**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.

**Q1.** 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

**Answer: **(d)

__Solution:__

**Statement 1** is based on an incorrect assumption. To confirm this, we can use the negation test, which involves negating the statement and observing whether it contradicts the main premise of the passage. In this case, negating Statement 1 does not undermine the premise, indicating that it is not a necessary assumption.

*Another approach to identify assumptions involves recognizing them as essential links between the premises and conclusions—like a linchpin that holds the argument together. Since the passage does not primarily discuss the comparison between the private and government sectors, neither statement serves as a valid assumption.*

*Consequently, Statement 2 also represents an incorrect assumption. We can further validate this through the negation test, which shows that negating Statement 2 does not affect the underlying premise of the passage.*

**Q2.** 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.

**Answer: **(c)

__Solution:__

*The crux of a problem refers to its most crucial or challenging aspect, essentially capturing the main point explicitly stated by the author. *

**Option (a)** is incorrect as it extends beyond the scope of the passage, which does not discuss expenses.

**Option (b) **is also incorrect. The phrase "most ideal" serves as a potential warning sign, prompting a review of whether the author explicitly uses such a definitive term and whether it aligns with the main point of the passage. The text refers to a "major" solution rather than the "most ideal" one, leading us to dismiss this option.

**Option (c) **is correct: The passage starts with the premise that “In India, the segregation of municipal waste at source is rare.” It concludes by advocating for biomethanation, a process that requires segregation. This option effectively ties the passage together and captures its main idea.

**Option (d)** is incorrect as it too goes beyond the scope of the passage, addressing a topic that the passage does not cover.

*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.

**Q3.** 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

**Answer:** (b)

__Solution:__

**Statement 1** is deemed an incorrect assumption: The passage begins with the premise that organic farming is a new and unregulated industry. The conclusion suggests that because of this lack of regulation, it's not guaranteed that organic products are superior in all scenarios. Using the negation test and a general assessment, similar to the approach in your previous example, we can see that negating this statement does not impact the passage’s argument, thus confirming it's not a valid assumption.

**Statement 2** is considered correct, as it aligns with the typical nature of assumptions in arguments—they are generally broad rather than specific and are intended to reinforce or support the conclusion. This is evident in the author's commentary within the passage that highlights confusion among farmers and consumers about what products are best, and the potential misuse of these products. This reinforces the argument that there is a lack of clarity and potential harm in the organic farming industry, which directly supports the conclusion regarding the uncertainty about the superiority of organic products.

**Q4.** 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.

**Answer:** (c)

__Solution:__

**Option (a)** is incorrect because it deals with promoting conventional farming or comparing it to organic farming, neither of which is the focus of the passage. Therefore, it does not align with the main message or logical conclusion that the passage is driving towards.

**Option (b)** is incorrect as it presents an extreme view. The passage only discusses specific issues with organic alternatives like datura spray and does not support a broad statement claiming the absence of any safe organic alternatives to chemical fertilizers. This over-generalization makes the option an unsuitable choice.

**Option (c) **is correct: The passage concludes that due to the youth and lack of regulation in the organic farming industry in India, both farmers and consumers face confusion about the best products for their needs and may use them harmfully. This core message supports the inference that farmers in India require guidance and assistance to achieve sustainable practices in organic farming. This option accurately reflects the passage’s discussion and conclusion, making it a valid inference rather than a direct statement.

**Option (d)** is incorrect as it extends beyond the content discussed in the passage. The passage does not cover topics related to the economic impact or profitability of organic farming, thus making this choice irrelevant to the passage’s focus.

*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.

**Q5.** 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

**Answer:** (b)

__Solution:__

**Statement 1** is based on an incorrect assumption: The passage doesn't discuss Sustainable Development Goals or the zero-hunger goal. It focuses solely on how changes in consumption patterns and the emphasis on stable crops have impacted nutrition security. Therefore, this option goes beyond the scope of the passage.

**Statement 2** is a valid assumption: it effectively connects the premise and conclusion.

**Statement 3** is also a valid assumption: The passage references the disappearance of nutritious foods like millets and notes that while food grain production has increased significantly since independence, it hasn't adequately addressed malnutrition.

**Statement 4** is based on an incorrect assumption: It fails the negation test and is also outside the scope of the passage.

**Q6.** 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

**Answer: **(c)

__Solution:__

*To determine the minimum number of balls needed to ensure that the drawn balls contain at least one full group of any color, we find the maximum number of balls we can draw without selecting a complete group of any color. By drawing one less ball from each color, we have a total of 174 balls. Adding just one more ball, regardless of its color, completes a group. Hence, the minimum number of balls required, n, is *

*174+1=175*

*For ensuring that the drawn balls include at least one ball of each color, we aim to maximize the number of balls drawn without selecting any black balls, as black balls are the least in number. We can draw 20 blue balls, 26 green balls, 28 yellow balls, 38 red balls, and 54 white balls, totaling 166 balls without any black balls. Adding just one black ball completes the requirement, making the minimum number of balls needed *

*166+1=167*

**Q7.** If 'ZERO' is written as 'CHUR', then how is 'PLAYER' written ?

(a) SOCAGT

(b) SODBGT

(c) SODBHT

(d) SODBHU

**Answer: **(d)

__Solution:__

*ZERO is written as CHUR. *

*Z + 3 = CE + 3 = H R + 3 = U O + 3 = R*

*for PLAYER -*

*P + 3 = SL + 3 = O A + 3 = D Y + 3 = B E + 3 = H R + 3 = U*

*Hence, option (d) is correct.*

**Q8. **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

**Answer:** (d)

__Solution:__

*To establish the relationships between all six persons, we require information from all statements. Statement 1 provides the relationship between A and B, while statement 2 gives the relationship between C and D. Statements 4 and 5 are necessary to establish the relationship between these two groups and F. Including statement 3 completes the information needed to determine the relationships between all six individuals. *

*Therefore, all statements are necessary, and option (d) is correct.*

**Q9.** 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.

**Answer: **(c)

__Solution:__

*Statements 1, 2, and 3 alone are not sufficient because they do not provide a link between B and E. Statements 1, 3, and 4 alone are also not sufficient for the same reason.*

*Analyzing the remaining options, we can utilize statements 2 and 4 to deduce that D is male and the father of two females, A and C. Additionally, statement 3 informs us that D has a son, E.*

*Further, statement 1 indicates the relationship between B and the known family members, revealing that E is B's brother-in-law.*

*Thus, by combining statements 1, 2, 3, and 4, we can establish the relationship between all six individuals, confirming that option (c) is correct.*

**Q10.** 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

**Answer: **(d)

__Solution:__

*All numbers except 91 in above options are prime number. So, the group (d) is different.*

**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*

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.

**Q11**. 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.

**Answer:** (b)

__Solution:__

**Option (a)** is indeed incorrect since the author doesn't suggest any implementation difficulties.

**Option (b) **is the correct choice. The author references "arbitrariness" and provides examples hinting at "knee-jerk" reactions, which is further emphasized by the concluding line of the passage.

**Option (c) **is incorrect as the author doesn't allude to heavy fines or any punitive measures.

**Option (d) **is also incorrect since the author doesn't imply the 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.

**Q12.** 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.

**Answer: **(c)

__Solution:__

**Option (a)** is indeed too far-fetched, as the passage only hints at the idea rather than explicitly states it.

**Option (b)** is incorrect. While the passage mentions the importance of credibility in financial reporting, this choice simply restates information from the passage, which doesn't qualify as an inference.

**Option (c)** is the correct choice. The passage discusses the rapid growth in international capital markets, which implies why corporate governance has become a global economic and political concern.

**Option (d)** is incorrect because there is no direct mention of supply chains in the passage, making it outside the scope of the text.

*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.

**Q13.** 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.

**Answer:** (b)

__Solution:__

*Option (a) is indeed beyond the scope of the passage and therefore incorrect.*

*Option (b) is correct as it can be inferred from the passage and encapsulates the main idea.*

*Option (c) is incorrect because it presents a definitive statement, whereas the passage does not explicitly state that rich biodiversity is impossible without elephants. This statement is too extreme.*

*Option (d) is incorrect due to the inclusion of "as per their requirement," which cannot be deduced from the passage.*

**Q14.** 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

**Answer:** (a)

__Solution:__

*7 + 9 + 10 = 26 | Sum of digits 2 + 6 = 89 + 11 + 30 = 50 | Sum of digits 5 + 0 = 511 + 17 + 21 = 49 | Sum of digits 4 + 9 = 1323 + 4 + 15 = 42 | Sum of digits 4 + 2 = 6*

*This means (a) is correct.*

**Q15.** 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

**Answer:** (c)

__Solution:__

*If 7x + 96 is divisible by x, Hence, 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.*

**Q16. **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

**Answer: **(b)

__Solution:__

*To maximize the value of (p + q) (r + s), take the 4 biggest digits- 6, 7, 8, and 9.*

*Take 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).*

**Q17.** 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

**Answer:** (a)

__Solution:__

*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) = 0Remainder 7 (9999999/13) = 9*

*Therefore, after this, the pattern repeats. Remainder 99 = 11 (as per pattern)Hence, answer is option (a).*

**Q18.** 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

**Answer: **(c)

__Solution:__

*The number provided, 111111111, is divisible by 9 according to the divisibility rule.*

*When multiplied by itself (111111111 x 111111111), the sum of digits in the result will also be divisible by 9 due to the properties of multiplication.*

*Hence, the correct answer is the option that is a multiple of 9, which is 81. Therefore, the answer is option (c).*

**Q19.** 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

**Answer: **(b)

__Solution:__

*There are 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.*

*sum of first n natural numbers = n (n + 1) / 2So, sum of 1 to 9 = 9 × 10/2 = 45Sum = 19 × 45 = 855*

*Adding 1 from 100, we get answer as 856.*

**Q20.** 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

**Answer: **(c)

__Solution:__

*As none of the 3 points are collinear, number of distinct triangles = 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.

**Q21.** 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.

**Answer:** (c)

__Solution:__

**Option (a) **is incorrect because the passage does not explicitly state that businesses would need to close down or pay for pollution in the future. It mentions the importance of businesses hedging against uncertain outcomes but does not specify the consequences for those that fail to do so.

**Option (b)** is also incorrect because the statement uses extreme terms ("only solution"), which cannot be inferred from the passage. The passage discusses the potential impact of technological change on transitioning away from fossil fuels but does not suggest that it is the sole solution.

**Option (c)** is correct. The passage indeed highlights the significance of technological change in potentially making a future transition away from fossil fuels cheaper or more expensive. This underscores the urgency for action and not waiting for technological advancements.

**Option (d) **is incorrect because the statement is too specific. Inferences are generally more generic and drawn from the given statements rather than detailing specific outcomes.

*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.

**Q22. **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.

**Answer: **(a)

*Solution:*

**Imply**- to indicate or suggest something without actually stating it**Infer**- to guess or use reasoning to come to a conclusion based on what has been suggested.

**Option (a)** is indeed correct. While the passage doesn't explicitly mention people avoiding prevention, it does discuss the challenge of adopting significant lifestyle changes to address environmental or health issues, implying a reluctance to take preventive measures.

**Option (b)** is incorrect as there is no mention of government jobs or roles in the passage.

**Option (c)** is also incorrect. While the author suggests prioritizing health over environmental concerns, the given statement implies a different concept that is not hinted at in the passage.

**Option (d)** is also incorrect as it is too far-fetched and not supported by the passage.

*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.

**Q23. **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.

**Answer:** (b)

__Solution:__

*Crux is the main point of the passage that is explicitly stated by the author. *

*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.*

**Q24. **Three of the five positive integers p, q, r, s, t are 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

**Answer:** (a)

__Solution:__

*When we add or subtract even number of odd numbers, (ex - 7-3 or 5+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. *

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

**Q25. **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

**Answer:** (d)

__Solution:__

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

**Q26.** 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

**Answer:** (a)

__Solution:__

*37DD can be written as 3700 + 10D + D = 3700 + 11DNow, ABC x D = 3700 + 11Dor 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. So, A + B + C = 9 + 3 + 6 = 18*

*Hence, option (a) is correct.*

**Q27.** 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

**Answer: **(d)

__Solution:__

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

*As, 1001 = 7 × 11 × 13*

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

**Q28.** 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

**Answer:** (a)

__Solution:__

*Each dimension—length, breadth, and height—consists of 5 cubes. Considering that the outermost layer has 2 exposed cubes per dimension, the inner layer, or the protected cube, has dimensions of 3 cubes in length, breadth, and height. Therefore, the total number of cubes within the inner layer is calculated as 3×3×3=27.*

**Q29.** 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

**Answer:** (c)

__Solution:__

*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 Number of ways 4 even numbers (2, 2, 4, 4) can be arranged is also 6So, total ways = 6 × 6 = 36 *

*Hence, option (c) is the correct answer.*

**Q30.** 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

**Answer: **(a)

__Solution:__

*in 1 day, A, B, C can do 1/8, 1/16 and 1/12 of total work respectively *

*Now, 1/8 + 1/16 + 1/12 = 13/48So, 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 :**

*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.

**Q31.** 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.

**Answer:** (a)

__Solution:__

**Option (a)** is indeed correct and the best choice as the passage discusses water being a state subject and emphasizes the need for a policy of basin-based approach with assessment, which aligns with the action required for fair and equitable allocation of water.

**Options (b) and (c)** are incorrect as they refer to concepts like interlinking of rivers, which are beyond the scope of the passage.

**Option (d)** is also incorrect as the question specifically asks about actions required to ensure fair and equitable allocation of water, which the passage does not directly address.

*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.

**Q32.** 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.

**Answer: **(d)

__Solution:__

**Options (a) and (b)** are indeed incorrect as the passage primarily focuses on nutrition and does not discuss education or skills.

**Option (c)** is also incorrect. The inclusion of the word "only" makes the statement extreme and unfounded as per the passage's content.

**Option (d)** is correct. The passage hints at the impact of health issues such as anemia and tuberculosis on productivity, as well as the effect of malnutrition on cognitive abilities in children. Therefore, it aligns with the passage's focus on nutrition and its broader implications for health and productivity.

*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.

**Q33.** 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.

**Answer:** (c)

__Solution:__

**Option (c) **is indeed correct. The passage highlights the significance of farmers' perception of the risks associated with climate change for adaptation. However, it also emphasizes that perception alone is not sufficient for adaptation. The author suggests that there may be a need for planned or policy-driven adaptation strategies by the government in addition to farmers' perceptions.

**Q34.** 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

**Answer: **(d)

__Solution:__

*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 take 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*

**Q35.** 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

**Answer:** (b)

__Solution:__

*Let the singles taken and the fours and the sixes scored by the batsman be a, b and c, respectively. So, as per the question:*

*a + 4b + 6c = 25, wherein a, b, c ≥ 0*

*If no six has been hit, i.e. c = 0 a + 4b = 25So, the possible values of (a, b) 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. c = 1 a + 4b = 19So, the possible values of (a, b) 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. c = 2a + 4b = 13So, the possible values of (a, b) may be (1, 3), (5, 2), (9, 1), (13, 0), i.e. 4 possible ways.*

*If three sixes have been hit, i.e. c = 3a + 4b = 7So, the possible values of (a, b) may be (3, 1), (7, 0), i.e. 2 possible ways.*

*If four sixes have been hit, i.e. c = 4a + 4b = 1So, the possible values of (a, b) may be (1, 0), i.e. 1 possible way.So, total number of possible ways = 7 + 5 + 4 + 2 + 1 = 19 *

**Q36. **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

**Answer: **(b)

__Solution:__

**Statement 1:** If one letter is placed in an incorrect envelope, then the letter that belongs to that envelope must also be placed in an incorrect envelope. Therefore, it’s not possible for only one letter to be misplaced; either no letter will be misplaced, or at least two letters will be misplaced. Thus, Statement 1 is incorrect.

**Statement 2: **To fulfill the requirement of placing two letters in correct envelopes and two in incorrect envelopes, we can choose the two letters to be placed in correct envelopes in 4C2 ways, which equals 6 ways. The remaining two letters will automatically be placed in each other’s envelopes (i.e., incorrect envelopes). Therefore, Statement 2 is correct. Hence, option (b) is the correct answer.

**Q37.** What is the remainder when 85 × 87 × 89 × 91 × 95 × 96 is divided by 100?

(a) 0

(b) 1

(c) 2

(d) 4

**Answer: **(a)

__Solution:__

*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. Hence, remainder will be zero. Hence, option (a) is correct.*

**Q38.** What is the unit digit in the expansion of (57242)9×7×5×3×1 ?

(a) 2

(b) 4

(c) 6

(d) 8

**Answer: **(a)

__Solution:__

*(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, *

*21 = 222 = 423 = 824 = 16 (unit digit 6)25 = 32 (unit digit 2)...And so on.*

*Exponent of any number ending in 2 will produce a number that will end in 2, 4, 8, or 6.Now, 945 = 944 + 1944 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.*

**Q39.** 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

**Answer: **(d)

*Solution:*

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

*C + F = 11, say 2 + 9 = 11B + E = 10, say 3 + 7 = 10A + 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*

**Q40.** 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

**Answer: **(c)

__Solution:__

*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.*

**Q36.** P, Q, R, S, T and U are six members of a family. R is the spouse of Q, U is the mother of T and S is the daughter of U. P's daughter is T and R's son is P. There are two couples in the family. Which one of the following is correct?

(a) is the grandfather of T

(b) is the grandmother of T

(c) R is the mother of P

(d) T is the granddaughter of Q

**Answer:** D

__Solution:__

*Solve by drawing a family tree.*

**Q37. **Consider the Question Statements given below in respect of and two three cities P, Q and R in a State:

Question: How far is city P from city Q ?

Statement-1: City Q is 18 km from city R.

Statement-2: City P is 43 km from city R.

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

(a) Statement-1 alone is sufficient to answer the Question

(b) Statement-2 alone is sufficient to answer the Question

(c) Both Statement-1 and Statement-2 are sufficient to answer the Question

(d) Both Statement-1 and Statement-2 are not sufficient to answer the Question

**Answer:** D

__Solution:__

*As we do not know the relative positions of P and Q, we cannot find the distance between them, even after using the information in both the statements.*

**Q38.** Two Statements followed by four Conclusions are given below. You have to take the Statements to be true even if they seem to be at variance from the commonly known facts. Read all the Conclusions and then decide which of the given Conclusions logically follows follow from the Statements, disregarding the commonly known facts :

Statement 1: All pens are books.

Statement 2: No chair is a pen.

Conclusion-I: All chairs are books.

Conclusion-II: Some chairs are pens.

Conclusion-III: All books are chairs.

Conclusion-IV: No chair is a book.

Which one of the following is correct?

(a) Only Conclusion-I

(b) Only Conclusion-II

(c) Both Conclusion-III and Conclusion-IV

(d) None of the Conclusion follows

**Answer:** D

__Solution:__

*Conclusion I contradicts with statement 1& 2Conclusion II contradicts with statement 2Conclusion III contradicts with statement 2Conclusion I contradicts with statement 1& 2*

**Q39. **Three Statements followed by three Conclusions are given below. You have to take the Statements to be true even if they seem to be at variance from the commonly known facts. Read all the Conclusions and then decide which of the given Conclusions logically follows/ follow from the Statements, disregarding the commonly known facts:

Statement 1: Some doctors are teachers.

Statement 2: All teachers are engineers.

Statement 3: All engineers are scientists.

Conclusion I: Some scientists are doctors.

Conclusion II: All engineers are doctors.

Conclusion III: Some engineers are doctors.

Which one of the following is correct?

(a) Only Conclusion-I

(b) Only Conclusion-II

(c) Both Conclusion-I and Conclusion-III

(d) Both Conclusion-I and Conclusion-II

**Answer: **C

__Solution:__

*draw the possible Venn diagrams based on the given statements:*

†

**Q40.** Eight students A, B, C, D, E, F, G and H sit around a circular table, equidistant from each other, facing the centre of the table, not necessarily in the same order. B and D sit neither adjacent to C nor opposite to C A sits in between E and D. and sits in between B and H. Which one of the following is definitely correct?

(a) B sits in between A and G

(b) C sits opposite to G

(c) E sits opposite to F

(d) None of the above

**Answer:** D

__Solution:__

*Draw the possible circular arrangements.*

*We can see that none of (a), (b), or (c) is definitely correct.*

**Directions for Read the following 4 (four) Items:**

**following two passages and answer that follow the passages. Your answer to these items should be based on the passages only.**

*Passage-1*

For two or three generations past, ever-increasing number of individuals have been living as workers merely, not as human beings. An excessive amount of labor is rule today in every circle of society, with the result that man's spiritual element cannot thrive. He finds it very difficult to spend his little leisure in serious activities. He does not want to think; or he cannot even if he wants to. He seeks not Self-improvement, but entertainment which would enable him to be mentally idle and to forget his usual activities. Therefore, the so-called culture of our age is dependent more on cinema than on theatre, more on newspapers, magazines and crime stories than on serious literature.

**Q41. **The passage is based on the idea that

(a) man should not work hard

(b) the great evil of our age is overstrain

(c) man cannot think well

(d) man cannot care for his spiritual welfare

**Answer:** B

__Solution:__

*The passage emphasizes the challenges associated with overworked individuals, distinct from the concept of hard work. Overworked individuals are so depleted at their workplace that they lack the energy for meaningful engagement in activities at home. *

*These activities include self-introspection, self-improvement, and spiritual pursuits. Instead, they opt for mentally undemanding activities such as watching cinema or crime stories. It's important to note that overworked individuals are fully capable of constructive thinking, self-improvement, and engaging in spirituality; however, overwork prevents them from doing so.*

*Given this discussion, options (c) and (d) can be dismissed.*

*The author's stance is against overworking individuals and not treating them merely as work units; this doesn't imply opposition to hard work itself. Thus, option (a) is incorrect, and option (b) is the correct answer.*

**Q42.** Man does not seek self-improvement because he

(a) is not intellectually capable

(b) has no time to do so

(c) is distracted by materialism

(d) loves amusement and is mentally idle

**Answer:** B

__Solution:__

**Option (b)** is correct as excessive work does not leave adequate time to engage in self-improvement.

*Passage-2*

The demographic dividend, which has begun in India and is expected to last another few decades, is a great window of opportunity. The demographic dividend is basically a swelling in the working age population, which conversely means that the relative ratio of very young and very old will, for a while, be on the decline. From the experience of Ireland and China, we know that this can be a source of energy and an engine of economic growth. The demographic dividend tends to raise a nation's savings rate since in any nation, it is the working age population that is the main saver. And since the savings rate is an important driver of growth, this should help elevate our growth rate. However, the benefits of demographic dividend depend on the quality of the working age population. And this implies bringing back the importance of education, acquisition of skills and human capital.

**Q43. ** Which of the following would invariably happen in a country, when the demographic dividend has begun to operate?

1. The number of illiterate people will decrease.

2. The ratio of very old and very young will decrease for a while.

3. Population growth rate will quickly stabilize.

Select the correct answer using the code given below.

(a) 1 and 2 only

(b) 2 only

(c) 1 and 3 only

(d) 1, 2 and 3

**Answer:** B

__Solution:__

**Statement 1 **is indeed incorrect. The demographic dividend refers to the increase in the share of the working-age population in the total population of a country, and it is not inherently related to illiteracy. While education helps in reaping the benefits of demographic dividend, it does not guarantee the elimination of illiteracy. Therefore, this statement cannot be accepted as invariably true.

**Statement 2 **is correct. The passage mentions that the relative ratio of the very young and very old will decline for a while, indicating an increase in the relative ratio of the elderly and children. Thus, this statement is accurate.

**Statement 3** is incorrect. There is no indication in the passage regarding the stabilization of population growth, nor can we make assumptions about the speed of such stabilization. Therefore, we cannot confirm the facts stated in this statement.

*Since only statement 2 is correct, option (b) is the most appropriate answer.*

**Q44.** With reference to the passage, which of the following inferences can be drawn?

1. Demographic dividend is an essential condition for a country to rapidly increase its economic growth rate.

2. Promotion of higher education is an essential condition for a country for its rapid economic growth.

Select the correct answer using the code given below.

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

**Answer:** D

__Solution:__

**Statement 1 **is indeed incorrect. While the passage acknowledges that demographic dividend provides an opportunity for economic growth, it does not imply that it is an essential condition for economic growth. Economic growth may still be possible even if a country is not in its demographic dividend phase. Therefore, the statement is far-fetched and incorrect.

**Statement 2** is also incorrect. While the passage discusses the importance of promoting higher education to capitalize on the demographic dividend, it does not state that promoting higher education is an essential or compulsory condition. The use of the extreme word "essential" or "compulsory" is unwarranted. Therefore, this statement is also rejected.

**Q45.** Five friends P. O, X, Y and Z purchased some notebooks. The relevant information is given below:

1. Z purchased 8 notebooks more than X did.

2. P and Q together purchased 21 notebooks.

3. O purchased 5 notebooks less than P did.

4. X and Y together purchased 28 notebooks.

5. P purchased 5 notebooks more than X did.

If each notebook is priced 40, then what is the total cost of all the notebooks?

(a) 2,600

(b) 2,400

(c) 2,360

(d) 2,320

**Answer: **A

__Solution:__

*As per the information provided in the question:Statement 1 -> Z = X + 8 ….(i)Statement 2 -> P + Q = 21 ….(ii)Statement 3 -> Q = P – 5 ….(iii)Statement 4 -> X + Y = 28 ….(iv)Statement 5 -> P = X + 5 ….(v)*

*Total number of Books = P + Q + X + Y + ZSolving equations (ii) and (iii), we get: P = 13Q = P – 5 = 8*

*Using above result and equation (v), we get: X = P – 5 = 8Using above result and equation (i), we get: Z = X + 8 = 16Using (iv), we get: Y = 28 – 8 = 20*

*So, P + Q + X + Y + Z = 13 + 8 + 8 + 20 + 16 = 65So, total cost of all the notebooks = 65 × 40 = Rs. 2600*

*There is no shortcut in this problem. If the options had very large differences, then we could simply have eliminated 3 options on basis of equations i, ii and iv, which gives 21+28+ x + 8 = so minimum 58 (x will be minimum 1). Now, 58x40 = 2320. So, answer can be this or any number bigger than this. *

**Q46.** A man started from home at 14:30 hours and drove to village, arriving there when the village clock indicated 15:15 hours. After staying for 25 minutes, he drove back by a different route of length 1.25 times the first route at a rate twice as fast reaching home at 16:00 hours. As compared to the clock at home, the village clock is

(a) 10 minutes slow

(b) 5 minutes slow

(c) 10 minutes fast

(d) 5 minutes fast

**Answer:** D

__Solution:__

*Total time taken by the man to come back home = 14:30 to 16:00 = 90 minutes*

*now subtract time for which he stayed in the village ie 25 minutes.therefore, total travelling time = 90 – 25 = 65 minutesusing, time speed distance formula, total time t1 + t2 = (distance 1/speed 1) + (distance 2/speed 2)*

*65 = d/s + 1.25d/2s solving we get, d/s = 65x2/3.25 = 40So, the man took 40 minutes to reach to the village.So, the correct time = 14:30 + 40 minutes = 15:10 hours*

*Therefore, the village clock is 15:15 – 15:10 = 5 minutes fast.*

**Q47. **A person X wants to distribute some pens among six children A B C D E and F. Suppose A gets twice the number of pens received by B, three times that of C, four times that of D, five times that of E and six times that of F. What is the minimum number of pens X should buy so that the number of pens each one gets is an even number?

(a) 147

(b) 150

(c) 294

(d) 300

**Answer:** C

__Solution:__

*number of pens with B = 60/2 = 30number of pens with C = 60/3 = 20number of pens with D = 60/4 = 15 (an odd number)number of pens with E = 60/5 = 12number of pens with F = 60/6 = 10*

*Now since adding is not an option, we can simply multiply by 2 convert odd numbers to even. Therefore A becomes 60 × 2 = 120*

*Similarly doubling all and adding we get total number of pens bought by X = 120 + 60 + 40 + 30 + 24 + 20 = 294*

**Q48.** Six Persons A, B, C, D, E and F are sitting equidistant form each other around a circular table (facing the centre of the table).

Consider the Question and two statements given below:

Question: Who is sitting on the immediate left of A?

Statement-1: B is sitting opposite to C and D is sitting opposite to E.

Statement -2: F is sitting on the immediate left of B.

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

(a) Statement-1 alone is sufficient to answer the question

(b) Statement-2 alone is sufficient to answer the question

(c) Both Statement-1 and Statement-2 are sufficient to answer the Question

(d) Both Statement-1 and Statement-2 are not sufficient to answer the Question

** Answer: **D

__Solution:__

*When considering each statement individually, neither provides enough information to determine the position of A relative to others.*

*Even when combining both statements, there's still uncertainty about the position of A relative to others. As a result, we cannot definitively answer the question about the position of A.*

*Therefore, option (d) is the most appropriate choice, indicating that both statements are not sufficient to answer the question.*

**Q49.** Consider the Question and two Statements given below:

Question: What is the age of Manisha?

Statement-1: Manisha is 24 years younger than her mother.

Statement-2: 5 years later, the ages of Manisha and her mother will be in the ratio 3: 5.

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

(a) Statements-1 alone is sufficient to answer the Question

(b) Statement-2 alone is sufficient to answer the question

(c) Both Statement-1 and Statement-2 are sufficient to answer the Question

(d) Both Statement-1 and Statement-2 are not sufficient to answer the Question

**Answer: **C

__Solution:__

*Let the present ages of Manisha and her mother be x and y respectively.*

*As per statement 1, y = x + 24*

*As per statement 2, (x + 5)/(y + 5) = 3/5Or 5x + 25 = 3y + 15Or 3y – 5x = 10Or 3(x + 24) – 5x = 10 (using statement 1)Or 3x + 72 – 5x = 10Or x = 31*

*Hence, Manisha is 31 years old at present.*

**Q50.** Six lectures A B C D E and F, each of one hour duration, are scheduled between 8:00 am, and 2:00 p.m.

Consider the Question and two Statements given below:

Question: Which lecture is in the third period?

Statement-1: Lecture F is preceded by A and followed by C

Statement-2: There is no lecture after lecture B.

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

(a) Statement-1 alone is sufficient to answer the question

(b) Statement-2 alone is sufficient to answer the question

(c) Both Statement-1 and Statement-2 are sufficient to answer the Question

(d) Both Statement-1 and Statement-2 are not sufficient to answer the Question

**Answer:** D

__Solution:__

*Neither statement alone nor the combination of both statements is sufficient to answer the question.*

**Directions for the following 3 (three) Items:**

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

*Passage-1*

In an economic organization, allowing mankind to benefit by the productivity of machines should lead to a very good life of leisure, and much leisure is apt to be tedious except to those who have intelligent activities and interests. If a leisured population is to be happy, it must be an educated population, and must be educated with a view to enjoyment as well as to the direct usefulness of technical knowledge.

**Q51. **Which of the following statements best reflects the underlying tone of the passage?

(a) Only an educated population can best make use of the benefits of economic progress.

(b) All economic development should be aimed at the creation of leisure.

(c) An increase in the educated population of a country leads to an increase in the happiness of its people.

(d) Use of machines should be encouraged in order to create a large leisured population.

**Answer: **C

__Solution:__

*Option (c) is correct. Refer to the last line or the conclusion. It conveys the tone clearly that author is advocating education as one of the solutions that increases happiness.*

*Passage-2*

If presents bring less thrill now that we are grown up, perhaps it is because we have too much already, or perhaps it is because we have lost the fullness of the joy of giving and with it the fullness of the joy of receiving. Children's fears are poignant, their miseries are acute, but they do not look too forward nor too far backward. Their joys are clear and complete, because they have not yet learnt always to add 'but' to every proposition. Perhaps we are too cautious, too anxious, too sceptical. Perhaps some of our cares would shrink if we thought less about them and entered with more single-minded enjoyment into the happiness that come our way.

**Q52.** With reference to the passage, which one of the following statements is correct?

(a) It is not possible for adults to feel thrilled by presents.

(b) There can be more than one reason why adults feel less thrilled by presents.

(c) The author does not know why adults feel less thrilled by presents.

(d) Adults have less capacity to feel the joy of loving or being loved.

**Answer:** B

__Solution:__

*The author explains that as we mature, we tend to become more cautious, anxious, and skeptical, leading to overthinking and a difficulty in enjoying the present moment. We often find ourselves either worrying about the future or analyzing the past, which detracts from our ability to appreciate the present. The author emphasizes that there's nothing inherently wrong with the natural capacity to enjoy the moment.*

*Given this explanation, Options (a) and (d) are incorrect because they overlook the reasons highlighted by the author for why adults may feel less thrilled by presents.*

**Option (c)** is also incorrect because the author specifically mentions the reasons behind adults feeling less thrilled by presents, such as being anxious, skeptical, and overthinking, rather than justifying it as a natural progression.

*Therefore, Option (b) is the most appropriate answer, as it aligns with the reasons provided by the author for why adults may feel less thrilled by presents.*

**Q53.** The author of the passage is against

(a) worrying too much about the past and future

(b) being in the habit of thinking about presents

(c) not being thrilled by new things

(d) giving and receiving joy only partially

**Answer:** A

__Solution:__

**Option (a)** is correct. The core agenda of the passage is discussing the importance of enjoying the present. This includes being thrilled by presents or gifts. According to the passage, as we grow there is a reduction in enjoying the moment. That’s because we tend to worry too much about the past and future. Tthe author is against worrying too much about past and future.

**Q54.** Let A, B and C represent distinct non-zero digits. Suppose x is the sum of all possible 3-digit numbers formed by A, B and C without repetition.

Consider the following statements:

1. The 4-digit least value of x is 1332.

2. The 3-digit greatest value of x is 888

Which of the above statements is/are correct?

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

**Answer: **A

__Solution:__

*The three-digit numbers have been represented by ABC, wherein A, B, and C are non-zero digits.*

*Using 3 distinct digits we can make 3 × 2 × 1 = 6 three-digit numbers.So, x will be the sum of these 6 three-digit numbers.*

*We need to find the two values of x closest to 1000, one just below it (which will be the greatest 3-digit value of x), and the other just above it (which will be the lowest 4-digit value of x).*

*Now, we have to do a bit of hit and try, so that the value of x reaches close to 1000.*

*Let the three digits be the minimum possible ones, i.e. 1, 2, and 3.So, we get x = 123 + 132 + 213 + 231 + 312 + 321 = 1332*

*This is the least possible value of x. So, statement 1 is correct, but statement 2 is incorrect.*

**Q55.** There is a numeric lock which has a 3-digit PIN. The PIN contains digits 1 to 7. There is no repetition of digits. The digits in the PIN from left to right are in decreasing order. Any two digits in the PIN differ by at least 2. How many maximum attempts does one need to find out the PIN with certainty?

(a) 6

(b) 8

(c) 10

(d) 12

**Answer: **C

__Solution:__

*The PIN contains three digits out of – 1, 2, 3, 4, 5, 6, and 7*

**Case I:** The rightmost digit is 1

The possible combinations are: 531, 631, 731, 641, 741, 751 (i.e. 6 possible combinations)

**Case II:** The rightmost digit is 2

The possible combinations are: 642, 742, 752 (i.e. 3 possible combinations)

**Case III: **The rightmost digit is 3

The possible combinations are: 753 (i.e. 1 possible combination)

The rightmost digit cannot be more than 3. (due to difference of 2 between each)

So, the total number of possible combinations of the PIN = 6 + 3 + 1 = 10

**Q56.** There are eight equidistant points on a circle. How many right-angled triangles can be drawn using these points as vertices and taking the diameter as one side of the triangle?

(a) 24

(b) 16

(c) 12

(d) 8

**Answer:** A

__Solution:__

*With eight equidistant points on a circle - A, B, C, D, E, F, G, and H. We can have 4 unique diameter lines connecting the opposite points.*

*We are aware of the property that whenever diameter of a circle is one side and opposite vertex is on the circle, it forms a right angle triangle. Therefore, we can get 6 unique right angle triangle using 6 remaining points. *

*Since, with each diameter we can form 6 unique triangles, we have total number of right-angled triangles that can be drawn = 4 x 6 = 24*

**Q57.** 24 men and 12 women can do a piece of work in 30 days. In how many days can 12 men and 24 women do the same piece of work?

(a) 30 days

(b) more than 30 days

(c) Less than 30 days or more than 30 days

(d) Data is inadequate to draw any conclusion

**Answer: **D

__Solution:__

*Since we have only one equation and 2 variables, it is not possible to solve.*

**Q58. **What is the remainder when 91x92x93x94x95x96x97x98x99 is divided by 1261?

(a) 3

(b) 2

(c) 1

(d) 0

**Answer: **D

__Solution:__

*We will check 1261 with all prime numbers one by one. First hit is 13 (2, 3 & 5 can easily be ruled out. Then try 7 and 11). *

*Remaining number ie 1261/13 is 97.*

*1261 = 1 × 13 × 97*

*Now, 91 is divisible by 13 and 97 itself is present. So, 1261 will completely divide the expression.*

*Hence, the remainder = 0*

**Q59.** Consider the following statements in respect of a rectangular sheet of length 20 cm and breadth 8 cm:

1. It is possible to cut the sheet exactly into 4 square sheets.

2. It is possible to cut the sheet into 10 triangular sheets of equal area.

Which of the above statements is are correct?

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

**Answer: **C

__Solution:__

**Statement I: **It is not possible to cut a rectangle into exactly 4 square sheets. But the 4 squares don't have to be equal in area. So, we can have 4 squares - 8x8, 8x8, 4x4, 4x4

**Statement II:** Now we know that by merging two equal area congruent triangles we can form a rectangle. So, we have 5 equal sized rectangles instead of 10 triangles. We can easily cut 1 rectangle into 5 equal sized rectangles.

**Q60.** When 70% of a number x is added to another number y, the sum becomes 165% of the value of y. When 60% of the number x is added to another number z, then the sum becomes 165% of the value of z. which one of the following is correct?

(a) z < x < y

(b) x < y < z

(c) y < x < z

(d) z < y < x

**Answer: **A

__Solution:__

*To simplify we write percentages in decimal form,0.7 x + y = 1.65 yOr 0.7 x = 0.65 yOr x/y = 0.65/0.70, which is less than 1.Hence, x < y …..(i)*

*Now, 0.6 x + z = 1.65 zOr 0.6 x = 0.65 zOr x/z = 0.65/0.60, which is greater than 1.Hence, x > z …..(ii)*

*From (i) and (ii), we get: z < x < y*

**Directions for the following 3 (three) items:**

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

*Passage–1*

The majority of people who fail to accumulate money sufficient for their needs, are generally, easily influenced by the opinions of others. They permit the newspapers and the gossiping neighbours to do their thinking for them. Opinions are the cheapest commodities on the earth. Everyone has a flock of opinions ready to be wished upon by anyone who will accept them. If you are influenced by opinions when you reach decisions, you will not succeed in any undertaking.

**Q61.** Which one of the following is implied by the passage?

(a) Most of the people do not accumulate money for their needs.

(b) Most of the people never fail to accumulate money for their needs.

(c) There are people who fail to accumulate money for their needs.

(d) There is no need to accumulate money.

**Answer:** C

__Solution:__

*To properly address this question, it's crucial to simplify the first line of the passage. It suggests that among those who struggle to accumulate enough money, the majority are easily influenced by external opinions. Nowhere does the author indicate that most people fail to accumulate sufficient money for their needs, nor does the author suggest that most people are successful in accumulating enough money. The passage maintains a balanced perspective while emphasizing the importance of money. Option (c) best captures all these aspects.*

**Q62.** What is the main idea of the passage?

(a) People should not be influenced by the opinions of others.

(b) People should accumulate as much money as they can.

(c) People should neither give nor accept the opinions.

(d) People will succeed in any undertaking if they do not accept any opinion at all

**Answer:** A

__Solution:__

*Statement (a) is correct. The author indeed begins by discussing the influence of others' opinions, as evident from the very first line of the passage. Furthermore, in the last line, the author unequivocally states that one will not succeed in any endeavor if they are swayed by others' opinions. Hence, there is a clear suggestion against being influenced by others' opinions throughout the passage.*

*Passage–2*

"The social order is a sacred right which is the basis of all other rights. Nevertheless, this right does not come from nature, and must therefore be founded on conventions."

**Q63.** With reference to the above passage which of the following statements is/are correct?

1. Conventions are the sources of rights of man.

2. Rights of man can be exercised only when there is a social order.

Select the correct answer using the code given below.

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

**Answer: **C

__Solution:__

*Statement 1 is indeed correct. The author explicitly states that the right of social order does not originate from nature but rather from convention. Social order emerges from conventions, and it serves as the foundation for all other rights. Therefore, this statement accurately reflects the content of the passage.*

*Statement 2 is also correct. If we negate this statement, it would contradict the passage because if the rights of man could be exercised without social order, it would not be considered the basis of all other rights. By applying the negation test, we can confirm the correctness of this statement as per the passage.*

**Q64.** Two candidates X and Y contested an election. 80% of voters cast their vote and there were no invalid votes. There was no NOTA (None of the above) option. X got 56% of the votes cast and won by 1440 votes. What is the total number of voters in the voters list?

(a) 15000

(b) 12000

(c) 9600

(d) 5000

**Answer:** A

__Solution:__

*Since there are only two candidates, if X got 56%, Y got 44%. Difference is of 12%.*

*Now, Difference is given as 1440 (12% of votes casted). Therefore, total casted votes = 12000Now, only 80% voted, so total voters = 12000/.80 = 15000*

**Q65.** What is the smallest number greater than 1000 that when divided by any one of the numbers 6, 9, 12, 15, 18 leaves a remainder of 3?

(a) 1063

(b) 1073

(c) 1083

(d) 1183

**Answer:** C

__Solution:__

*LCM of 6, 9, 12, 15 and 18 = 180*

*Smallest number greater than 1000 which is a multiple of 180 is 1080.*

*So, the required number with remainder 3 = 1080 + 3 = 1083*

**Q66.** Let p be a two-digit number and q be the number consisting of same digits written in reverse order. If p x q = 2430, then what is the difference between p and q?

(a) 45

(b) 27

(c) 18

(d) 9

**Answer:** D

Solution:

The given product p × q = 2430 ...(i)

The last digit is 0, so one two of the digits must be 5 and other one an even number 2, 4, 6 or 8.

Let this unknown digit be x.

So, p = 10x + 5 and q = 50 + x

putting in (i),

(10x + 5) × (50 + x) = 2430

Now, try 2, 4, 6 and 8,

x = 4 (we can easily eliminate others as they will yield either too big or small number than 2430)

Therefore, p = 45 and q = 54

Required difference = q - p = 54 – 45 = 9

**Q67. **Consider the following statements in respect of two natural numbers p and q such that p is a prime number and q is a composite number:

1. p x q can be an odd number.

2. q / p can be a prime number.

3. p + q can be a prime number.

Which of the above statements are correct?

(a) 1 and 2 only

(b) 2 and 3 only

(c) 1 and 3 only

(d) 1, 2 and 3

**Answer:** D

__Solution:__

*Since all statements say "can be", we just need to find one case that is possible for each statement. This is not tough to do as shown below. *

*p is a prime number. So, p can be 2, 3, 5, 7, 11, 13, .….q is a composite number. So, q can be 4, 6, 8, 9, 10, .….*

**Statement 1:** p × q can be an odd number, e.g. (3 × 9 = 27). Thus, statement 1 is correct.**Statement 2:** q/p can be a prime number, e.g. (4/2 = 2). Thus, statement 2 is correct.**Statement 3:** p + q can be a prime number, e.g. (3 + 4 = 7). Thus, statement 3 is correct.

*Thus, all the statements 1, 2 and 3 are correct.*

**Q68. **Consider the following statements :

1. Between 3:16 p.m. and 3:17 p.m., both hour hand and minute hand coincide.

2. Between 4:58 p.m. and 4:59 p.m.. both minute hand and second hand coincide.

Which of the above statements is/are correct?

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

**Answer:** C

__Solution:__

**Statement 1**: In 1 minute, Hour hand covers 0.5 degrees. So, at 3.16 pm, hour hand position in degrees = 192x0.5 = 96

*In 1 minute, minute hand covers 6 degrees. So, at 3.16 pm ie 16 minutes, minute hand position in degrees = 16x6 = 96*

*Hence, statement 1 is correct.*

**Statement 2** is bound to be correct as second hand travels through entire clock in one minute. So, it will coincide with minute hand when it is between 4:58 p.m. and 4:59 p.m.

*Thus, both statements 1 and 2 are correct.*

**Q69.** There are two containers X and Y. X contains 100 ml of milk and Y contains 100 ml of water. 20 ml of milk from X is transferred to Y. After mixing well, 20 ml of the mixture in Y is transferred back to X. If m denotes the proportion of milk in X and n denotes the proportion of water in Y, then which one of the following is correct?

(a) m=n

(b) m> n

(c) m<n

(d) Cannot be determined due to insufficient data

**Answer: **A

*Solution:*

*After 20 ml of milk transferred from container X to container Y, Milk in container X = 100 – 20 = 80 mlAmount of solution in container Y becomes = 100 ml water + 20 ml milk = 120 ml*

*Ratio of milk in container Y solution = 20 : 120 = 1 : 6By corollary, ratio of water in Y solution = 5 : 6 (100 : 120)*

*After 20 ml of milk transferred from container Y to container X, Milk in container X = 80 + 1/6 *20 = 83.33 ml*

*Amount of water in Y = 5/6 * 100 = 83.33 mlThus, m = n*

**Q70.** A pie chart gives the expenditure on five different items A, B, Q D and E in a household. If B, C, D and E correspond to 90o, 50o, 45o, and 75o respectively, then what is the percentage of expenditure on item A?

(a) 112/9

(b) 125/6

(c) 155/9

(d) 250/9

**Answer: **D

Solution:

Angle A in the pie-chart = 360 – (90 + 50 + 45 + 75) = 100

Percentage of expenditure on item A = (100/360) × 100 = (250/9)%

**Directions for the following 3 (three) items:**

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

*Passage–1*

To encourage research is one of the functions of a university. Contemporary universities have encouraged research, not only in those cases where research is necessary, but on all sorts of entirely unprofitable subjects as well. Scientific research is probably never completely valueless. However silly and insignificant it may seem, however mechanical and unintelligent the labours of the researchers, there is always a chance that the results may be of value to the investigator of talent, who can use the facts collected for him by uninspired but industrious researchers as the basis of some fruitful generalization. But where research is not original, but consists in the mere rearrangement of existing materials, where its objects is not scientific but literary or historical, then there is a risk of the whole business becoming merely futile.

**Q71.** The author's assumption about scientific research is that

(a) it is never very valuable

(b) it is sometimes very valuable

(c) it is never without some value

(d) it is always very valuable

**Answer:** C

*Solution:*

*This question primarily pertains to the tone of the passage regarding the value of research. The line "Scientific research is probably never completely valueless" suggests an optimistic perspective on the outcome of scientific research. *

**Option (c) **reflects this viewpoint precisely. The author adopts an optimistic approach toward the potential value of scientific research. The main concern expressed in the passage relates to the nature of research, emphasizing the importance of originality rather than literary or historical content. Therefore, option (c) accurately captures the tone and perspective of the passage.

**Q72. **According to the author

(a) not many research results can be of value to an intelligent investigator

(b) a research result is always valuable to an intelligent investigator

(c) any research result can be of value to an intelligent investigator

(d) a research result must always be of some value to an intelligent investigator

**Answer:** C

__Solution:__

*To determine the correct answer, it's crucial to consider the tone of the author.*

*In the line "there is always a chance that the result is of value to the investigator of talent," the author suggests that the result of scientific research is likely to be valuable to an intelligent investigator in some manner. *

*However, the author stops short of taking an extreme stance, such as asserting that the result is always valuable to the intelligent investigator. This cautious approach of the author is accurately reflected in option (c).*

*Passage–2*

How best can the problems of floods and droughts be addressed so that the losses are minimal and the system becomes resilient? In this context, one important point that needs to be noted is that India gets "too much' water (about 75% of annual precipitation) during 120 days (June to September) and "too little' for the remaining 245 days. This skewed water availability has to be managed and regulated for its consumption throughout the year.

**Q73.** Which one of the following best reflects the practical, rational and lasting solutions?

(a) Constructing huge concrete storage tanks and canals across the country

(b) Changing the cropping patterns and farming practices

(c) Interlinking of rivers across the country

(d) Buffer stocking of water through dams and recharging aquifers

**Answer: **D

__Solution:__

*Option (d) is correct as buffer stocking of water through dams and recharging aquifers would mean that the excess water is being stored above and below ground for later use ie managed and regulated for future consumption during lean season. *

**Q74. **15 x 14 x 13 x ... x 3 x 2 x 1 = 3m x n

Where m and n are positive integers, then what is the maximum value of m?

(a) 7

(b) 6

(c) 5

(d) 4

**Answer:** B

__Solution:__

*15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3m × n*

*Numbers which are multiple of 3 = 15 × 12 × 9 × 6 × 3 = (3 × 5) × (3 × 4) × (3 × 3) × (3 × 2) × 3 = (3x3x3x3x3x3) × (5 ×4 × 2)*

*Therefore, the maximum value of m is 6.*

**Q75.** What is the value of X in the sequence 2, 12, 36, 80, 150, X?

(a) 248

(b) 252

(c) 258

(d) 262

**Answer:** B

__Solution:__

*We need to break down the numbers into their multiples to observe the pattern clearly :*

*1 x 1 x 2, 2 x 2 x 3, 3 x 3 x 4, 4 x 4 x 5, 5 x 5 x 6, .....Next number is 6 x 6 x 7 = 252Hence, option (b) is the correct answer.*

**Q76.** One non-zero digit, one vowel and one consonant from English alphabet (in capital) are to be used in forming passwords, such that each password has to start with a vowel and end with a consonant. How many such passwords can be generated?

(a) 105

(b) 525

(c) 945

(d) 1050

**Answer:** C

__Solution:__

*There are 9 non-zero digits ie 1, 2, 3, 4, 5, 6, 7, 8 or 9There are 5 vowels and 21 consonants in English alphabet (capitals only)*

*The password starts with a vowel and ends with a consonant. So, the digit will come at the middle.The number of such passwords = 5 × 9 × 21 = 945*

*Hence, 945 such passwords can be generated.*

**Q77.** There are 9 cups placed on a table arranged in equal number of rows and columns out of which 6 cups contain coffee and 3 cups contain tea. In how many ways can they be arranged so that each row should contain at least one cup of coffee?

(a) 18

(b) 27

(c) 54

(d) 81

**Answer: **D

__Solution:__

*The cups will be arranged in a 3 × 3 matrix. We need to remove cases where any one row contains only Tea i.e. all 3 Teas in a single row.*

*This can happen in 3 ways - first, second or third row. Therefore 3 cases need to subtracted from total combinations possible.*

*Total arrangements = 9! /(6! x 3!) Required answer = total arrangements possible - 3 = 84 - 3 = 81*

*Hence, option (d) is the correct answer.*

**Q78.** The sum of three consecutive integers is equal to their product. How many such possibilities are there?

(a) Only one

(b) Only two

(c) Only three

(d) No such possibility is there

**Answer:** C

__Solution:__

*Let the 3 consecutive integers be x - 1, x, and x + 1*

*According to the question, sum = product, therefore(x – 1) + x + (x + 1) = (x - 1) × x × (x + 1)⇒ 3x = x × (x - 1) × (x + 1)⇒ x = 0, 2 or -2*

*Therefore, there are 3 such possibilities.*

**Q79.** What is the number of numbers of the form 0.XY, where X and Y are distinct non-zero digits?

(a) 72

(b) 81

(c) 90

(d) 100

**Answer: **A

__Solution:__

*Since, X and Y are distinct non-zero digits - 1 to 9XY can be arranged in = 9 × 8 ways = 72*

**Q80.** The average weight of A, B, C is 40 kg, the average weight of B, D, E is 42 kg and the weight of F is equal to that of B. What is the average weight of A, B, C, D, E and F?

(a) 40.5 kg

(b) 40.8 kg

(c) 41 kg

(d) Cannot be determined as data is inadequate

**Answer: **C

__Solution:__

*(A + B + C)/3 = 40 (given)=> (A + B + C) = 120 ………(i)*

*(B + D + E)/3 = 42 (given)=> (B + D + E) = 126 ..……(ii)*

*F = B .…….(iii)*

*From equations (i) and (ii), we get: A + B + C + B + D + E = 120 + 126Or A + B + C + D + E + F = 246 (replacing one B with F as F = B from equation iii)*

*So, average weight of A + B + C + D + E + F = 246/6 = 41*

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