of (57242)9×7×5×3×1 ?

(a) 2

(b) 4

(c) 6

(d) 8

Soln: (57242)9×7×5×3×1 = (57242)945

The unit digit of the resultant number only depends on the unit digit of the given number 57242, i.e. 2. Now, we know that:

21 = 2

22 = 4

23 = 8

24 = 16 (unit digit 6)

25 = 32 (unit digit 2)

And so on.

So, 2 has a cyclicity of 4. Exponent of any number ending in 2 will produce a number that will end in 2, 4, 8, or 6.

Now, 945 = 944 + 1

944 is divisible by 4. So, the last digit of (57242)945 will be the same as that of (57242)1, which is 2. Hence, option (a) is correct.

39. If ABC and DEF are both 3-digit numbers such that A, B, C, D, E, and F are distinct non-zero digits such that ABC+ DEF= 1111, then what is the value of A+B+C+D+E+F ?

(a) 28

(b) 29

(c) 30

(d) 31

Soln: ABC + DEF = 1111, wherein A, B, C, D, E, and F are distinct non-zero digits. We may get a resultant of 1111 if:

C + F = 11, say 2 + 9 = 11

B + E = 10, say 3 + 7 = 10

A + D = 10, say 4 + 6 = 10

We can double check this by adding 432 + 679 = 1111 So, A + B + C + D + E + F = 4 + 3 + 2 + 6 + 7 + 9 = 31

Hence, option (d) is correct.

40. D is a 3-digit number such that the ratio of the number to the sum of its digits is least. What is the difference between the digit at the hundred’s place and the digit at the unit’s place of D?

(a) 0

(b) 7

(c) 8

(d) 9

Soln: Let the three-digit number be XYZ.

This number is such that (100X + 10Y + Z) / (X + Y + Z) is the least possible.

For 100, this ratio is 100/1 = 100 For 101, this ratio is 101/2 = 50.5 For 109, this ratio is 109/10 = 10.9 For 110, this ratio is 110/2 = 55

For 119, this ratio is 119/11 = 10.81 For 129, this ratio is 129/12 = 10.75

So, we can see that in 100-199 range, this ratio will be the least for 199, which is 199/19 = 10.47 Similarly, in 200-299 range, this ratio will be the least for 299, which is 299/20 = 14.95 Similarly, in 300-399 range, this ratio will be the least for 399, which is 399/21 = 19

We can see this ratio is slowly increasing. For 999, it would be 999/27 = 37 So, this ratio is the least for 199.

The difference between the digit at the hundred’s place and the digit at the unit’s place = 9 – 1 = 8 Hence, option (c) is correct.

Directions for the following 3 (three) items:

Read the following three passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.

Passage – 1

In India, while the unemployment rate is a frequently used measure of poor performance of the economy, under conditions of rising school and college enrolment, it paints an inaccurate picture. The reported unemployment rate is dominated by the experience of younger Indians who face higher employment challenges and exhibit greater willingness to wait for the right job than their older peers. The unemployment challenge is greater for people with secondary or higher education, and rising education levels inflate unemployment challenges.

41. Which one of the following statements most likely reflects as to what the author of the passage intends to say?

(a)      Enrolment in schools and colleges is high but there is no quality education.

(b)      Unemployment must be seen as a function of rising education and aspirations of young Indians.

(c)       There are no labour-intensive industries to accommodate the huge number of unemployed people.

(d)      The education system should be properly designed so as to enable the educated people to be self-employed.

Soln: Option (a) is incorrect: The passage does not discuss the quality of education. Instead, it points out how rising enrollment in schools and colleges might distort the unemployment rate. Thus, this option doesn’t reflect the author’s intended message.

Option (b) is correct: This Option aligns well with the passage. The author suggests that higher education levels inflate unemployment challenges and that younger, more educated Indians face a higher employment challenge. Therefore, unemployment is indeed tied to the rising education and aspirations of young Indians.

Option (c) is incorrect: The passage doesn’t mention anything about the availability or lack thereof of labour-intensive industries. Therefore, this Option doesn’t accurately represent the author’s intended

message.

Option (d) is incorrect: The passage does not discuss the design of the education system or the concept of self-employment. Thus, this option does not reflect the author’s intended message.

Passage – 2

“Science by itself is not enough, there must be a force and discipline outside the sciences to coordinate them and point to a goal. It is not possible to run a course aright when the goal itself has not been rightly placed. What science needs is philosophy – the analysis of scientific method and the coordination of scientific purposes and results; without this, any science must be superficial. Government suffers, precisely like science, for lack of philosophy. Philosophy bears to science the same relationship which statesmanship bears to politics: movement guided by total knowledge and perspective, as against aimless and individual seeking. Just as the pursuit of knowledge becomes scholasticism when divorced from the actual needs of men and life, so the pursuit of politics becomes a destructive bedlam when divorced from science and philosophy.”

42. Which one of the following statements best reflects the most rational, logical and practical message conveyed by the passage?

(a)      Modern statesmen need to be well trained in scientific methods and philosophical thinking to enable them to have a better perspective of their roles, responsibilities and goals.

(b)      It is not desirable to have Governments managed by empirical statesmen unless well mixed with others who are grounded in learning and reflect wisdom.

(c)       As the statesmen/bureaucrats are the products of a society, it is desirable to have a system of education in a society that focuses on training its citizens in scientific method and philosophical thinking from a very early age.

(d)      It is desirable that all scientists need to be philosophers as well to make their work goal oriented and thus purposeful and useful to the society.

Soln: We have been asked to choose the most rational, logical and practical message. Hence, each of the options need to be tested for these three mentioned aspects.

Option (a) is incorrect: This statement suggests training modern statesmen in scientific methods and philosophical thinking, which is ideal but not practical. The passage stresses that government should not just be an empirical machine, bereft of values. We need ingredients of philosophy and scientific aptitude in government. However, it nowhere states how to achieve this. The need for training of statesmen has not been explicitly or implicitly mentioned. This can also be achieved via guidance, external consultancy, etc. 

Option (b) is correct: The passage makes an analogy between the relationship of science and philosophy with that of politics and statesmanship. Just like philosophy is the guiding light of science, statesmanship is the guiding light of politics. The passage indirectly calls for the presence of politics backed by perspective and knowledge of real needs of society. This line, “… so the pursuit of politics becomes a destructive bedlam when divorced from science and philosophy.” indicates that it is not desirable to have a form of politics which is divorced from scientific thinking and philosophical backing that orients politicians to work for the larger good of society rather than for short-term selfish goals. In other words, it is desirable to have a blend of empirical statesmen and men of farsightedness and wisdom in politics. This is also a practical option as it may not be possible that all politicians have a philosophic orientation and vice-versa. 

Moreover, the passage has indicated at two places that it is referring to outside help, rather than training scientists and statesmen to be philosophers themselves. This can be seen in the line, “Science by itself is not enough, there must be a force and discipline outside the sciences to coordinate them and point to a goal.”, and “Philosophy bears to science the same relationship which statesmanship bears to politics: movement guided by total knowledge and perspective”. The words “outside” and “guided” indicate more towards external guidance/consistency for statesmen, rather than training them themselves. 

Note: The term “empirical statesmen” mean statesmen that are facts, observation and data driven, and not value-laden (philosophy can be equated to values). It does not have “colonial empire” connotations here, i.e. we are not talking about British empire or any other empire of any sorts here. 

Option (c) is incorrect: While the passage mentions the importance of philosophy in science and statesmanship, it doesn’t specifically discuss the role of education in cultivating these skills from an early age.

Option (d) is incorrect: This reflects the sentiment of the passage to an extent, emphasizing the importance of philosophy in directing and giving purpose to scientific efforts. However, it might be a stretch to say that all scientists need to be philosophers. This statement sounds impractical and extreme.

Passage-3

“The last end of the state is not to dominate men, nor to restrain them by fear; rather it is so to free each man from fear that he may live and act with full security and without injury to himself or his neighbour. The end of the state, I repeat, is not to make rational beings into brute beasts and machines. It is to enable their bodies and their minds to function safely. It is to lead men to live by, and to exercise, a free reason; that they may not waste their strength in hatred, anger and guile, nor act unfairly toward one another.”

43. Based on the above passage, which one of the following terms expresses the ultimate goal of the state?

(a)      Personal safety

(b)      Health of body and mind

(c)       Communal harmony

(d)      Liberty

Soln: Option (a) is incorrect: The passage mentions that the end of the state is to “free each man from fear that he may live and act with full security and without injury to himself or his neighbour,” which does suggest personal safety. However, this might be considered as one aspect rather than the ultimate goal.

Option (b) is incorrect: While the passage does talk about enabling bodies and minds to function safely, it doesn’t suggest this as the ultimate goal of the state.

Option (c) is incorrect: The text does imply communal harmony as one of the goals – “that they may not waste their strength in hatred, anger and guile, nor act unfairly toward one another” – but again, this seems more like one of the aspect of the ultimate goal rather than the ultimate goal itself.

Option (d) is correct: The passage strongly emphasises that the end of the state is to lead men to live by, and exercise, a free reason. This suggests liberty as a core goal, encompassing elements of personal safety, the health of body and mind, and communal harmony. Based on the passage, “Liberty” – seems to best express the ultimate goal of the state.

44.     What is the remainder if 2192 is divided by 6?

(a)      0

(b)      1

(c)       2

(d)      4

Soln:

To find the remainder when 2¹⁹² is divided by 6, we can observe a pattern in the remainders of powers of 2 when divided by 6.

 When we divide powers of 2 by 6, we get the following sequence of remainders:

• divided by 6 leaves a remainder of 2.
• divided by 6 leaves a remainder of 4.
• divided by 6 leaves a remainder of 2.
• divided by 6 leaves a remainder of 4.
• divided by 6 leaves a remainder of 2.

We notice that when power of 2 is odd, the remainder is 2; and when power of 2 is even, the remainder is 4. Therefore, the answer would be 4.

45.     Consider the sequence ABC_ _ABC_DABBCD_ABCD that follows a certain pattern.  Which of the following completes the sequence?

(a)      DACB

(b)      CDAB

(c)       DCCA

(d)      DDCA

46. AB and CD are 2-digit numbers. Multiplying AB with CD results in a 3-digit number DEF. Adding DEF to another 3-digit number GHI results in 975. Further A, B, C, D. E, F, G, H, I are distinct digits. If E= 0, F=8, then what is A+B+C equal to?

(a)      6

(b)      7

(c)       8

(d)      9

Soln: As per the question, 

AB × CD = DEF     …… (i)

And, DEF + GHI = 975   …… (ii)

Also, E = 0, and F = 8 

So, equation (ii) can also be written as, D08 + GHI = 975   

Let’s consider the given sum, i.e. D08 + GHI = 975   

At unit’s place of the resulting sum we have 5. This is possible only if I = 7.  So, 8 + 7 = 15. So, we will get a carry of 1.  

Now, 1 + 0 + H = 7

Or H = 6

Now, D + G = 9. This can be obtained in following ways:

9 + 0, 8 + 1, 7 + 2, 6 + 3, 5 + 4

Since, value of E is 0, therefore 9 + 0 can be eliminated.

Since value of F is 8, therefore 8 + 1 can be eliminated.

Since value of I is 7, therefore 7 + 2 can be eliminated.

Since value of H is 6, therefore 6 + 3 can be eliminated.

Therefore, the values of D and G must be 4 or 5.

Let’s consider the given sum, i.e. D08 + GHI = 975, again. 

If D = 4 and G = 5, 408 + 567 = 975

If D = 5 and G = 4, 508 + 467 = 975

Now, considering equation (i).

If D = 5, AB × C5 = 508. This is not possible, as on multiplying any number that has 5 as unit’s digit, with any other number, we get either 0 or 5 as the unit’s digit in the resultant number.  If D = 4, AB × C4 = 408. This is possible. So, D = 4, and G = 5. 

Let’s list down the digits: A = ?

• = ?
• = ?
• = 4
• = 0
• = 8
• = 5
• = 6
• = 7

Now, we are only left with the digits 1, 2, 3, and 9. 

Analyzing AB × C4 = 408, we can see that 12 × 34 = 408

Therefore, A + B + C = 1 + 2 + 3 = 6 Hence, option (a) is correct. 

47. Consider the following statements in respect of five candidates P, Q, R, S, and T. Two statements are true and one statement is false. 

True Statement: One of P and Q was selected for the job.

False Statement: At least one of R and S was selected for the job. 

True Statement: At most two of R, S and T were selected for the job. 

Which of the following conclusions can be drawn?

1. At least four were selected for the job.
2. S was selected for the job.

Select the correct answer using the code given below:

• 1 only
• 2 only
• Both 1 and 2
• Neither 1 nor 2

Soln: The five candidates are P, Q, R, S, and T. The given statements are:

True statement: One of P and Q was selected for the job. So, either P was selected or Q was selected. 

False statement: At least one of R and S was selected for the job. As this statement is false, we can deduce that neither R nor S was selected for the job.

True statement: At most two of R, S and T were selected for the job. But we already know that neither R nor S was selected for the job. So, we are only left with T. It may or may not be selected.  

The selected candidates maybe: 

P, PT, Q, QT

So, the number of candidates that can be selected is either 1 or 2.  

So, none of the given conclusions is correct. 

Hence, option (d) is correct. 

48.     Let P, Q, R, S and T be five statements such that: I. If P is true, then both Q and S are true. II. If R and S are true, then T is false.

Which of the following can be concluded?

1. If T is true, then at least one of P and R must be false.
2. If Q is true, then P is true.

Select the correct answer using the code given below:

• 1 Only
• 2 Only
• Both 1 and 2
• Neither 1 nor 2

Soln:

1. If P is true, then both Q and S are true. However, if P is false, we cannot say anything about Q and S.

1. If R and S are true, then T is false. However, if only one of R and S is true, or both of them are false, then we cannot say anything about T.

Now, let’s analyze the given conclusions. 

Conclusion 1: If T is true, then at least one of P and R must be false.

If T is true, then it means that at least one of R and S must be false. 

Now, if S is false then it means that P must also be false. 

So, Conclusion 1 is correct. 

Conclusion 2: If Q is true, then P is true.

If Q is true, then it doesn’t necessarily mean that P must be true.  So, Conclusion 2 is not correct.

Hence, option (a) is correct. 

49. A cuboid of dimensions 7cm × 5cm × 3cm is painted red, green and blue colour on each pair of opposite faces of dimensions 7cm × 5cm × 5cm, 5cm × 3cm, 7cm × 3cm respectively. Then the cuboid is cut and separated into various cubes each of side length 1cm. Which of the following statements is/are correct?

1. There are exactly 15 small cubes with no paint on any face.
2. There are exactly 6 small cubes with exactly two faces, one painted with blue and the other with green.

Select the correct answer using the code given below:

• 1 Only
• 2 Only
• Both 1 and 2
• Neither 1 nor 2

Soln: A cuboid of dimensions 7 cm × 5 cm × 3 cm will have:

• Two faces of dimensions 7 cm x 5 cm. These faces are painted red.
• Two faces of dimensions 5 cm x 3 cm. These faces are painted green.
• Two faces of dimensions 7 cm x 3 cm. These faces are painted blue.

Statement 1:

Only the internal cubes will have no paint on any face. So, we basically need to find out the number of internal cubes in the cuboid. 

Number of internal cubes in the cuboid = (7 – 2) × (5 – 2) × (3 – 2) = 5 × 3 × 1 = 15 

So, Statement 1 is correct. 

Statement 2:

We need to find the number of cubes having only two painted faces, one with blue and the other with green colour. These cubes can be found in the middle of the four 3 cm edges. There is only one such cube at the middle of each of these four 3 cm edges. So, there are only 4 such cubes. 

So, Statement 2 is incorrect. 

Hence, option (a) is correct. 

50. The letters of the word “INCOMPREHENSIBILITIES” are arranged alphabetically in reverse order. How many positions of the letter/letters will remain unchanged?

• None
• One
• Two
• Three

Soln: The given word is INCOMPREHENSIBILITIES. 

On arranging its letters alphabetically in reverse order, we will get: TSSRPONNMLIIIIIHEEECB 

Now, let’s compare the two to identify the letters with unchanged positions. We find that only two I’s remain in the same position:

Hence, option (c) is correct. 

Directions for the following 4(four) items:

Read the following four passage and answer the items that follow the passages. Your answers to these items should be based on the passages only.

Passage-1

The paradox of choice is illustrated by the story of Buridan’s ass. Jean Buridan, the 14^th century philosopher, wrote about free will and the inability to choose due to numerous choices and uncertainties. In the story, a donkey stands between two equally appealing stacks of hay. Unable to decide which to eat, it starves to death. Changes in technology and innovations such as smart phones and tablets only exacerbate our glut of choices. Constant connectivity and overconsumption of real-time data and social media can leave little room for self-reflection and rest, making decisions more difficult. Life is about choices. Many people are overwhelmed with attractive life choices, yet find themselves unhappy and anxious. 

51.  Which one of the following statements best reflects the most logical message implied by the above passage?

• Modern technology enfeebles societal structure and makes life difficult.
• Modern life is full of uncertainties and endless difficult choices.
• We are influenced by the opinion of others and have no courage to follow our own convictions.
• In our lives, having too few choices may not be a good thing, but having too many can be equally as difficult.

Soln: Option (a) is incorrect: While the passage mentions technology and its role in amplifying our number of choices, it does not directly address how it weakens the societal structure. So, this option might not be the most accurate representation of the passage.

Option (b) is incorrect: This Option aligns with the passage’s theme, which discusses the paradox of choice and how an abundance of options can cause difficulties in decision-making. However, the passage does not explicitly discuss the uncertainties of modern life.

Option (c) is incorrect: The passage does not discuss the influence of others’ opinions on our decisionmaking or our lack of courage to follow our convictions. Therefore, this option does not reflect the passage’s implied message.

Option (d) is correct: This Option captures the essence of the passage well, which focuses on the paradox of choice—how both the lack of choices and an overabundance of them can lead to decisionmaking difficulties.

Passage-2

Household finance in India is unique. We have a tendency to invest heavily in physical assets such as gold and property. Steps to encourage the financialization of savings are critical. A populace accustomed to traditional processes will not simply jump into financialization. Hurdles to change include onerous bureaucracy, a scepticism of organized financial institutions, a lack of basic information about which of the myriad services and providers is best for each family, and how (and even if) one can make the transition between them if necessary.

52.   Regarding the financialization of household savings, which of the following statements best reflect the solutions that are implied by the passage?

1. A flexible environment is needed to develop solutions.
2. Households need customized solutions.
3. Innovations in financial technology are required.

Select the correct answer using the code given below:

• 1 and 2 only
• 2 and 3 only
• 1 and 3 only
• 1, 2 and 3

Soln: The passage highlights the critical need to encourage the financialization of savings. However, it also opines that people would only jump into financialization after addressing some hurdles. 

Statement 1 is correct: The line “Hurdles to change include onerous bureaucracy…”  implies a rigid and challenging environment creating challenges in the financialization of household savings. Thus,  a flexible environment is required to develop solutions to address the challenges related to the financialization of savings. Thus, it is a correct statement. 

Statement 2 is correct: The line “A lack of basic information about which of the myriad services and provers is best for each family.” reflects that families do not have information and access to solutions that meet their specific needs. This can be solved by providing customized solutions to each household. Thus, it is a correct statement. 

Statement 3 is incorrect: The passage focuses more on the scepticism of organized financial institutions and the lack of knowledge among households. While financial technology innovations can be beneficial in improving access to information and services, they are not directly implied as a solution in the passage. 

Passage-3

Pharmaceutical patents grant protection to the patentee for the duration of the patent term. The patentees enjoy the liberty to determine the price of medicines, which is time-limited to the period of monopoly, but could be unaffordable to the public. Such patent protection offered to the patentees is believed to benefit the public over the longer term through innovations and research and development (R&D), although it comes at a cost, in the nature of higher prices for patented medicine. The patent—provide the patentee with a legitimate mechanism to get returns on the costs incurred in innovation and research.

53.       Based on the above passage, the following assumptions have been made:

1. Patent protection given to patentees puts a huge burden on public’s purchasing power in accessing patented medicines.
2. Dependence on other countries for pharmaceutical products is a huge burden for developing and poor countries.
3. Providing medicines to the public at affordable prices is a key goal during the public health policy design in many countries.
4. Governments need to find and appropriate balance between the rights of patentees and the requirements of the patients.

Which of the above assumptions are valid?

• 1 and 2
• 1 and 4
• 3 and 4
• 2 and 3

Soln: Statement 1 is correct: The line, “The patentees enjoy the liberty to determine the prices of medicines, which is time-limited to the period of monopoly, but could be unaffordable to the public” assumes that patent protection puts a huge burden on the purchasing power of the public and may even make its access unaffordable. 

Statement 2 is incorrect: Although this statement is true in general, it is beyond the scope of the passage as it nowhere talks about the burden imposed on developing and poor countries as a whole in accessing pharmaceutical products. 

Statement 3 is incorrect: This statement is also true in general, however, the passage does not talk about the public health policy design of the countries and its goals. 

Statement 4 is correct: The line, “Such patent protection offered to the patentees is believed to benefit the public over the long term through innovation and research and development (R&D), although it comes at a cost, in the nature of higher prices for the patented medicines” indicates the desirability of the patent regime and price protection. At the same time, higher medicines prices put a burden on the public. Therefore, governments need to balance short-term needs with long-term goals. 

Passage-4

India should ensure the growth of the digital economy while keeping personal data of citizens secure and protected. No one will innovate in a surveillance-oriented environment or in a place where an individual’s personal information is compromised. The ultimate control of data must reside with the individuals who generate it; they should be enabled to use, restrict or monetize it as they wish. Therefore, data protection laws should enable the right kind of innovation–one that is user-centric and privacy protecting.

• Based on the above passage, the following assumptions have been made:
  • Protection of privacy is not just a right, but it has value to the economy.
  • There is a fundamental link between privacy and innovation.

Which of the above assumptions is/are valid?

• 1 only
  • 2 only
  • Both 1 and 2
  • Neither 1 nor 2

Soln: Statement 1 is correct:  The lines, “The ultimate control of data must reside with the individuals who generate it; they should be enabled to use, restrict or monetise it as they wish” highlights how privacy is a matter of right. Also, giving control over the monetisation of this data indicates that privacy has an economic value as well. 

Statement 2 is correct: The line, “No one will innovate in a surveillance-oriented environment or in a place where an individual’s personal information is compromised” establishes a direct link between innovation and privacy. Innovation fosters an environment, where privacy is protected. 

• In an examination, the maximum marks for each of the four papers namely P, Q, R and S are

100. Marks scored by the students are in integers. A student can score 99% in n different ways. What is the value of n?

• 16
  • 17
  • 23
  • 35

Soln: The maximum marks = 100 + 100 + 100 + 100 = 400

The marks scored by the student = 99% of 400 = 396

So, basically he has lost 4 marks in total. He can lose these 4 marks in the following ways:

• (4, 0, 0, 0): Scored 100 in three papers, and scored 96 is one paper. This can be done in 4!/3! = 4 possible ways.
• (3, 1, 0, 0): Scored 100 in two papers, 99 in one and 97 in one. This can be done in 4!/2! = 12 possible ways.
• (2, 1, 1, 0): Scored 100 in one paper, 99 in two papers, and 98 in one. This can be done in 4!/2! = 12 possible ways.
• (2, 2, 0, 0): Scored 100 in two papers, and 98 in other two. This can be done in 4!/(2! 2!) = 6 possible ways.
• (1, 1, 1, 1): Scored 99 in all the four papers. This can be done only in 1 possible way.

So, n = 4 + 12 + 12 + 6 + 1 = 35 Hence, option (d) is correct. 

56.  A flag has to be designed with 4 horizontal strips using some or all of the colours red, green and yellow. What is the number of different ways in which this can be done so that no two adjacent stripes have the same colour?  

(a)       12

(b)      18

(c)      24

(d)      36

Soln: Let’s consider the possibilities for each stripe:

For the first stripe, we have three colour options – (red, green, yellow).

For the second stripe, we need to choose a colour different from the first stripe. So, we have two colour options.

For the third stripe, we need to choose a colour different from the second stripe. So, we have two colour options.

For the fourth stripe, we need to choose a colour different from the third stripe. So, we have two colour options.

So, total number of possible ways to design the flag = 3 x 2 x 2 x 2 = 24 Hence, option (c) is correct. 

 57.    A rectangular floor measures 4 m in length and 2.2m in breadth. Tiles of size 140 cm by 60 cm have to be laid such that the tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges of the floor. What is the maximum number of tiles that can be accommodated on the floor?

• 6
• 7
• 8
• 9

Soln: Length of the rectangular floor = 4 m = 400 cm Breadth of the floor = 2.2 m = 220 cm

No matter how we arrange the given tiles, we cannot arrange more than 8 tiles on the given floor. The two possible arrangements of tiles have been depicted below.

Arrangement 1:

Arrangement 2:

Hence, option (c) is correct. 

58.  There are five persons, P, Q, R, S and T each one of whom has to be assigned one task. Neither P nor Q can be assigned Task-1. Task-2 must be assigned to either R or S. In how many ways can the assignment be done?

• 6
• 12
• 18
• 24

Soln: There are five tasks that need to be assigned to five persons. Here two cases are possible.

Case 1: Task-2 is assigned to R

Case 2: Task-2 is assigned to S

Tasks	Case 1	Case 2
1	S or T. So, 2 possible ways	R or T. So, 2 possible ways
2	R	S
3	3 possible ways	3 possible ways
4	2 possible ways	2 possible ways
5	1 possible way	1 possible way

In Case 1, total number of possible ways = 2 × 1 × 3 × 2 × 1 = 12 ways In Case 2, total number of possible ways = 2 × 1 × 3 × 2 × 1 = 12 ways  So, the assignment can be done in 12 + 12 = 24 ways.

Hence, option (d) is correct. 

59.  There are large number of silver coins weighing 2gm, 5gm, 10gm, 25gm, 50gm each. Consider the following statements:

1. To buy 78 gm of coins one must buy at least 7 coins.
2. To weigh 78 gm using these coins one can use less than 7 coins.

Which of the statements given above is/are correct?

• 1 only
• 2 only
• Both 1 and 2
• Neither 1 nor 2

Soln: The weights of the coins are 2gm, 5gm, 10gm, 25gm, and 50gm.

Statement 1:

Let’s find out the minimum number of coins required to make 78gm. For this we need to maximize the number of heavier coins. So, we will use:

1. coin of 50gm
2. coins of 10gm

4 coins of 2gm 

So, the minimum number of coins required to buy 78gm = 1 + 2 + 4 = 7 So, Statement 1 is correct. 

Statement 2:

To weigh 78 grams, we can use 80 grams on one side and 2 gram coin on the other side. 

To make 80 grams, we need:

1 coin of 50gm

1 coin of 25gm 1 coin of 5gm

So, we need 4 coins to weigh 78 grams – one coin each of 50gm, 25gm, 5gm and 2gm. 

So, Statement 2 is correct. 

Hence, option (c) is correct. 

60.  Consider the following:

I. A + B means A is neither smaller nor equal to B. II. A – B means A is not greater than B.

1. A × B means A is not smaller than B.
2. A ÷ B means A is neither greater nor equal to B.
3. A ± B means A is neither smaller nor greater than B.

Statement: P × Q, P – T, T ÷ R, R ± S 

Conclusion-1: Q±T

Conclusion-2: S+Q

Which one of the following is correct in respect of the above Statement and the Conclusions?

• Only Conclusion-1 follows from the Statement.
• Only Conclusion-2 follows from the Statement.
• Both Conclusion-1 and Conclusion-2 follow from the Statement.
• Neither Conclusion-1 nor Conclusion-2 follows from the Statement.

Soln: According to the question,

A + B means A > B

A – B means A ≤ B 

A × B means A ≥ B 

A ÷ B means A < B

A ± B means A = B

It’s given that, P × Q, P – T, T ÷ R, R ± S

Or P ≥ Q, P ≤ T, T < R, R = S

Using this we get: S = R > T ≥ P ≥ Q

Conclusion I: Q ± T or Q = T. This is not necessarily true. 

Conclusion II: S + Q or S > Q. This is true. 

Hence, option (b) is correct. 

Directions for the following 3(three) items:

Read the following three passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.

Passage-1

Sourcing food from non-agricultural lands (uncultivated systems such as forests, wetlands, pastures, etc) in addition to agricultural lands enables a systemic approach to food consumption. It allows rural and tribal communities to sustain themselves for the whole year and steer clear of natural disasters and season-inducted shortfalls of agricultural food. Since the productivity of trees is often more resilient to adverse weather conditions than annual crops, forest foods often provide a safety net during periods of food shortages caused by crop failure; forest foods also make important contributions during seasonal crop production gaps.

61.  Which one of the following statements best reflects the most logical and rational massage conveyed by the author of the passage?

• Food yielding trees should replace other trees in rural and tribal areas and community owned lands.
• Food security cannot be ensured in India with the present practice of conventional agriculture.
• Wastelands and degraded areas in India should be converted into agroforestry systems to help the poor.
• Agroecosystems should be developed in addition to or along with conventional agriculture.

Soln: Option (a) is incorrect: The passage talks about the significance of food from non-agricultural lands such as forests, peatlands, etc., in terms of ensuring food security during food shortages and production gaps and complementing the agricultural system. But it does not recommend replacing other trees with food-yielding trees.

Option (b) is incorrect: Although the passage highlights the resilience of forest foods through the lines

“Since the productivity of trees is often more resilient to adverse weather conditions…..forest food provides safety net… ”, it does not mention that conventional agriculture on its own can not ensure food safety.

Option (c) is incorrect: The line “It allows rural and tribal communities to sustain themselves for the whole year and steer clear of natural disasters and season-induced shortfalls of agriculture food” indicates the vulnerability of the rural and tribal communities. However, the passage nowhere mentions the conversion of wastelands and degraded areas to develop forests and help the poor.

Option (d) is correct: The tribal and rural communities are vulnerable to food shortages due to crop failures and during seasonal production gaps as seen in the line “..forest food provides a safety net during periods of food shortages caused by crop failures; forest foods also make important contributions during seasonal crop production gaps.” The development of agroecosystems along with conventional agriculture would reduce the vulnerability of these communities and ensure their food security.

Passage-2

While awareness on use/misuse and abuse of antibiotics is common knowledge, as is the impact of dosing poultry with antibiotics, the environmental impact of antibiotics-manufacturing companies not treating their waste has scarcely been discussed at any length or seriousness thus far. Pollution from antibiotics factories is fuelling the rise of drug-resistant infections. The occurrence of drug-resistant bacteria surrounding the pharma manufacturing plants is well known.

62.  Which one of the following statements best reflects the most logical and practical message conveyed by the passage?

• It is necessary to put proper effluent treatment protocols in place.
• It is necessary to promote environmental awareness among people.
• Spread of drug-resistant bacteria cannot be done away with, as it is inherent in modern medical care.
• Pharma-manufacturing companies should be set up in remote rural areas, away from crowded towns and cities.

Soln: Option (a) is correct: The passage highlights the environmental impact of antibiotics manufacturing companies not treating their waste through the line “..the environmental impact of antibioticsmanufacturing companies not treating their waste has scarcely been discussed at any length or seriousness thus far. Pollution from antibiotics factories is fueling the rise of drug-resistant infections.” Therefore, the passage emphasizes the need for these companies to implement proper effluent treatment protocols to prevent pollution and minimize the spread of drug-resistant bacteria.

Option (b) is incorrect: The passage specifically discusses the environmental impact of antibiotics manufacturing companies not treating their waste and how it contributes to the rise of drug-resistant infections. Therefore, promoting environmental awareness, although a good idea, alone may not directly address the issue at hand. 

Option (c) is incorrect: This is a pessimistic and broad statement that does not align with the main theme of the passage. Nowhere the passage mentions or suggests that it is not possible to control the spread of drug-resistant bacteria, although it may be challenging. 

Option (d) is incorrect: Although this statement presents a solution, it is not the most practical and logical solution conveyed by the passage. The passage primarily emphasizes the importance of proper waste treatment by antibiotics manufacturing companies to reduce pollution and the spread of drugresistant bacteria in the line “Pollution from antibiotics factories is fueling the rise of drug-resistant infections”. 

Passage-3

Benefits of good quality school education accrue only when students complete and leave school after having acquired the gateway skills. Like one learns to walk before running, similarly one picks up advanced skills only after picking the basic foundational skills. The advent of the knowledge economy poses new challenges, and one of the severe consequences of having an uneducated workforce will be our inability to keep pace with the global economy. Without a strong learning foundation at the primary level, there can be no improvement in higher education or skill development.

63.        Which one of the following statements best reflects the crux of the passage?

• To become a global power, India needs to invest in universal quality education.
• India is unable to become a global power because it is not focusing or promoting knowledge economy.
• Our education system should focus more on imparting skills during higher education.
• Parents of many school children are illiterate and are unaware of the benefits of quality education.

Soln: Option (a) is correct: The passage highlights the significance of quality education in imparting foundations skills, and its contribution to the knowledge economy through the lines “the advent of the knowledge economy poses new challenges, and one of the severe consequences of having an uneducated workforce will be our inability to keep pace with the global economy”. Thus the statement aligns with the message of the passage on the significance of quality education. 

Option (b) is incorrect: This statement is not supported by the passage directly. The passage only talks about the challenges posed by the knowledge economy. It does not explicitly state that India is not focusing on or promoting a knowledge economy. 

Option (c) is incorrect: The lines, “Like one learns to walk before running, similarly one picks up advanced skills only after picking the basic foundational skills.” and “Without a strong learning foundation at the primary level, there can be no improvement in higher education or skill development” clearly emphasize the importance of school education rather than the higher education. 

Option (d) is incorrect: This statement is beyond the scope of the passage, as the passage does not talk about the literacy and awareness of the parents anywhere. 

64.  40 children are standing in a circle and one of them (say child-1) has a ring. The ring is passed clockwise. Child-1passes on the child-2, child-2 passes on to child-4, child-4 passes on to child7 and so on. After how many such changes (including child-1) will the ring be in the hands of  child-1 again?

• 14
• 15
• 16
• 17

Soln: According to the question, the ring is passed clockwise starting from child 1, then child 2, then child 4, then child 7, and so on. 

Therefore, the series is formed by adding +1, +2, +3, +4, +5, +6, +7, …….. and so on. 

So, the series is: 1    2    4    7    11    16     22     29      37     6      16     27     39     12      26     1 So, after 15 changes the ring will again be in the hands of child 1.

Hence, option (b) is correct. 

65.  What is the middle terms of the sequence

Z, Z, Y, Y, Y, X, X, X, X, W, W, W, W, W,…….,A?

• H
• I
• J
• M

Soln: The given sequence is: Z, Z, Y, Y, Y, X, X, X, X, W, W, W, W, W, ……., A

So, the number of terms in the given sequence = 2 + 3 + 4 + ….. + 27 = [27 (27 + 1)/2] – 1 = [27 ×

28/2] – 1 = 378 – 1 = 377 

So, the middle term is 378/2, i.e. 189^th 

Now, 377 – (27 + 26 + 25 + 24 + 23 + 22 + 21 + 20) = 189 So, the 189^th term must be I. 

Hence, option (b) is correct. 

66.   Questions: Is p greater than q?

Statement-1: p × qis greater than zero.

Statement-2: p² is greater than q².

Which one of the following is correct in respect of the above Question and the Statements?

• The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
• The Question can be answered by using either Statement alone.
• The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
• The Question cannot be answered even by using both the Statements together.

Soln:  

Statement 1: (p × q) > 0

It means neither p nor q can be 0, and both of them must be positive, or both negative. Say, 2 × 3, or (2) × (-3)

So, by using statement1 is alone we cannot determine whether p > q. 

So, Statement 1 alone is not sufficient. 

Statement 2: p² > q² 

But we do not know whether p and q are positive or negative. Say, 3² > 2², or (-3)² > (-2)² So, we cannot determine whether p > q. 

So, Statement 2 alone is not sufficient. 

Even by using both the statements together, we cannot determine whether p > q. 

Hence, option (d) is correct. 

67.     Questions: Is (p + q- r) greater than (p – q + r), where p, q and r are integers?

Statement-1: (p – q) is positive.

Statement-2: (p-r) is negative.

Which one of the following is correct in respect of the above Question and the Statements?

• The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
• The Question can be answered by using either Statement alone.
• The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
• The Question cannot be answered even by using both the Statements together.

Soln: Statement 1: (p – q) is positive. 

This is possible only when p > q

Statement 2: (p – r) is negative. 

This is possible only when p < r

Now, (p + q – r) – (p – q + r) = 2q – 2r

So, we basically need to find out if q > r, or not. For this, we obviously have to use both the given statements. 

Using both of the statements, we get:

r > p > q So, q < r

It means that, (p + q – r) – (p – q + r) = 2q – 2r < 0

In other words, (p + q – r) is not greater than (p – q + r). 

Hence, option (c) is correct. 

68.         In a party, 75 persons took tea, 60 persons took coffee and 15 persons took both tea and coffee.

No one taking milk takes tea. Each person takes at least one drink.

Question:  how many persons attended the party?

Statement-1: 50 persons took milk.

Statement-2: Number of persons who attended the party is five times the number of persons who took milk only.

Which one of the following is correct in respect of the above Question and the Statements?

• The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
• The Question can be answered by using either Statement alone.
• The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
• The Question cannot be answered even by using both the Statements together.

Soln: In a party, 75 persons took tea, 60 persons took coffee and 15 persons took both tea and coffee. We can represent this information via a Venn diagram for better visualization.

You may notice that the circles representing Tea and Milk are not overlapping. That’s because no one taking milk takes tea. 

We can further deduce the following information from the Venn diagram given above.

So, the total number of persons that attended the party = 75 + 45 + y = 120 + y

Now, let’s consider the given statements. 

Statement 1: 50 persons took milk.

So, x + y = 50. But using this we cannot find out the total number of persons that attended the party, as we cannot find the value of y.  So, Statement 1 alone is not sufficient. 

Statement 2: Number of persons who attended the party is five times the number of persons who took milk only. So, 120 + y = 5y 

Or 4y = 120

Or y = 30

So, the total number of persons that attended the party = 120 + y = 120 + 30 = 150 So, Statement 2 alone is sufficient. 

Hence, option (a) is correct. 

69.  Consider a 3-digit number.

Question: What is the number?

Statement-1: The sum of the digits of the number is equal to the product of the digits.

Statement-2: The number is divisible by the sum of the digits of the number.

Which one of the following is correct in respect of the above Question and the Statements?

• The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
• The Question can be answered by using either Statement alone.
• The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
• The Question cannot be answered even by using both the Statements together.

Soln: Statement 1: The sum of the digits of the number is equal to the product of the digits. 

If the 3-digit number is 123, 132, 213, 231, 312, or 321, then the sum of the digits of the number would be equal to the product of the digits. 

As, 1 + 2 + 3 = 1 × 2 × 3

Or 6 = 6

So, Statement 1 alone is not sufficient. 

Statement2: The number is divisible by the sum of the digits of the number.

We can see that, 132/6 = 22, and 312/6 = 52 So, Statement 2 alone is not sufficient. 

Even after using both the statements together, we cannot determine a unique 3-digit number. 

Hence, option (d) is correct. 

70.            For five children with ages a < b < c < d < e; any two successive ages differs by 2 years.

Question: What is the age of the youngest child?

Statement-1: The age of the eldest is 3 times the youngest.

Statement-2:  The average age of the children is 8 years

Which one of the following is correct in respect of the above Question and the Statements?

• The Question can be answered by using one of the Statement alone.
• The Question can be answered by using either Statement alone.
• The Question can be answered by using both the Statement together, but cannot be answered using either Statement alone.
• The Question cannot be answered even by using both the Statements together.

Soln: Given: a < b < c < d < e

Since, any two successive ages differ by 2 years, the ages can also be written as:

a, a + 2, a + 4, a + 6, a + 8

Statement 1: The age of the eldest is 3 times the youngest.

So, a + 8 = 3a

Or 2a = 8

Or a = 4

So, Statement 1 alone is sufficient.

Statement 2: The average age of the children is 8 years.

(a + a + 2 + a + 4 + a + 6 + a + 8) / 5 = 8

Or (5a + 20) / 5 = 8

Or 5a + 20 = 40

Or 5a = 20

Or a = 4

So, Statement 2 alone is sufficient.

Hence, option (b) is correct. 

Directions for the following 3 (three) items:

Read the following three passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.

Passage-1

Scientist studied the vernal window – transition period from winter to the growing season. They found that warmer winters with less snow resulted in a longer lag time between spring events and a more protracted vernal window. This change in the spring timetable has ecological, social and economic consequences – for agriculture, fisheries and tourism. As the ice melts earlier, the birds don’t return, causing a delay, or lengthening in springtime ecological events.

71.               With reference to the above passage, the following assumptions have been made:

1. Global warming is causing spring to come early and for longer durations.
2. Early spring and longer period of spring is not good for bird populations. Which of the above assumptions is/are correct?
3. 1 only
4. 2 only
5. Both 1 and 2
6. Neither 1 nor 2

 

Passage-2

A global analysis of nitrogen use efficiency–measure of the amount of nitrogen a plant takes in to grow versus what is left behind as pollution–says that using too much fertilizers will lead to increased pollution of waterways and the air. Currently, the global average for nitrogen use efficiency is approximately 0.4, meaning 40 per cent of the total nitrogen added to cropland goes into the harvested crop while 60 per cent is lost to the environment, says a study. More than half of the world’s population is nourished by food grown with fertilizers containing synthetic nitrogen, which is needed to produce high crop yields. Plants take the nitrogen they need to grow, and the excess is left in the ground, water and air. This results in significant emissions of nitrous oxide, a potent greenhouse and ozone depleting gas, and other forms of nitrogen pollution, including eutrophication of lakes and rivers and contamination of river water.

72.  Which one of the following statements best reflects the most logical, rational and crucial message implied by the passage?

• An enhanced efficiency of use of nitrogen is imperative for both food production and environment.
• Production of synthetic nitrogen fertilizers cannot be stopped as it will adversely affect global food security.
• Alternatives to crops that require excess of nitrogen should be identified and cultivated.
• Conventional agriculture using synthetic fertilizers should be replaced with agroforestry, agroecosystems and organic farming.

Soln: Option (a) is correct: The lines “Currently, the global average for nitrogen use efficiency is approximately 0.4, meaning 40 per cent of the total nitrogen added to cropland goes into the harvested crop while 60 per cent is lost to the environment, says a study….Plants take the nitrogen they need to grow, and the excess is left in the ground, water and air.” and  “This results in significant emissions of nitrous oxide…and other forms of nitrogen pollution, … contamination of river water.” highlight the need of nitrogen for plant growth and the result of unused nitrogen on water and air. Thus, improving the nitrogen use efficiency can not only lead to better production but also to reduced pollution. 

Option (b) is incorrect: While the passage mentions, “more than half of the world’s population is nourished by food grown with fertilizers containing synthetic nitrogen”, it does not state that the production of synthetic nitrogen fertilizers cannot be stopped.

Option (c) is incorrect: The question is asking us to identify the most logical, rational and crucial message implied by the passage, rather than an inference or solution. The passage only talks about nitrogen use efficiency and the impact of excess nitrogen on the environment. It does not go beyond this to suggest that we must identify and cultivate crops that require excess nitrogen. 

Option (d) is incorrect: These alternatives may have their merits, but the passage only highlights the environmental consequences of excessive nitrogen use and pollution caused by synthetic nitrogen fertilizers.  It does not explicitly advocate replacing conventional agriculture using synthetic fertilizers with specific alternatives such as agroforestry, agroecosystems, and organic farming.

Passage-3

Along with sustainable lifestyles, climate justice is regarded as a significant principle in environmental parlance. Both the principles have bearings on political and economic choices of the nation. So far, in our climate change summits or compacts, both the principles have eluded consensus among nations. Justice, in the judicial sense, is well defined. However, in the context of climate change, it has scientific as well as socio-political connotations. The crucial question in the next few years will be how resources, technologies and regulations are used to support the victims of climate  change. Justice in climate is not confined to actions relating to mitigation, but includes the wider notion of support for adaptation to climate change and compensation for loss and damage.

73.  Which one of the following statements best reflects the most logical, rational and crucial message conveyed by the passage?

• Climate justice should be ingrained in detail in the rules of all the new climate compacts/agreements.
• Environmental resources are unevenly distributed and exploited across the globe.
• There is an impending issue of dealing with a huge number of climate change victims/climate refugees.
• Climate changes in all its connotations is mostly due to developed countries and therefore their share of burden should be more.

Soln: Answer: (a) Option (a) is correct: The line “The crucial question in the next few years will be how resources, technologies, and regulations are used to support the victims of climate change.” highlights the need for climate justice. To achieve it, it is imperative that climate justice is ingrained in detail in the rules of all the new climate compacts/agreements. Hence this option seems to be the logical, rational, and crucial message conveyed by the passage.

Option (b) is incorrect: This statement goes beyond the scope of the passage, which primarily focuses on climate justice rather than the distribution and exploitation of environmental resources.

Option (c) is incorrect: While the passage mentions the crucial question of how resources, technologies, and regulations are used to support the victims of climate change, it does not specifically address the impending issue of dealing with a huge number of climate change victims or climate refugees. Thus, this option is beyond the scope of the passage 

Option (d) is incorrect: Although the passage recommends compensation loss and damages, it does not mention that climate change is mostly due to developed countries or that their share of the burden should be more. Thus this option goes beyond the scope of the passage.  

74. A principal P becomes Q in 1 year when compounded half-yearly with R% annual rate of interest. If the same principal P becomes Q in 1 year when compounded annually with S% annual rate of interest, then which one of the following is correct?

• R = S
• R > S
• R < S
• R ≤ S

Soln: Principal P becomes Q in 1 year when compounded half-yearly with R% annual rate of interest. 

Principal = P, Amount = Q, Rate = R%, Time = 1 year

Q = P [1 + R/(2×100)]²  

Q/P = [1 + R/(2×100)]²  …………. (1)

Principal P becomes Q in 1 year when compounded annually with S% annual rate of interest. 

Q = P [1 + S/(100)]¹   

Q/P = [1 + S/(100)]¹   …………. (2)

From equation (1) and equation (2), we get:

[1 + R/(2×100)]² = [1 + S/(100)]¹  …………. (3)

Let R = 20%. Putting the value of R = 20 in equation (3), we get:

[1 + 20/(2×100)]² = [1 + S/(100)]¹

Or 1.21 = 1 + (S/100)

Or S/100 = 1.21 – 1 = 0.21

Or S = 0.21 × 100 = 21% Thus, S > R.

Hence, option (c) is correct.  

75. How many natural numbers are there which given a remainder of 31 when 1186 is divided by these natural numbers?

• 6
• 7
• 8
• 9

Soln: Divisor = Dividend × Quotient + Remainder

So, 1186 = Dividend × Natural number + 31

Or Dividend × Natural number = 1186 – 31 = 1155

Hence, the required natural number must be a factor of 1155.

Now, 1155 = 1 × 3 × 5 × 7 × 11

When 1186 is divided by the required natural number, we get 31 as remainder. Thus, the required natural number must be greater than 31. 

Factors of 1155 which are greater than 31 are: 33, 35, 55, 77, 105, 165, 231, 385, and 1155. 

Thus, there are 9 natural numbers which give a remainder of 31 when 1186 is divided by them.

Hence, option (d) is correct.

76.     Let pp, qq and rr be 2 digit numbers where p < q < r. If pp + qq + rr =tt0, where tt0 is a 3-digit number ending with zero, consider the following statements:

1. The number of possible values of p is 5. 2. The number of possible values of q is 6

Which of the above statements is/are correct?

• 1 only
• 2 only
• Both 1 and 2
• Neither 1 nor 2

Soln: tt0 is a 3-digit number ending with zero, such that pp + qq + rr = tt0

As pp, qq, and rr are 2-digit numbers, the value of tt0 can be either 110 or 220. Thus, we get:

If tt0 = 110 pp + qq + rr = 110   or (10p + p) + (10q + q) + (10r + r) = 110       or 11p + 11q + 11r = 110 or p + q + r = 10    ……. (1)

If tt0 = 220 pp + qq + rr = 220 

or (10p + p) + (10q + q) + (10r + r) = 220       or 11p + 11q + 11r = 220 or p + q + r = 20     ……. (2)

Statement 1: 

As p < q < r, the possible value of p in equation (1) can be 1 and 2.

As p < q < r, the possible value of p in equation (2) can be 1, 2, 3, 4 and 5.

Hence, the number of possible values of p is 5.

Thus, Statement 1 is correct.

Statement 2: 

As p < q < r, the possible value of q in equation (1) can be 2, 3 and 4.

As p < q < r, the possible value of q in equation (2) can be 6, 7 and 8.

Hence, the number of possible values of q is 6.

Thus, Statement 2 is correct.

Hence, option (c) is correct.

77. What is the sum of all 4-digit numbers less than 2000 formed by the digits 1, 2, 3 and 4, where none of the digits is repeated?

• 7998
• 8028
• 8878
• 9238

Soln: 4-digit numbers less than 2000 formed by the digits 1, 2, 3 and 4, where none of the digits is repeated are:

1234, 1243, 1324, 1342, 1423, 1432

Required sum = 1234 + 1243 + 1324 + 1342 + 1423 + 1432 = 7998  Hence, option (a) is correct.

78. What is the number of selections of 10 consecutive things out of 12 things in a circle taken in the clockwise direction?

• 3
• 11
• 12
• 66

Soln: Let 12 consecutive things in the circle be x₁, x₂, x₃, …….. x_12.

We need to select 10 consecutive things out of these 12 things in the circle taken in the clockwise direction.

This selection can be made as follows:

(x₁ to x₁₀), (x₂ to x₁₁), (x₃ to x₁₂), (x₄ to x₁), (x₅ to x₂), (x₆ to x₃), (x₇ to x₄), (x₈ to x₅), (x₉ to x₆), (x₁₀ to x₇), (x₁₁ to x₈), (x₁₂ to x₉)

So, there are 12 possible ways to do so.

Hence, option (c) is correct.

79. If today is Sunday, then which day is it exactly on 10¹⁰th day?

• Wednesday
• Thursday
• Friday
• Saturday

Soln: 10¹⁰ = 10000000000

Number of odd days in 10¹⁰ = Remainder [10000000000/7] = 4

If today is Sunday, then 10¹⁰ th day from now will be 4 days after Sunday, i.e. Thursday.

Hence, option (b) is correct.

80. There are three traffic signals. Each signal changes colour from green to red and then from red to green. The first signal takes 25 seconds, the second signal takes 39 seconds and the third signal takes 60 seconds to change the colour from green to red. The durations for green and red colours are same. At 2:00 p.m, they together turn green. At what time will they change to green next, simultaneously?

• 4:00 p.m.
• 4:10 p.m.
• 4:20 p.m.
• 4:30 p.m.

Soln: The three traffic signals turn from green to red at an interval of 25 seconds, 39 seconds and 60 seconds.

So, the time after which all the three traffic signals will turn red from green together = LCM of 25 seconds, 39 seconds and 60 seconds = 3900 seconds = 65 minutes = 1 hour 5 minutes

Now, durations for green and red colours are same. 

So, the time after which all the three traffic signals will turn green from red together = 1 hour 5 minutes  So, the total time taken by all the three traffic signals to turn green together = 1 hour 5 minutes + 1 hour 5 minutes = 2 hours 10 minutes

Thus, the time after which all the three traffic signals will simultaneously change to green again = 2:00 p.m. + 2 hours 10 minutes = 4:10 p.m.

Hence, option (b) is correct.