UPSC CSE 2024 CSAT (SET A) 

 

 

Passage - 1

According to the Food and Agriculture Organization, one-third of food produced for human consumption is lost or wasted globally. Food is lost or wasted throughout the supply chain, from initial agricultural production to final household consumption. The increasing wastage also results in land degradation by about 45%, mainly due to deforestation, unsustainable agricultural practices, and excessive groundwater extraction. The energy spent over wasted food results in about 3.5 billion tonnes of carbon dioxide production every year. Decay also leads to harmful emissions of other gases in the atmosphere. Addressing the loss and wastage of food in all forms is critical to complete the cycle of food efficiency and food sustainability.

1.Which of the following statements best reflect the most logical and rational inferences that can be made from the passage?

1. The current methods of food distribution are solely responsible for the loss and wastage of food.
2. Land productivity is adversely affected by the prevailing trend of food loss and wastage.
3. Reduction in the loss and wastage of food results in lesser carbon footprint.
4. Post-harvest technologies to prevent or reduce the loss and wastage of food are not available.

Select the correct answer using the code given below:

 (a) 1, 2, and 3

(b) 2 and 3 only

(c) 1, 3, and 4

 (d) 1, 2, and 4

Answer (b)

The passage provides information about the food wastage problem and its consequences:

1. The current methods of food distribution are solely responsible for the loss and wastage of food.
   • The passage indicates that food is lost or wasted throughout the supply chain, from production to consumption. Therefore, it is not solely the distribution methods that are responsible. Hence, this statement is incorrect.
2. Land productivity is adversely affected by the prevailing trend of food loss and wastage.
   • The passage mentions land degradation due to deforestation, unsustainable agricultural practices, and excessive groundwater extraction, all of which are linked to food wastage. This makes the statement correct.
3. Reduction in the loss and wastage of food results in lesser carbon footprint.
   • The passage states that wasted food contributes to about 3.5 billion tonnes of carbon dioxide production annually. Hence, reducing food wastage would indeed result in a smaller carbon footprint, making this statement correct.
4. Post-harvest technologies to prevent or reduce the loss and wastage of food are not available.
   • The passage does not provide any information about the availability or unavailability of post-harvest technologies. Hence, this statement cannot be inferred from the passage.

Therefore, the correct answer is: (b) 2 and 3 only

 

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

1.The food distribution mechanism needs to be reimagined and made effective to reduce the loss and wastage of food.

2.Ensuring the reduction of wastage and loss of food is a social and moral responsibility of all citizens.

Which of the assumptions given above is/are valid?

(a) 1 only

 (b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

Answer (a)

Option (a) is the correct answer

Assumption 1 is valid: The passage indicates that one-third of food produced for human consumption is lost or wasted globally due to inefficiencies throughout the supply chain. To address this significant problem, it is necessary to rethink and improve the food distribution mechanism to reduce wastage effectively.

Assumption 2 is invalid: While the passage underscores that food loss and wastage have major environmental consequences, such as increased carbon dioxide emissions and land degradation, it does not explicitly state that reducing food wastage is a social and moral responsibility for all citizens. The emphasis is more on the economic and environmental impacts rather than on a universal moral obligation.

Therefore, option (a) is the correct answer

 

Passage - 2

As inflation rises, even governments previously committed to budget discipline are spending freely to help households. Higher interest rates announced by central banks are supposed to help produce modest fiscal austerity, because to maintain stable debts while paying more to borrow, governments must cut spending or raise taxes. Without the fiscal backup, monetary policy eventually loses traction. Higher interest rates become inflationary, not disinflationary, because they simply lead governments to borrow more to pay rising debt-service costs. The risk of monetary unmooring is greater when public debt rises, because interest rates become more important to budget deficits.

 

1. Central banks cannot bring down inflation without budgetary backing.
2. The effects of monetary policy depend on the fiscal policies pursued by the government.

Select the correct answer using the code given below:

Answer ( C) 

Among the given options:

• (a) Central banks cannot bring down inflation without budgetary backing. (Correct) This inference aligns with the passage's discussion that monetary policy's effectiveness in controlling inflation depends on supportive fiscal policies.
• (b) The effects of monetary policy depend on the fiscal policies pursued by the government. (Correct) This inference is directly supported by the passage, which discusses how fiscal policies impact the outcomes of monetary policy measures.

Therefore, the correct answer is:

(c) Both 1 and 2

 

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

1. Fiscal policies of governments are solely responsible for higher prices.
2. Higher prices do not affect the long-term government bonds.

Which of the assumptions given above is/are valid?

Answer (d)

1. Fiscal policies of governments are solely responsible for higher prices.
   • This assumption is not valid according to the passage. The passage discusses inflation as a result of various factors, including government spending in response to inflation, but it does not attribute inflation solely to fiscal policies.
2. Higher prices do not affect the long-term government bonds.
   • This assumption is not valid. The passage implies that higher interest rates, influenced by inflation and government debt dynamics, affect long-term government bonds. It discusses the risk of higher debt-service costs and the impact on budget deficits due to rising interest rates.

Therefore, the correct answer is:

(d) Neither 1 nor 2

 

Answer (b)

To divide a cube into 64 identical pieces, you need to make cuts that slice through the cube's dimensions. Initially, you make 6 cuts—two along each dimension (length, width, and height)—to create smaller cubes. However, to ensure all 64 pieces are identical, additional cuts are needed at the ends of the cube, totaling 9 cuts in all

Answer (d)

By selecting the symbols in the expression as follows:

5−4−3+2×1=5−7+2=05 - 4 - 3 + 2 \times 1 = 5 - 7 + 2 = 05−4−3+2×1=5−7+2=0

We achieve a sequence of operations where subtraction and multiplication are used in such a way that the result is minimized to its smallest non-negative value, which in this case is 0. This combination ensures that each operation is strategically applied to reduce the cumulative result. Therefore, option d is identified as the correct answer because it reflects this minimized outcome of the expression

 

Answer ( C )

Imagine we have a project that needs to be completed by a certain number of workers. The fewer workers we have, the longer it will take to finish. This is called an inverse relationship.

• Let's say initially we have N1 workers and it takes them 6k days to complete the project (where k is a whole number).
• We can represent the total workload required for the project as the product of number of workers and the number of days. So, in this case, the initial workload is N1 workers * 6k days.
• Since the total amount of work stays the same regardless of how many workers we have, this concept is called a constant workload.
• Now, suppose we want to finish the project in a shorter time, say 5k days. To achieve this with the same total workload, we need to increase the number of workers.
• Let's call the new number of workers N2.
• Because the workload is constant, we can set up an equation: Initial workload = Final workload
• This translates to: N1 workers * 6k days = N2 workers * 5k days
• Solving for the new number of workers (N2), we get: N2 = (6/5) * N1
• This means we need (6/5) times more workers than initially to complete the project in 5k days.
• To express this increase as a percentage, we can calculate: Percentage increase = [(New number of workers - Initial number of workers) / Initial number of workers] * 100
• Plugging in the values, we get: Percentage increase = [((6/5) * N1) - N1] / N1 * 100
• Simplifying the equation, we get: Percentage increase = (1/5) * 100 = 20%

Therefore, the number of workers needs to be increased by 20% to complete the project in 5k days

 

Answer ( C) 

1. Restriction on working hours: No person can work for two consecutive hours. This limitation creates a challenge in scheduling their work efficiently.
2. Identify common ground: Both Y and Z take 8 hours to complete the work individually. This suggests they can potentially contribute equal amounts of work per hour.

Solution Strategy:

1. Alternate work schedule: To avoid consecutive working hours, we can create an alternating work schedule:
   • Hour 1: X works (1/6 of the work done)
   • Hour 2: Y works (1/8 of the work done)
   • Hour 3: Z works (1/8 of the work done)
2. Repeating pattern: This alternating pattern (X-Y-Z) can be repeated continuously.
3. Calculate work progress: After 3 hours, they will have completed:
   • X: 1/6 of the work
   • Y: 1/8 of the work
   • Z: 1/8 of the work
   • Total progress after 3 hours = (1/6) + (2/8) = 7/24 of the work done.
4. Remaining work: There's still (1 - 7/24) = 17/24 of the work remaining.
5. Complete remaining work: Since Y and Z have the same work rate, they can take turns completing the remaining portion in alternating hours:
   • Hour 4: Y works (another 1/8 of the work done)
   • Hour 5: Z works (another 1/8 of the work done)
   • Hour 6: Y works (completing the remaining 1/24 of the work)

Minimum Time:

Therefore, with this alternating work schedule, they can finish the work in a minimum of 6 hours.

Answer: (c) 6 hours 45 minutes

 

Answer (d)

The number of trailing zeros in a number indicates how many times it is divisible by 10.

Since 10=2×510 = 2 \times 510=2×5, a trailing zero is formed by a pair of factors of 2 and 5.

Therefore, the number of trailing zeros is determined by the lesser count of factors of 2 or 5.

The base numbers where 5 is a factor are 5, 10, 15, 20, and 25.

Number of 5’s in 510 = 10

Number of 5’s in 1020 = 20

Number of 5’s in 1530 = 30

Number of 5’s in 2040 = 40

Number of 5’s in 2550 = 50 x 2 = 100

Total number of 5s = 10 + 20 + 30 + 40 + 100 = 200

There are generally more factors of 2 than factors of 5. For example, 24×48×81624 \times 48 \times 81624×48×816 has 4, 16, and 48, which are all multiples of 2.

Therefore, the number of trailing zeros is determined by the lesser count of 2s or 5s, which is 200 in this case.

Thus, there are 200 zeros at the end.

Therefore, option d is the correct answer

 

 

Answer (b)

"Starting with a savings of Rs. 1 on day 1, the savings pattern increases by Rs. 2 each subsequent day: Rs. 3 on day 2, Rs. 5 on day 3, and so forth, following the sequence 1, 3, 5, 7, 9, etc.

Consequently, the total savings form a pattern of perfect squares: 1, 4, 9, 16, 25, etc.

To meet the condition of being both a perfect square and a perfect cube, the savings must reach the first number that fits both criteria, which is 64.

By adding the daily savings up to the 8th day: 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64

Therefore, the total savings become both a perfect square and a perfect cube after 8 days, i.e., on January 8th, 2023.

Thus, the correct answer is option b

 

Passage-1

Today, if we consider cities such as New York, London and Paris as some of the most iconic cities in the world, it is because plans carrying a heavy systems approach were imposed on their precincts. The backbone of the systems theory is the process of translating social, spatial and cultural desirables into mathematical models using computing, statistics, optimization and an algorithmic way of formulating and solving problems. The early universities of the West which began to train professionals in planning, spawned some of the most ingenious planners, who were experts in these domains. This was because these very subjects were absorbed into the social sciences, geography and architecture. Planning in India, and its education differ from the West.

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

1. a) Curriculum for urban planning courses should have diverse and interdisciplinary approach.
2. b) In India, city administration is under bureaucracy which lacks formal training in urban planning and management.
3. c) In India, the management of urban areas is a local affair with a chronic problem of insufficient funds.
4. d) With high density of population and widespread poverty in our urban areas, planned development in them is very difficult

Answer (a)

1. a) Curriculum for urban planning courses should have diverse and interdisciplinary approach.

• This statement aligns with the passage, which emphasizes the success of Western cities due to a comprehensive systems approach in urban planning education.

1. b) In India, city administration is under bureaucracy which lacks formal training in urban planning and management.

• While this may be true, it is not directly inferred from the passage.

1. c) In India, the management of urban areas is a local affair with a chronic problem of insufficient funds.

• This statement is not supported by the passage.

1. d) With high density of population and widespread poverty in our urban areas, planned development in them is very difficult.

• This statement, while potentially accurate, is not the main inference from the passage.

1. a) Curriculum for urban planning courses should have diverse and interdisciplinary approach.

 

1. India needs a new generation of urban professionals with knowledge relevant to modern urban practice.
2. Indian universities at present have no capacity or potential to impart training in systems approach.

Which of the assumptions given above is/are correct?

Answer (d)

Assumption 1 is incorrect because the passage highlights the contrast between planning education in India and the West without explicitly stating a need for new urban professionals in India with modern knowledge.

Assumption 2 is incorrect since the passage does not clearly indicate that Indian universities lack the capacity or potential to teach the systems approach. It mainly focuses on the historical development of planning education in the West and its influence

 

Passage-2

Not every voice on the internet commands the same kind of audience. When anonymous private entities with high capital can pay for more space for their opinions, they are effectively buying a louder voice. If political discourse in the digital sphere is a matter of outshining one’s opponent till the election is won, then the quality of politics suffers. The focus of social media is restricted to the promotion of content that generates more user engagement, regardless of how inflammatory the content maybe.

 

Answer (b)

1. a) Constructed as a marketplace of views, social media ensures instant access to information.

• This statement is true, but it doesn't capture the central criticism in the passage about the negative impact of capital on political discourse and the promotion of inflammatory content.

1. b) Social media are not ideal or moral institutions but the products built by companies to make profits.

• This statement aligns well with the passage's central idea, highlighting the profit-driven nature of social media and its impact on political discourse.

1. c) Social media have been created to strengthen democracies.

• This statement is contrary to the passage, which suggests that social media may actually harm political discourse.

1. d) In today’s world, social media are inevitable for well-informed social life.

• This statement is not the focus of the passage, which critiques the negative aspects of social media.

Answer: b) Social media are not ideal or moral institutions but the products built by companies to make profits

 

Which of the assumptions given above is/are valid?

Answer ( C)

Assumption Analysis:

1. Internet is not inclusive enough.
   • The passage implies that the internet can be dominated by entities with high capital, suggesting a lack of inclusivity.
2. Internet can adversely affect the quality of politics in a country.
   • This assumption is directly supported by the passage, which discusses how political discourse suffers due to the influence of capital and the promotion of inflammatory content on social media.

Answer Analysis:

1. a) 1 only

• This assumption is valid based on the passage's implications.
• b) 2 only
• This assumption is also valid, as the passage explicitly discusses the adverse effects on political discourse.
• c) Both 1 and 2
• Both assumptions are supported by the passage.
• d) Neither 1 nor 2
• Incorrect, as both assumptions are supported.

Answer: c) Both 1 and 2

 

 

(a) 2 and 3 but not 37

(b) 3 and 37 but not 2

(c) 2 and 37 but not 3

(d) 2, 3 and 371

Answer (b)

 + =

+ (

=  (+ )

As, 111 = 3 x 37

So, the number is divisible by 3 and 37.

When we divide number by 2,

2³³³ x 111¹¹¹ is divisible but 3²²² is an odd number and not divisible

So, the number is an odd number and not divisible by 2.

Hence option b is the correct answer

 

 

(a) 20%

(b) 10%

(c) 5%

(d) 4%

Answer (a)

Let's approach this step-by-step:

1. Let's assume we start with 100 units of honey.
2. We want to add water and sell the mixture at the same price as pure honey, but make a 20% profit.
3. This means our selling price should be 120% of our cost price.
4. Let x be the amount of water added (in units).
5. The cost of the mixture is the same as the cost of 100 units of honey, as water is free.
6. But we're selling (100 + x) units at the price of 100 units of honey.
7. For this to give us a 20% profit: (100 + x) = 120% of 100 100 + x = 120 x = 20
8. So we need to add 20 units of water to 100 units of honey.
9. To calculate the percentage: 20 / (100 + 20) * 100 = 16.67%

The closest answer to 16.67% from the given options is 20%.

Therefore, the answer is (a) 20%

 

17.What is the rightmost digit preceding the zeros in the value of ?

(a) 1

(b) 3

(c) 7

(d) 9

Answer (d)

To determine the rightmost digit preceding the zeros in the value of 30³⁰, we can look at the properties of the number and its modulo 10 properties.

First, note that 30³⁰ has trailing zeros due to the factors of 10 in it (since 30=2×3×5).

We want to find the rightmost non-zero digit of 30³⁰. This is equivalent to finding the last non-zero digit  30³⁰mod10.

However, due to trailing zeros, it's easier to consider the problem modulo 10. Because the number 30³⁰ is a multiple of 10³⁰, it will have 30 trailing zeros. To find the digit just before these trailing zeros, we need to look at 30³⁰ mod10

Step-by-step calculation:

1. Pattern of Powers of 3 modulo 10:

  ≡3 mod 10

 ≡9 mod 10

 ≡27≡7 mod 10

 ≡81≡1 mod 10

Observing the pattern, the powers of 3 modulo 10 repeat every 4 terms: 3,9,7,1

2. Finding 30³⁰ mod10

30÷4=7 remainder 2

30³⁰    ≡ 9 mod 10

Therefore, the last non-zero digit of 30³⁰ is 9

The correct answer is: (d) 9

18.421 and 427, when divided by the same number, leave the same remainder 1. How many numbers can be used as the divisor in order to get the same remainder 1?

(a) 1

(b) 2

(c) 3

(d) 4

Answer (c)

• First, we need to understand what the question is asking. We're looking for a number that, when dividing both 421 and 427, leaves a remainder of 1 in both cases.
• Mathematically, we can express this as: 421 ≡ 1 (mod d) 427 ≡ 1 (mod d) Where d is the divisor we're looking for.
• This means that (421 - 1) and (427 - 1) should both be divisible by d. 420 should be divisible by d 426 should be divisible by d
• Another way to look at this is that d should divide the difference between 427 and 421: 427 - 421 = 6
• So, we're looking for divisors of 6 that also satisfy our original conditions.
• The divisors of 6 are: 1, 2, 3, 6
• Let's check each: For 1: This always leaves a remainder of 0, so it doesn't work. For 2: 421 ÷ 2 = 210 remainder 1 427 ÷ 2 = 213 remainder 1 This works. For 3: 421 ÷ 3 = 140 remainder 1 427 ÷ 3 = 142 remainder 1 This works. For 6: 421 ÷ 6 = 70 remainder 1 427 ÷ 6 = 71 remainder 1 This works.
• We've found 3 numbers that work as divisors: 2, 3, and 6.

Therefore, the correct answer is (c) 3.

 

19.A can X contains 399 litres of petrol and a can Y contains 532 litres of diesel. They are to be bottled in bottles of equal size so that whole of petrol and diesel would be separately bottled. The bottle capacity in terms of litres is an integer. How many different bottle sizes are possible?

(a) 3

(b) 4

(c) 5

(d) 6

Answer (b)

We need to find the common divisors of 399 and 532, as these will represent the possible bottle sizes in litres.

To find the common divisors, let's first find the factors of each number: 399 = 3 × 7 × 19 532 = 2^2 × 7 × 19

The common factors are 7 and 19.

Now, let's list all the possible combinations of these common factors: 1 (always a divisor) 7 19 7 × 19 = 133

These four numbers (1, 7, 19, and 133) are all the possible bottle sizes in litres that would allow both 399 litres of petrol and 532 litres of diesel to be bottled completely with no remainder.

 

20.Consider the following statements in respect of the sum S = x + y + z, where x, y and z are distinct prime numbers each less than 10:

1.The unit digit of S can be 0.

2.The unit digit of S can be 9.

3.The unit digit of S can be 5.

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 (c)

• First, let's list out the prime numbers less than 10: 2, 3, 5, 7
• Now, let's consider all possible combinations of three distinct primes from this list: 2 + 3 + 5 = 10 2 + 3 + 7 = 12 2 + 5 + 7 = 14 3 + 5 + 7 = 15
• Now, let's examine each statement: Statement 1: The unit digit of S can be 0. This is true, as we can see from 2 + 3 + 5 = 10. Statement 2: The unit digit of S can be 9. This is false. None of the sums end in 9. Statement 3: The unit digit of S can be 5. This is true, as we can see from 3 + 5 + 7 = 15.
• Therefore, statements 1 and 3 are correct, while statement 2 is incorrect.

The correct answer is (c) 1 and 3 only

 

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

By the time children reach class 8, the bulk of them tend to be in the age range of 13 years to 15 years. But in our country, about a quarter of children in class 8 struggle with reading simple texts and more than half are still unable to do basic arithmetic operations like division. Every year about 25 million young boys and girls from elementary school move into the life that lies for them beyond compulsory schooling. They cannot enter the workforce at least in the organized sector till they are 18. For many of them, these children are the first from their families ever to get this far in school. Parents and children expect that such 'graduates' from school will go on to high school and college. Hardly anyone wants to go back to agriculture. On the other hand, abilities in terms of academic competencies are far lower than they should be even based on curricular expectations of class 8.

Which of the assumptions given above is/are valid?

 (a) 1 only

 (b) 2 only (c) Both 1 and 2

(d) Neither 1 nor 2

Answer (d)

The passage doesn't provide enough information to validate either assumption:

1. The passage doesn't discuss the role of parents versus governments in education. It only mentions that for many children, they are the first in their families to reach this level of education.
2. While the passage mentions issues with curriculum expectations, it doesn't suggest that a uniform curriculum would address these issues. The problem seems to be more about achievement levels rather than curriculum uniformity.

Therefore, neither assumption can be considered valid based solely on the information in the passage.

The correct answer is (d) Neither 1 nor 2

 

 (a) Total eradication of poverty in the country will resolve the issue of under-performance of our school-children.

(b) Monetary incentives to parents and teachers is a strategy to improve the children’s academic performance.

(c) Public policy should ensure that competencies and achievements of young people are aligned with their expectations.

 (d) India is not going to take advantage of the demographic dividend unless some school pass-outs go back to agriculture.

Answer (c)

To find the central idea, let's summarize the key points of the passage:

• Many children in class 8 struggle with basic reading and arithmetic.
• About 25 million children finish elementary school each year.
• These children can't enter the organized workforce until 18.
• There's an expectation for these children to continue to high school and college.
• There's a mismatch between these expectations and the actual academic competencies of the children.

The statement that best reflects these points is:

(c) Public policy should ensure that competencies and achievements of young people are aligned with their expectations.

This option captures the essence of the mismatch between expectations and actual competencies, which is a central theme of the passage.

The other options are not supported by the passage: (a) Poverty eradication is not mentioned. (b) Monetary incentives are not discussed. (d) The passage doesn't suggest that some should go back to agriculture; in fact, it states that hardly anyone wants to.

Therefore, the correct answer is (c)

 

Passage—2

We take it for granted now that science has a social responsibility. The idea would not have occurred to Newton or Galileo. They thought of science as an account of the world as it is, and the only responsibility that they acknowledged was to tell the truth. The idea that science is a social enterprise is modern, and it begins at the industrial revolution. We are surprised that we cannot trace a social

because we nurse the illusion that the industrial revolution ended a golden age.

(a) Science must value the commitment of the scientists.

(b) Science is a product of civilized society and must be used for the promotion of scientific awareness in people.

 (c) Industrial revolution was made possible by the advancements in science.

(d) Science must pursue truth but be responsible for social welfare.

Answer (d)

The key points from the passage are:

1. The idea that science has social responsibility is a modern concept.
2. Earlier scientists like Newton and Galileo didn't consider social responsibility; they focused solely on describing the world accurately.
3. The concept of science as a social enterprise began with the industrial revolution.
4. There's a common misconception that the industrial revolution ended a "golden age."

Now, let's look at the options:

(a) Science must value the commitment of the scientists. This isn't directly addressed in the passage.

(b) Science is a product of civilized society and must be used for the promotion of scientific awareness in people. While the passage mentions science as a social enterprise, it doesn't discuss promoting scientific awareness.

(c) Industrial revolution was made possible by the advancements in science. The passage doesn't make this claim. It only states that the idea of science as a social enterprise began with the industrial revolution.

(d) Science must pursue truth but be responsible for social welfare. This option best reflects the author's thinking. It combines the historical view of science (pursuing truth, as Newton and Galileo did) with the modern concept of social responsibility that the author introduces.

The correct answer is (d) Science must pursue truth but be responsible for social welfare.

This answer captures the evolution in thinking about science that the author describes - from a purely truth-seeking endeavor to one that also considers its social impact and responsibilities

 

Answer (c)

1. First part: A
2. Second part: BCD
3. Third part: BBCDABC This seems to be a combination of the previous two parts (BCD + A + BC)
4. Fourth part: DABC This is the last three letters of the previous part
5. Fifth part: D This is the first letter of the previous part

Now, to complete the sequence, we should follow the same pattern:

6. The sixth part should be a combination of the fourth and fifth parts, plus the beginning of the fourth part: DABC (4th part) + D (5th part) + DA (beginning of 4th part)

So the complete sixth part should be: DABCDDA

The question asks which option completes the sequence, so we're looking for the last four letters: CDDA

Looking at the given options: (a) B, A, D, C (b) B, A, C, D (c) A, A, C, D (d) A, A, D, C

The correct answer is (c) A, A, C, D.

This matches the last four letters of our derived sixth part: CDDA

 

Answer (a)

1. Let's say Q's investment is x. Then, P's investment is x + 14,000.
2. The profit share is proportional to the product of investment and time. P's share : Q's share = (x + 14,000) * 8 : x * 10
3. We know that P's share is ₹400 more than Q's share out of ₹2,000. So, P's share = 1200 and Q's share = 800
4. We can set up the equation: (x + 14,000) * 8 : x * 10 = 1200 : 800 = 3 : 2
5. This can be written as: (x + 14,000) * 8 = 3/2 * x * 10
6. Simplifying: 8x + 112,000 = 15x 112,000 = 7x x = 16,000
7. Remember, x is Q's investment. P's investment is x + 14,000. So, P's investment = 16,000 + 14,000 = 30,000

Therefore, the capital contributed by P is ₹30,000.

The correct answer is (a) ₹30,000

 

Answer (b)

1. Let's assume R's salary is 100 units (for easy calculation).
2. Q's salary is 20% lower than R's: Q's salary = 100 - 20% of 100 = 100 - 20 = 80 units
3. P's salary is 20% lower than Q's: P's salary = 80 - 20% of 80 = 80 - 16 = 64 units
4. Now, we need to calculate by what percentage R's salary (100 units) is more than P's salary (64 units).
5. The formula for percentage increase is: Percentage increase = (Increase / Original Amount) × 100 = (Difference / Lower Value) × 100
6. In this case: Percentage increase = (100 - 64) / 64 × 100 = 36 / 64 × 100 = 0.5625 × 100 = 56.25%

Therefore, R's salary is 56.25% more than P's salary.

The correct answer is (b) 56.25%.

 

Answer (d)

1. Let's say the original number is x.
2. The correct operation should have been: x × 4
3. But instead, the number was divided by 4: x ÷ 4
4. To find the percentage change, we need to compare these two results.
5. The difference between the correct and incorrect result is: (x × 4) - (x ÷ 4) = 4x - x/4 = 16x/4 - x/4 = 15x/4
6. We need to express this difference as a percentage of the incorrect result (x ÷ 4): Percentage change = (Difference / Incorrect result) × 100 = ((15x/4) / (x/4)) × 100 = (15x/4 × 4/x) × 100 = 15 × 100 = 1500%
7. However, this is the percentage by which the correct result is larger than the incorrect result. The question asks for the percentage change in the result due to the mistake, which would be a decrease.
8. To express this as a decrease, we use the formula: Percentage decrease = (Difference / Correct result) × 100 = ((15x/4) / (4x)) × 100 = (15/16) × 100 = 0.9375 × 100 = 93.75%

Therefore, the result decreased by 93.75% due to this mistake.

The correct answer is (d) 93.75%

 

Answer (b)

1. Let's assume the total number of students is 100 for easy calculation.
2. 80% passed in English, so 20% failed in English. 70% passed in Hindi, so 30% failed in Hindi.
3. We're told that 15% failed in both subjects.
4. Now, let's use the concept of sets:
   • Let E be the set of students who failed in English
   • Let H be the set of students who failed in Hindi
5. We know: |E| = 20 (20% failed in English) |H| = 30 (30% failed in Hindi) |E ∩ H| = 15 (15% failed in both)
6. We need to find students who failed in only one subject. This is: (Students who failed in English only) + (Students who failed in Hindi only)
7. Students who failed in English only = |E| - |E ∩ H| = 20 - 15 = 5
8. Students who failed in Hindi only = |H| - |E ∩ H| = 30 - 15 = 15
9. Total students who failed in only one subject = 5 + 15 = 20

Therefore, 20% of students failed in only one subject.

The correct answer is (b) 20%

 

Answer (a)

1. Let's define some variables: F = Father's present age S = Son's present age n = number of years mentioned in the statement
2. From the given information: F - n = S (Father's age n years ago was equal to son's present age) F = 4(S - n) (Father's present age is four times son's age n years ago)
3. We also know that F + S = 130
4. From the first equation: S = F - n
5. Substitute this into the second equation: F = 4((F - n) - n) F = 4(F - 2n) F = 4F - 8n 3F = 8n F = 8n/3
6. Now, let's use F + S = 130: (8n/3) + (8n/3 - n) = 130 (8n/3) + (5n/3) = 130 13n/3 = 130 13n = 390 n = 30
7. Now we can find F: F = 8n/3 = 8(30)/3 = 80
8. And S: S = F - n = 80 - 30 = 50
9. The difference in their ages: 80 - 50 = 30

Therefore, the difference in their ages is 30 years.

The correct answer is (a) 30 years

 

Which of the 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)

Let's examine each statement one by one:

1. 1000 litres = 1 m³ This is correct. One cubic meter (m³) is equal to 1000 liters.
2. 1 metric ton = 1000 kg This is correct. One metric ton is defined as 1000 kilograms.
3. 1 hectare = 10000 m² This is correct. A hectare is a unit of area equal to 10,000 square meters.

Since all three statements are correct, the answer is:

(d) 1, 2 and 3

Passage – 1

The history of science is the real history of mankind. In this striking epigram, a nineteenth-century writer links science with its background. Like most epigrams, its power lies in emphasizing by contrast an aspect of truth which may be easily overlooked. In this case, it is easy to overlook the relations between science and mankind, and to treat the former as some abstract third party, which can sometimes be praised for its beneficial influences, but frequently and conveniently blamed for the horrors of war. Science and mankind cannot be divorced from time to time at men’s convenience. Yet we have seen that, in spite of countless opportunities of improvement, the opening years of the present period of civilization have been dominated by international conflict. Is this the inevitable result of the progress of science or does the fault lie elsewhere?

 

Select the correct answer using the code given below.

Answer (d)

The passage doesn't emphatically convey either of the given statements:

1. While the author emphasizes the importance of science in human history, they don't claim that mankind couldn't have existed without it.
2. The author doesn't state that science will ultimately determine mankind's destiny. Instead, they question whether the progress of science inevitably leads to conflict or if the fault lies elsewhere.

The author's main point is that science and mankind are inseparable, and we can't conveniently blame science for human conflicts.

Therefore, the correct answer is (d) Neither 1 nor 2

 

 

Which of the assumptions given above is/are correct?

Answer (b)

Let's examine each assumption:

1. The passage actually questions this assumption. The author asks, "Is this the inevitable result of the progress of science or does the fault lie elsewhere?" This implies that the author doesn't believe that the horrors of modern life are necessarily the inevitable result of scientific progress.
2. This assumption aligns more closely with the passage. The author emphasizes that science and mankind cannot be divorced, and that it's easy to overlook the relations between science and mankind. This suggests that science is indeed what man has made it, and this is an aspect of truth that might be overlooked.

Therefore, the correct answer is (b) 2 only.

Passage – 2

Only with long experience and opening of his wares on many a beach where his language is not spoken, will the merchant come to know the worth of what he carries, and what is parochial and what is universal in his choice. Such delicate goods as justice, love and honour, courtesy, and indeed all the things we care for, are valid everywhere but they are variously moulded and often differently handled, and sometimes nearly unrecognizable if you meet them in a foreign land, and the art of learning fundamental common values is perhaps the greatest gain of travel to those who wish to live at ease among their fellows. 

Answer (c)

The passage discusses how travel helps us understand the universal nature of certain values, while also recognizing their local variations. The key phrase is "the art of learning fundamental common values is perhaps the greatest gain of travel." This suggests that travel helps us differentiate between:

1. c) local values and universal values

This option best captures the essence of the passage, which emphasizes how values like justice, love, honor, and courtesy are universal but may be "variously moulded and often differently handled" in different places

 

Which of the assumptions given above are valid?

Answer (d)

Assumption 1 is valid because the passage indicates that travel fosters an understanding of humanity by exposing people to diverse cultures and values, which helps them appreciate universal concepts like justice, love, honor, and courtesy.

Assumption 2 is valid as well; the passage clearly mentions that travel aids those who want to learn fundamental common values by revealing different cultural expressions of justice, love, honor, and courtesy.

Therefore, all three assumptions are backed by the ideas in the passage, making option (d) the correct answer

35) Let X be a two-digit number and Y be another two-digit number formed by interchanging the digits of X. If (X+Y) is the greatest two-digit number, then what is the number of possible values of X?

Answer (d)

Given that X is a two-digit number and Y is another two-digit number formed by interchanging the digits of X, let's denote X by 10a+b where a and b are the digits of X (with aaa and bbb ranging from 1 to 9 and 0 to 9, respectively, because X is a two-digit number).

When we interchange the digits of X, we get Y=10b+a

According to the problem, the sum of X and Y is the greatest two-digit number. The greatest two-digit number is 99. Therefore, we have: X+Y=99

Substituting X and Y:

(10a+b)+(10b+a)=99

10a+b+10b+a=99

11a+11b=99

11a+11b=99

11(a+b)=99

 a+b=9a

Since a and b are digits, we need to find pairs (a,b) such that a+b=9.

The possible pairs are:

• a=1,b=8
• a=2,b=7
• a=3,b=6
• a=4,b=5
• a=5,b=4
• a=6,b=3
• a=7,b=2
• a=8,b=1

Each pair (a,b) corresponds to a unique two-digit number X=10a+b

Therefore, the number of possible values of X is 8

Weight of 6 boys = Weight of 7 girls = Weight of 3 men = Weight of 4 women

If the average weight of the women is 63 kg, then what is the average weight of the boys?

Answer (b)

1. First, let's establish the relationships given: 6 boys = 7 girls = 3 men = 4 women
2. We're told that the average weight of women is 63 kg. Let's use this information: 4 women = 4 × 63 kg = 252 kg
3. Now we know that 252 kg is also equal to the weight of 3 men, 7 girls, or 6 boys.
4. We need to find the average weight of boys. To do this, we need to divide the total weight by the number of boys: Average weight of boys = Total weight of boys ÷ Number of boys = 252 kg ÷ 6 = 42 kg

Therefore, the correct answer is b) 42 kg

Answer (a)

To determine how many times the hour hand and the minute hand coincide in a clock between 10:00 a.m. and 2:00 p.m., we need to analyze the positions of the hands over this period.

1. Basic Understanding:
   • The hour hand and the minute hand coincide 11 times in a 12-hour period (from 12:00 to 12:00).
   • These coincidences occur approximately every 1 hour and 5 minutes (1 hour + 5/11 of an hour).
2. Time Calculation:
   • From 10:00 a.m. to 2:00 p.m. is a 4-hour interval.
3. Exact Coincidence Times:
   • Starting from 10:00 a.m., the next few coincidences occur at approximately:
     • 10:00 a.m. + 1 hour 5 minutes ≈ 11:05 a.m.
     • 11:05 a.m. + 1 hour 5 minutes ≈ 12:10 p.m.
     • 12:10 p.m. + 1 hour 5 minutes ≈ 1:15 p.m.
     • 1:15 p.m. + 1 hour 5 minutes ≈ 2:20 p.m. (which is outside our interval)

4. Conclusion:
   • Therefore, the hour hand and the minute hand coincide at approximately 11:05 a.m., 12:10 p.m., and 1:15 p.m.

Thus, the hour hand and the minute hand coincide 3 times between 10:00 a.m. and 2:00 p.m.

So, the correct answer is: a) 3 times

Answer (c)

1. First, we need to recall the rules for when calendars repeat:
   • Calendars repeat every 28 years in the Gregorian calendar system, but there are shorter repetitions.
   • Non-leap years repeat every 6 years, 11 years, or 12 years, depending on how leap years fall in between.
   • Leap years repeat every 28 years.
2. 2025 is not a leap year (it's not divisible by 4).
3. Let's check each option: a) 2029: This is 4 years after 2025. It's not a leap year either. But 4 years is too short for a calendar to repeat. b) 2030: This is 5 years after 2025. Again, too short for a repeat. c) 2031: This is 6 years after 2025. This is a possibility, as calendars often repeat after 6 years for non-leap years. d) 2033: This is 8 years after 2025. This is too long without hitting one of the common repeat periods.
4. The most likely answer is 2031, as it's 6 years after 2025, which is a common repeat period for non-leap years.
5. To be absolutely certain, we'd need to check if there's a leap year between 2025 and 2031 that might disrupt the pattern. 2028 is a leap year, but it doesn't affect the repetition in this case.

Therefore, the correct answer is c) 2031

Which of the statements given above are correct?

Answer (d)

1. (p - r)² (qs) is even.
   • p is odd and r is even, so (p - r) is odd.
   • An odd number squared is odd.
   • q is odd and s is even, so qs is even.
   • Odd × Even = Even Therefore, statement 1 is correct.
2. (q - s) q² s is even.
   • q is odd and s is even, so (q - s) is odd.
   • q² is odd (odd squared is odd).
   • s is even.
   • Odd × Odd × Even = Even Therefore, statement 2 is correct.
3. (q + r)² (p + s) is odd.
   • q is odd and r is even, so (q + r) is odd.
   • An odd number squared is odd.
   • p is odd and s is even, so (p + s) is odd.
   • Odd × Odd = Odd Therefore, statement 3 is correct.

Since all three statements are correct, the answer is:

1. d) 1, 2 and 3
2. What is the angle between the minute hand and hour hand when the clock shows 4:25 hours?
3. a) 12.5^O
4. b) 15^O
5. c) 17.5^O
6. d) 20^O

Answer (c)

1. First, let's recall how fast each hand moves:
   • The hour hand makes a complete 360° rotation in 12 hours, so it moves at 0.5° per minute.
   • The minute hand makes a complete 360° rotation in 60 minutes, so it moves at 6° per minute.
2. At 4:25, we need to calculate the position of each hand: Hour hand:
   • In 4 hours, it moves 4 × 30° = 120°
   • In additional 25 minutes, it moves 25 × 0.5° = 12.5°
   • Total movement: 120° + 12.5° = 132.5°

Minute hand:

• In 25 minutes, it moves 25 × 6° = 150°

3. The angle between the hands is the absolute difference between these angles: |150° - 132.5°| = 17.5°

Therefore, the correct answer is c) 17.5°

Passage-1

Conventional classrooms, by emphasizing fixed duration over learning effectiveness, resign themselves to variable outcomes. The tyranny of the classroom is that every learner is subjected to the same set of lectures in the same way for the same duration. In the end, a few learners shine, some survive, and the rest are left behind. After the fixed duration, the classroom model moves on, with not a thought spared for those left behind. This is how we end up with 10 percent employability in our graduates after a decade and half of formal education. Repeating the same ineffectual script in the realm of skill education will not produce different results.

 

Select the correct answer using the code given below.

Answer (c)

1. "In conventional classroom learning, the central goal is duration of learning rather than attainment of competency."

This statement is strongly supported by the passage. The author criticizes conventional classrooms for "emphasizing fixed duration over learning effectiveness" and mentions that they "resign themselves to variable outcomes." The passage also states that after a fixed duration, the classroom model moves on without concern for those left behind. This clearly implies that the focus is on the duration rather than ensuring all students attain competency.

2. "Conventional classrooms encourage one-size-fits-all approach and stamp out all differentiation."

This statement is also supported by the passage. The author mentions "The tyranny of the classroom is that every learner is subjected to the same set of lectures in the same way for the same duration." This directly describes a one-size-fits-all approach. The passage also highlights that this approach leads to variable outcomes, with some students shining, some surviving, and others being left behind, which implies a lack of differentiation to meet individual needs.

Both statements are logical inferences that can be drawn from the passage. The passage clearly criticizes conventional classrooms for their focus on fixed duration over effective learning and their lack of individualized approach.

Therefore, the correct answer is c) Both 1 and 2

Which of the assumptions given above is/are valid?

Answer (d)

Passage Summary:

• The passage criticizes the conventional classroom system for focusing on fixed duration rather than learning effectiveness.
• It highlights the issue of varied outcomes, with many students being left behind.
• It mentions that this approach results in low employability among graduates.
• Repeating this ineffective approach in skill education will not yield different results.

Assumption Analysis:

1. "As a large number of workers in our country are employed in the unorganized sector, India does not need to change its present conventional classroom system of education."
   • This assumption implies that the employment in the unorganized sector somehow justifies the current education system. However, the passage argues for the ineffectiveness of the conventional system and the need for change, suggesting that employment in the unorganized sector does not negate the need for educational reform.
2. "Even with its present conventional classroom system of education, India produces a sufficient number of skilled workers to fully realize the benefits of demographic dividend."
   • This assumption contradicts the passage, which states that the conventional system results in only 10 percent employability among graduates, indicating a lack of sufficient skilled workers. The passage clearly calls into question the effectiveness of the current system in producing skilled workers.

Given that both assumptions conflict with the key points made in the passage, neither assumption is valid.

Thus, the correct answer is: d) Neither 1 nor 2

Passage-2

When a child reaches adolescence, there is apt to be a conflict between the parents and the child, since the latter considers himself to be by now quite capable of managing his own affairs, while the former are filled with parental solicitude, which is often a disguise for love of power. Parents consider, usually, that the various moral problems which arise in adolescence are peculiarly their province. The options they express, however, are so dogmatic that the young seldom confide in them, and usually go their own way in secret.

 

Which of the assumptions given above is/are valid?

Answer (a)

Assumption 1: "The adolescent does not feel comfortable with his parents because they tend to be dominating and assertive."

This assumption is valid. The passage states that parents are "filled with parental solicitude, which is often a disguise for love of power." It also mentions that parents' opinions are "so dogmatic that the young seldom confide in them." This supports the idea that adolescents are uncomfortable with their parents due to their dominating nature.

Assumption 2: "The adolescent of modern times does not have much respect for parents."

This assumption is not explicitly supported by the passage. While the passage suggests that adolescents often go their own way in secret, it doesn't necessarily imply a lack of respect for parents. The conflict described seems more about independence and communication issues rather than respect.

Therefore, the correct answer is a) 1 only

 

Answer (a)

1. a) Parents in general may not be of much help when children are on their way to becoming adults.

This option best reflects the central idea of the passage. The passage describes a conflict between parents and adolescents, where parents' attempts to help or guide are often ineffective due to their dogmatic approach, leading adolescents to "go their own way in secret."

1. b) When children reach adolescence, involvement of parents in their lives is unnecessary.

The passage doesn't suggest that parental involvement is unnecessary, only that it's often ineffective in its current form.

1. c) Modern-day nuclear families are not capable of bringing up children properly.

The passage doesn't mention nuclear families or compare different family structures.

1. d) In modern societies, adolescents tend to be stubborn, disobedient and careless.

While the passage mentions that adolescents often don't follow their parents' advice, it doesn't characterize them as stubborn, disobedient, or careless. It rather emphasizes the adolescents' desire for independence.

Therefore, the correct answer is a) Parents in general may not be of much help when children are on their way to becoming adults

45.What is the number of fives used in numbering a 260-page book?

Answer (b)

Counting '5' in the units place:

We count the number of pages from 1 to 260 where the units digit is '5'. These pages are: 5, 15, 25, 35, ..., 255.

The sequence forms an arithmetic series where:

• The first term (a) is 5.
• The common difference (d) is 10.
• The last term (l) is 255.

To find the number of terms (n) in this arithmetic series, we use the formula for the nth term of an arithmetic sequence: a_n=a+(n−1)d

Setting a_n=255:

255=5+(n−1)⋅10

255=5+10n−10

 255=−5+10n

260=10n

 n=26

So, there are 26 pages where '5' is in the units place.

2. Counting '5' in the tens place:

We count the number of pages from 1 to 260 where the tens digit is '5'. These pages are: 50-59, 150-159, and 250-259.

Each range contains 10 pages:

• 50 to 59: 10 pages
• 150 to 159: 10 pages
• 250 to 259: 10 pages

Total pages with '5' in the tens place: 10+10+10=30

3. Counting '5' in the hundreds place:

In a 260-page book, the hundreds digit can only be '1' or '2'. Thus, there are no pages where '5' appears in the hundreds place.

Total count of '5's:

• Units place: 26
• Tens place: 30
• Hundreds place: 0

Summing these values: 26+30+0=56

Therefore, the total number of '5's used in numbering a 260-page book is: b) 56

46.What is the sum of the first 28 terms in the following sequence?

1,1,2,1,3,2,1,4,3,2,1,5,4,3,2,..

Answer (b)

Sequence Analysis:

The given sequence is: 1,1,2,1,3,2,1,4,3,2,1,5,4,3,2,1,6,5,4,3,2,1,7,6,5,4,3,2,1,…

We observe that:

• The sequence consists of segments starting with 1, followed by an increasing number of terms.
• Each segment ends when it reaches the starting number of the next segment minus 1.

Specifically:

• The first segment has 1 term: 1
• The second segment has 2 terms: 1,2
• The third segment has 3 terms: 1,3,2
• The fourth segment has 4 terms: 1,4,3,2
• And so on.

To find the sum of the first 28 terms, we need to determine how many full segments are included and the sum of the terms within those segments.

Calculating the Segments and Their Terms:

1. First Segment: 1 term → 1
2. Second Segment: 2 terms → 1,2
3. Third Segment: 3 terms → 1,3,2
4. Fourth Segment: 4 terms → 1,4,3,2
5. Fifth Segment: 5 terms → 1,5,4,3,2
6. Sixth Segment: 6 terms → 1,6,5,4,3,2
7. Seventh Segment: 7 terms → 1,7,6,5,4,3,2

To count the total number of terms in each segment, we sum up:

1+2+3+4+5+6+7=28

Thus, the first 28 terms exactly cover the first 7 segments.

Summing Each Segment's Terms:

1. First Segment: Sum = 1
2. Second Segment: Sum = 1+2=3
3. Third Segment: Sum = 1+3+2=6
4. Fourth Segment: Sum = 1+4+3+2=10
5. Fifth Segment: Sum = 1+5+4+3+2=15
6. Sixth Segment: Sum = 1+6+5+4+3+2=21
7. Seventh Segment: Sum = 1+7+6+5+4+3+2=28

Finally, adding these sums gives us:

1+3+6+10+15+21+28=84

Therefore, the sum of the first 28 terms in the sequence is:
b) 84

Answer (d)

1. Let's assume the cost of Q is x.
2. Given that R costs 20% more than Q: Cost of R = x + 20% of x = 1.2x
3. P costs 25% more than R: Cost of P = 1.2x + 25% of 1.2x = 1.2x + 0.3x = 1.5x
4. Now we can set up an equation based on the total cost: P + Q + R = 3,330 1.5x + x + 1.2x = 3,330 3.7x = 3,330
5. Solve for x: x = 3,330 ÷ 3.7 = 900
6. Now that we know Q costs ₹900, we can calculate P: P = 1.5 × 900 = ₹1,350

Therefore, the cost of P is ₹1,350.

The correct answer is d) ₹1,350

Answer (a)

1. First, let's understand what the question is telling us: AB + CD = 1CE, where AB, CD are two-digit numbers and 1CE is a three-digit number.
2. In a two-digit number AB, A represents tens and B represents units. So, AB = 10A + B
3. Similarly, CD = 10C + D
4. And 1CE = 100 + 10C + E
5. Now, we can write an equation: (10A + B) + (10C + D) = 100 + 10C + E
6. Simplifying: 10A + B + 10C + D = 100 + 10C + E
7. Further simplifying: 10A + B + D = 100 + E
8. Now, we know that A, B, C, D, E are all distinct digits. The left side of the equation (10A + B + D) must equal 100 + E.
9. The maximum value for E is 9, which would make the right side 109.
10. For the left side to be at least 100, A must be at least 9.
11. But A can't be more than 9 (as it's a single digit), so A must be exactly 9.

Therefore, the value of A is 9.

The correct answer is a) 9

Answer (d)

To determine the number of distinct triplets (x,y,z) that satisfy the condition x>2y>3z, we need to explore the possibilities with the given set of the first seven natural numbers {1,2,3,4,5,6,7}

1. Start with the largest possible value of z:
   • Since z is the smallest term and 3z must be less than 2y, we need to start with z and increment it to check all possible valid combinations.
2. Check z=1:
   • If z=1, then 3z=33. So, 2y must be greater than 3, i.e., y>3/2 The smallest integer greater than 32. Hence, y can be 2,3,4,5,6,7.
   • For each value of yyy:
     • y=2, 2y=4. So, x>4. Hence, xxx can be 5,6,7.
     • y=3, 2y=6. So, x>6. Hence, x can be 7.
     • For y≥4, 2y≥8, which is not possible since the maximum value for xxx is 7.
   • Thus, the valid triplets for z=1 are:
     • (5,2,1)
     • (6,2,1)
     • (7,2,1)
     • (7,3,1)

3. Check z=2:
   • If z=2, then 3z=6. So, 2y must be greater than 6, i.e., y>3. The smallest integer greater than 3 is 4. Hence, yyy can be 4,5,6,7.
   • For each value of y:
     • y=4, 2y=8. So, x>8, which is not possible since the maximum value for x is 7.
     • Hence, no valid combinations exist for y≥4 since 2y exceeds the maximum possible value for x.

4. Check z≥3:
   • If z=3, then 3z=9. So, 2y must be greater than 9, which is not possible since 2y exceeds the maximum possible value for x.

Therefore, the only valid distinct triplets are for z=1, resulting in:

(5,2,1),(6,2,1),(7,2,1),(7,3,1)

Thus, the number of such distinct triplets is: d) Four triplets

Consider the following statements:

Which of the statements given above is/are correct?

Answer (c)

Let's approach this step-by-step:

1. Let's define variables: o = cost of one orange m = cost of one mango a = cost of one apple
2. From the given information: 4o + 6m + 8a = 2(o + 2m + 5a)
3. Simplifying the right side: 4o + 6m + 8a = 2o + 4m + 10a
4. Subtracting the right side from both sides: 2o + 2m - 2a = 0 o + m = a

Now, let's examine the statements:

Statement 1: The total cost of 3 oranges, 5 mangoes and 9 apples is equal to the total cost of 4 oranges, 6 mangoes and 8 apples.

This can be written as: 3o + 5m + 9a = 4o + 6m + 8a Simplifying: o + m = a

This is exactly what we derived from the original equation. So, statement 1 is correct.

Statement 2: The total cost of one orange and one mango is equal to the cost of one apple.

This can be written as: o + m = a

Again, this is exactly what we derived. So, statement 2 is also correct.

Therefore, both statements are correct.

The answer is c) Both 1 and 2

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

When an international team of scientists pumped a carbon dioxide and water mix into underground basalt rocks, basic chemistry took over. The acidic mixture dissolved rocks' calcium and magnesium and formed limestone. Basically, carbon dioxide is converted into stone, exclaimed the scientists.

51.Which one of the following statements best reflects the most logical, rational, and practical suggestion implied by the passage?

(a) It is a cheap and practical method to produce limestone at a commercial level for building purposes.

(b) This can be used as one of the methods of carbon sequestration.

(c) Basalt rock can be made a good source of calcium and magnesium minerals by this method.

(d) Good rock-dissolving acid can be produced by mixing carbon dioxide and water.

Answer (b)

1. a) While the process does produce limestone, the passage doesn't suggest this as a commercial method for building purposes. The focus seems to be on the carbon dioxide conversion.
2. b) This option aligns most closely with the implications of the passage. The scientists are excited about converting carbon dioxide into stone, which is essentially a form of carbon sequestration (removing CO2 from the atmosphere and storing it long-term).
3. c) Although the process does involve dissolving calcium and magnesium from basalt, the passage doesn't imply this as a primary purpose or suggestion.
4. d) While the mixture of CO2 and water does dissolve rocks, the passage doesn't emphasize this as a method for producing rock-dissolving acid. The focus is on the end result of CO2 conversion.

The most logical and practical suggestion implied by the passage is that this process could be used as a method of carbon sequestration. The scientists' excitement about converting CO2 into stone suggests that this could be a way to address excess atmospheric carbon dioxide.

Therefore, the best answer is (b) This can be used as one of the methods of carbon sequestration

 

Passage—2

Geographers analyzed 175 satellite images of ocean color, which is an indicator of phytoplankton productivity at the ocean’s surface, and found that giant icebergs are responsible for storing up to 20 percent of carbon in the Southern Ocean. The researchers discovered that melting water from giant icebergs which contains iron and other nutrients, supports hitherto unexpectedly high levels of phytoplankton growth.

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

Which of the assumptions given above is/are valid?

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

Answer (a)

Assumption 1: Giant icebergs have a bearing on primary productivity and food chains of the Southern Ocean.

This assumption is valid. The passage states that giant icebergs are responsible for storing up to 20 percent of carbon in the Southern Ocean through increased phytoplankton growth. Phytoplankton are at the base of the marine food chain and are a key indicator of primary productivity in oceans. Therefore, if giant icebergs significantly affect phytoplankton growth, they indeed have a bearing on primary productivity and, by extension, the food chains of the Southern Ocean.

Assumption 2: Melting of giant icebergs can produce climate change effects and impact world fisheries.

This assumption is partially supported by the passage, but not fully validated. The passage does indicate that melting icebergs release nutrients that support phytoplankton growth, which could potentially impact climate (as phytoplankton absorb CO2) and fisheries (as phytoplankton are the base of the marine food chain). However, the passage doesn't explicitly mention climate change effects or global fisheries impacts. It's a reasonable extrapolation but goes beyond the direct information provided.

Given these analyses:

• Assumption 1 is clearly valid based on the information in the passage.
• Assumption 2, while plausible, is not fully supported by the information given.

Therefore, the correct answer is (a) 1 only

 

Passage—3

Evolution has endowed caterpillars that feed on corn with a unique ability, they can induce predators. This helps caterpillars to eat more and grow faster. The agent that causes this effect is the caterpillar's faeces or frass. The finding could throw new light on compounds associated with plant response to pathogens like fungi or bacteria.

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

(a) Farmers can use caterpillars to feed on weeds in their crop fields/plantations.

(b) This finding can help in the development of clinically useful antimicrobial compounds.

(c) This finding can help in the development of organic, ecologically sustainable pesticides.

(d) Caterpillars can be genetically modified to be predators of the other plant pests.

Answer (c)

Let's analyze each option in the context of the passage:

1. a) Using caterpillars to feed on weeds: This is not related to the main point of the passage, which focuses on caterpillars' ability to induce predators and its potential implications for understanding plant responses to pathogens.
2. b) Development of antimicrobial compounds: While the passage mentions pathogens like fungi or bacteria, it doesn't directly suggest that this finding could lead to antimicrobial compounds. This is a bit of a stretch from the information provided.
3. c) Development of organic, ecologically sustainable pesticides: This option aligns most closely with the information in the passage. The finding about caterpillar frass inducing predators and affecting plant responses could potentially be applied to develop more natural, ecology-based pest control methods.
4. d) Genetically modifying caterpillars: The passage doesn't mention genetic modification, and this option doesn't align with the main point about caterpillars inducing predators through their frass.

The most logical, rational, and practical message conveyed by the passage is that this finding about caterpillars and their frass could have implications for understanding and potentially manipulating plant responses to pests and pathogens. This understanding could be applied to develop more natural and sustainable pest control methods.

Therefore, the best answer is (c) This finding can help in the development of organic, ecologically sustainable pesticides.

(a) 3

(b) 7

(c) 10

(d) 11

Answer (c)

Simplifying the given expression,

32⁵ + 2²⁷ = (2⁵)⁵ + 2²⁷ = 2²⁵ + 2²⁷

= 2²⁵ ( 1 + 2²) = 2²⁵ x 5 = 2²⁴ x 10

So, the above number is divisible by 10.

Hence option c is the correct answer.

(a) 3

(b) 4

(c) 5

(d) 6

Answer (c)

1. First, we need to understand what the equation p + q = k means. It's telling us that k is the sum of two positive integers p and q, where p is smaller than q.
2. For k = 3, the only possibility is p = 1 and q = 2. This determines p and q uniquely.
3. For k = 4, we again have only one possibility: p = 1 and q = 3. This also determines p and q uniquely.
4. For k = 5, we have two possibilities: p = 1 and q = 4 p = 2 and q = 3
5. Since k = 5 gives us more than one possibility for p and q, this is the smallest value of k that does not determine p and q uniquely.

Therefore, the correct answer is (c) 5.

(a) North-West

(b) West

(c) South

(d) South-West

Answer (c)

1. Initial Walk:
   • The person walks 100 meters straight from his house. We need to determine this initial direction.
2. First Turn:
   • The person turns left and walks 100 meters.
3. Second Turn:
   • The person turns left again and walks 300 meters.
4. Third Turn:
   • The person turns right and walks 100 meters to reach his office.

Given that his office is in the North-East direction from his house, we can infer the directions based on the movement.

Analysis:

Let's assume the initial direction from his house is South (since we need to determine this, starting with one possibility helps in verification):

1. If the initial direction is South:
   • Walk 100 meters South.
2. First Turn (left from South):
   • Turn left from South, which means now heading East, and walk 100 meters.
3. Second Turn (left from East):
   • Turn left from East, which means now heading North, and walk 300 meters.
4. Third Turn (right from North):
   • Turn right from North, which means now heading East, and walk 100 meters.

By following these steps:

• The initial movement is South (100 meters).
• Then East (100 meters).
• Then North (300 meters).
• Then East (100 meters).

By visualizing this, you can see the final position:

• The net movement in the North direction is 200 meters (300 meters North minus 100 meters South initially).
• The net movement in the East direction is 200 meters (100 meters East + 100 meters East).

Hence, the office is 200 meters North-East of the starting point (house).

So, the initial direction from his house must be South to make his office exactly North-East of his starting position.

The correct answer is:

(c) South

(a) South-West

(b) South-East

(c) North-West

(d) North-East

Answer (d)

1. First, let's visualize the initial movements:
   • 100 m Westward
   • Turn left (90° counterclockwise) and walk 100 m Southward
2. At this point, the person is facing South.
3. Now, they take a 225° turn clockwise. To understand this:
   • A 180° turn would make them face North
   • An additional 45° turn (to make 225°) would make them face North-East
4. To confirm:
   • South to West is 90°
   • West to North is another 90° (total 180°)
   • North to North-East is 45° (total 225°)
5. Therefore, after the 225° clockwise turn, the person is facing North-East.

The correct answer is (d) North-East

Statement:

India is the world’s largest producer of milk.

Conclusion-I:

India is the world’s largest exporter of milk.

Conclusion-II:

India does not import milk.

Which one of the following is correct?

(a) Only Conclusion-I follows

(b) Only Conclusion-II follows

(c) Both Conclusion-I and Conclusion-II follow

(d) Neither Conclusion-I nor Conclusion-II follows

Answer (d)

1. Statement: India is the world's largest producer of milk.
2. Conclusion-I: India is the world's largest exporter of milk. Analysis: Being the largest producer doesn't necessarily mean being the largest exporter. A country might produce a lot for domestic consumption without exporting much. Therefore, this conclusion doesn't logically follow from the given statement.
3. Conclusion-II: India does not import milk. Analysis: Being the largest producer doesn't guarantee that a country doesn't import any milk. There could be various reasons for importing, such as different varieties of milk products, regional shortages, or economic factors. This conclusion also doesn't logically follow from the given statement.
4. Neither conclusion can be definitively drawn from the given statement. The statement only provides information about production, not about export, import, or consumption patterns.

Therefore, the correct answer is (d) Neither Conclusion-I nor Conclusion-II follows.

 

59.The content following the image is a question in logical reasoning, followed by two statements and two more questions.

The question is:

What are the values of m and n, where m and n are natural numbers?

Statement I: m + n = mn and m > n.

Statement II: The product of m and n is 24.

The two additional questions are:

Which one of the following is correct in respect of the above question and the statements?

(a) The question can be answered by using one of the statements alone, but cannot be answered using the other statement alone

(b) The question can be answered by using either statement alone

 (c) The question can be answered by using both the statements together, but cannot be answered using either statement alone

(d) The question cannot be answered even by using both the statements together

Answer (c)

1. Question: What are the values of m and n where m and n are natural numbers?
2. Statement-I: m+n > mn and m > n Analysis: This statement alone doesn't give us specific values for m and n. It only provides inequalities which could be satisfied by multiple pairs of natural numbers.
3. Statement-II: The product of m and n is 24 Analysis: This statement alone narrows down the possibilities, but still doesn't give us unique values. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. So, (m,n) could be (1,24), (2,12), (3,8), or (4,6).
4. Using both statements together:
   • From Statement-II, we know the possible pairs are (1,24), (2,12), (3,8), or (4,6).
   • From Statement-I, we know m > n, so we can eliminate (1,24) and (2,12).
   • We also need to check m+n > mn for the remaining pairs: For (3,8): 3+8 = 11, which is not > 38 = 24 For (4,6): 4+6 = 10, which is > 46 = 24
   • Therefore, the only pair that satisfies both statements is m=6 and n=4.
5. Neither statement alone can give us the unique values of m and n, but using both statements together, we can determine the unique values.

Therefore, the correct answer is (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.

 

60.The content following the image is a question about determining the values of m and n, followed by two statements and two more questions.

The question asks: "What are the values of m and n, where m and n are natural numbers?"

Statement I reads: "The product of m and n is 24."

Statement II reads: "The size of the software is 12 megabytes."

The second question asks: "What is the time required to download the software?"

The passage then includes four answer choices (a), (b), (c), and (d), but the image doesn't show which is the correct answer.

Which one of the following is correct in respect of the above question and the statements?

(a) The question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.

(b) The question can be answered by using either statement alone.

(c) The question can be answered by using both the statements together, but cannot be answered using either statement alone.

(d) The question cannot be answered even by using both the statements together.

Answer (c)

1. Question: What is the time required to download the software?
2. Statement-I: The size of the software is 12 megabytes. Analysis: This statement alone doesn't provide enough information to calculate the download time. We need the transfer rate as well.
3. Statement-II: The transfer rate is 2-4 kilobytes per second. Analysis: This statement alone doesn't provide enough information to calculate the download time. We need the size of the software as well.
4. Using both statements together:
   • We have the size: 12 megabytes = 12,288 kilobytes
   • We have a range for the transfer rate: 2-4 kilobytes per second
   • We can calculate a range for the download time: Minimum time = 12,288 / 4 = 3,072 seconds (about 51 minutes) Maximum time = 12,288 / 2 = 6,144 seconds (about 102 minutes)
5. While we can't determine an exact time, we can provide a range for the download time using both statements together.

Therefore, the correct answer is (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.

 

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 a robust democracy, reality, howsoever inconvenient it may be, finds its expression both in the speech of political leaders and the other social forms of assertion. The existence of the real has to be transparent, both through its circulation in and by the media as well as its argumentative articulation in deliberative democracy. A normatively responsible media through its communication effect has the responsibility to circulate the content of reality without distortion.

 

Answer (a)

1. The passage emphasizes the importance of expressing reality in a robust democracy, even if it's inconvenient.
2. It highlights the role of political leaders' speech and other social forms of assertion in expressing this reality.
3. The passage stresses the need for transparency in the existence of the real, through media circulation and deliberative democracy.
4. It specifically mentions the responsibility of a "normatively responsible media" to circulate the content of reality without distortion.

Now, let's look at the options:

1. a) This option directly reflects the main point of the passage, especially the last sentence about media responsibility.
2. b) The passage doesn't mention or imply anything about fake news being inherent in democracy.
3. c) While the passage talks about expression, it doesn't argue for unrestricted freedom of expression.
4. d) The passage doesn't discuss the control of irresponsible media or political leaders.

The statement that best reflects the crux of the passage is option (a) "Responsible media should not distort the real in an ideal democracy."

This option captures the key ideas of the passage:

1. The importance of reality in democracy
2. The role of media in circulating this reality
3. The responsibility of media to avoid distortion

Therefore, the correct answer is (a) Responsible media should not distort the real in an ideal democracy.

Passage-2

Now-a-days there is a growing trend to use interconnected home devices. As consumers. their homes, the increasingly network connected home device manufacturers and service providers will seek to overcome “thin profit margins by gathering more of our personal data-with or without our agreement- turning the home into a corporate storefront”. have powerful Corporate marketers will incentives to observe consumer behaviour to understand the buying needs and preferences of the device owners.

 

Answer (d)

1. The passage discusses the increasing use of interconnected home devices.
2. It mentions that manufacturers and service providers are likely to gather more personal data to overcome "thin profit margins".
3. The passage suggests that this data collection might happen with or without consumer agreement.
4. It states that corporate marketers will have strong incentives to observe consumer behavior to understand buying needs and preferences.
5. The passage implies a transformation of the home into a "corporate storefront".

Now, let's examine each option:

1. a) The passage doesn't discuss capital expenditure in manufacturing.
2. b) While the passage implies that knowledge of consumer behavior is valuable to companies, it doesn't explicitly state that this leads to overall economic development.
3. c) The passage doesn't mention comfort or quality of life improvements from these devices.
4. d) This option aligns most closely with the implications of the passage. The collection of personal data "with or without our agreement" suggests potential privacy risks for home users.

The most logical, rational, and practical message implied by the passage is that the increasing use of interconnected home devices, while potentially beneficial, comes with risks to user privacy and security. Companies' desire to collect data for marketing purposes could lead to unauthorized or excessive data gathering from these devices.

Therefore, the correct answer is (d) Interconnected devices can be at security risk and home users may have privacy risk

Passage-3

Green growth involves rethinking growth strategies with regard to the impacts on environmental sustainability and the environmental resources available to poor and vulnerable groups. In rethinking growth, we need to focus on the current reality of world. Resource resource-constrained intensive and, in particular energy intensive processes will need to make way for more efficient and resource frugal development strategies if we are to avoid an economic dead end or a world in which only a small elite is able to enjoy affluence in the midst of a sea of poverty.

 

Answer (c)

The crux of the passage is about the necessity of rethinking growth strategies to ensure environmental sustainability and equitable resource distribution, particularly in a resource-constrained world. The passage argues that without adopting more efficient and resource-frugal development strategies, economic and social inequalities will persist or worsen.

Given this understanding, the statement that best reflects the crux of the passage is:

1. c) Maintaining high environmental standards is now a prerequisite for achieving a steady, sufficient and inclusive growth
2. A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Question: What are the unique values of x and y, where x, y are distinct natural numbers?

Statement-I: x / y is odd.

Statement-II: xy = 12

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

Answer (c)

1. First, let's consider Statement I: "x / y is odd"
   • This tells us that x must be odd and y must be odd
   • However, this alone doesn't give us unique values for x and y
2. Now, let's consider Statement II: "xy = 12"
   • The factors of 12 are 1, 2, 3, 4, 6, and 12
   • The possible (x, y) pairs are (1,12), (2,6), (3,4), (4,3), (6,2), and (12,1)
   • However, this alone doesn't give us unique values for x and y either
3. Now, let's combine both statements:
   • From Statement I, we know x and y must both be odd
   • From Statement II, the only pair of odd factors of 12 is (1,3)
   • Therefore, x = 3 and y = 1 (or vice versa)
4. However, the question specifies that x and y are distinct natural numbers
   • This means we can't have x = 1 and y = 3, because 1 is not considered a natural number in some definitions
   • So we have a unique solution: x = 3 and y = 1

Therefore, we can answer the question uniquely only by using both statements together. Neither statement alone is sufficient.

A certain amount was distributed among X, Y and Z.

Question: Who received the least amount?

Statement-1: X received 4/5 of what Y and Z together received.

Statement-II: Y received 2/7 of what X and Z together received.

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

Answer (c)

The correct answer is (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.

Here's why:

• Statement I alone: We know X gets 4/5 of the combined amount of Y and Z. This doesn't tell us definitively who received the least. X could still have gotten less than either Y or Z individually.
• Statement II alone: We know Y gets 2/7 of the combined amount of X and Z. Again, this doesn't tell us definitively who received the least. Y could still have gotten less than either X or Z individually.

However, by combining both statements:

• From Statement I, let's say Y+Z = T (total amount for Y and Z). Then, X = 4/5 * T.
• From Statement II, let's say X+Z = U (total amount for X and Z). Then, Y = 2/7 * U.

Here's where it gets interesting:

• If X > U, then X would be more than both Y and Z combined (which contradicts Statement I). So, X cannot be greater than U.
• If X = U, then from Statement I, 4/5 * T = U. This implies T > U, meaning the combined amount for Y and Z is greater than the combined amount for X and Z. This contradicts Statement II.

Therefore, the only possibility is X < U. This translates to X being less than the combined amount of Y and Z (which is T).

Now, to determine who gets the least:

• We know X < T (combined amount for Y and Z).
• We don't have any information about the individual amounts of Y and Z compared to X.

 

66.A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Question: If the average marks in a class are 60, then what is the number of students in the class?

Statement-I: The highest marks in the class are 70 and the lowest marks are 50.

Statement-II: Exclusion of highest and lowest marks from the class does not change the average.

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

1. a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
2. b) The Question can be answered by using either Statement alone.
3. c) The Question can be answered by both the Statements together, but cannot be answered using either Statement alone.
4. d) The Question cannot be answered even by using both the Statements together

Answer (d)

The correct answer is (d) The Question cannot be answered even by using both the Statements together.

Here's why:

• Question: This asks for the number of students in the class.
• Statement I: This tells us the highest and lowest marks, but it doesn't provide any information about the number of students or the distribution of marks within the class.
• Statement II: This is a general principle about averages, but it doesn't help us determine the number of students either. Even if we remove the highest and lowest scores, we still wouldn't know how many scores are left to calculate the average and how those scores are distributed.

Combining both statements:

Even knowing the highest and lowest marks and the fact that removing them wouldn't change the average doesn't provide any information about the number of students or the distribution of the remaining marks. We could have a class of 2 students (one with 70 and another with 50) or a class of 100 students with various scores averaging out to 60 after removing the highest and lowest.

67.A Question is given followed by two Statements I and II. Consider the Question and the Statements. There are three distinct prime numbers whose sum is a prime number.

Question: What are those three numbers?

Statement-1: Their sum is less than 23.

Statement-II: One of the numbers is 5.

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

1. a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
2. b) The Question can be answered by using either Statement alone.
3. c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
4. d) The Question cannot be answered even by using both the Statements together.

Answer (c)

1. First, consider Statement I alone: "Their sum is less than 23."
   • This narrows down the possibilities, but there are still multiple combinations of three prime numbers that could satisfy this condition.
   • For example, 2 + 3 + 5 = 10, 2 + 3 + 7 = 12, 2 + 5 + 7 = 14, etc.
   • We can't determine the exact three numbers from this statement alone.
2. Now, consider Statement II alone: "One of the numbers is 5."
   • This tells us one of the numbers, but doesn't give us enough information to determine the other two.
   • There are still multiple possibilities, like 2 + 3 + 5, 2 + 5 + 7, 3 + 5 + 7, etc.
   • We can't determine the exact three numbers from this statement alone either.
3. Now, let's combine both statements:
   • We know one number is 5, and the sum is less than 23 and is prime.
   • The prime numbers less than 23 are 2, 3, 5, 7, 11, 13, 17, 19.
   • Given that one number is 5 and the sum is prime and less than 23, the only possibility is 2 + 3 + 5 = 10.

Therefore, we can determine that the three prime numbers are 2, 3, and 5, but only by using both statements together.

The correct answer is c)

Question: Is (x + y) an integer?

Statement-I: (2x+y) is an integer.

Statement-II: (x+2y) is an integer.

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

Answer (d)

• Question: This asks whether (x + y) is an integer (whole number).
• Statement I: (2x+y) is an integer tells us that the sum of twice x and y is an integer.
• Statement II: (x+2y) is an integer tells us that the sum of x and twice y is an integer.

Neither statement alone is sufficient:

• Looking at Statement I alone, we can't determine if x and y are both even or odd. If they're both even, then (x + y) will be even (integer). But if one is even and the other odd, then (x + y) will be odd (not an integer).
• Similarly, for Statement II alone, the same logic applies. We can't determine if (x + y) is even or odd based on the information provided.

Combining both statements also doesn't help:

• Even if both (2x+y) and (x+2y) are integers, it doesn't guarantee that (x + y) is an integer. We can manipulate the equations to see this:
• From Statement I: 2x+y = Integer (let's call it A)
• From Statement II: x+2y = Integer (let's call it B)

Adding both equations: 3x + 3y = A + B (which is still an integer)

However, we can't isolate x or y from this combined equation to determine if (x + y) is even or odd.

A person buys three articles p, q and r for 50. The price of the article q is 16 which is the least.

Question: What is the price of the article p?

Statement-I: The cost of p is not more than that of r.

Statement-II: The cost of r is not more than that of p.

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

1. a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
2. b) The Question can be answered by using either Statement alone
3. c) The Question can be answered by the Statements using both together, but cannot be answered using either Statement alone
4. d) The Question cannot be answered even by using both the Statements together

Answer (c)

1. From the given information:
   • Total cost of p + q + r = 50
   • Price of q = 16 (the least)
   • So, p + r = 50 - 16 = 34
2. Now, let's consider Statement I alone: "The cost of p is not more than that of r."
   • This means p ≤ r
   • But we can't determine the exact price of p from this alone
3. Now, let's consider Statement II alone: "The cost of r is not more than that of p."
   • This means r ≤ p
   • Again, we can't determine the exact price of p from this alone
4. Now, let's combine both statements:
   • From Statement I: p ≤ r
   • From Statement II: r ≤ p
   • The only way both these can be true is if p = r
   • We know p + r = 34
   • So, p + p = 34
   • Therefore, p = 17

By using both statements together, we can determine that the price of article p is 17.

The correct answer is c)

P, Q, R and S appeared in a test.

Question: Has P scored more marks than Q?

Statement-I: The sum of the marks scored by P and Q is equal to the sum of the marks scored by R and S.

Statement-II: The sum of the marks scored by P and S is more than the sum of the marks scored by Q and R.

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

Answer (d)

1. The question we need to answer is: Has P scored more marks than Q?
2. Let's examine each statement: Statement I: P + Q = R + S This statement alone doesn't tell us anything about the relative scores of P and Q. Statement II: P + S > Q + R This statement suggests that P's score is higher relative to Q's, but it doesn't definitively prove that P > Q.
3. Now, let's consider both statements together: From Statement I: P + Q = R + S From Statement II: P + S > Q + R If we substitute R + S from Statement I into Statement II: P + S > Q + (P + Q - S) P + S > P + Q S > Q This tells us that S has scored more than Q, but it still doesn't definitively tell us whether P has scored more than Q.
4. Even with both statements, we can't conclusively determine if P has scored more than Q.

Therefore, the correct answer is d) The Question cannot be answered even by using both the Statements together.

 

Unlike religion and science, poetry does not posit or expect any belief in absolute truths. Those forces or individuals who claim to have absolute truths in their grasp tend to turn dictatorial and tyrannical. Truth usually does not admit any contradictions or imperfections. It is unitarian. It is, therefore, not of much use for poetry. Poetry abides by the plurality of life and existence. Perhaps poetry follows reality which is plural, anachronistic, full of Contradictions. Against the tyranny of truth, poetry remains a partisan of democratic reality. Against the arrogance of power, wealth and hierarchy, poetry proposes both humility and defiance.

 

71) Which one of the following statements best reflects the most logical and rational message conveyed by the above passage?

Answer (d)

The passage primarily discusses how poetry differs from religion and science in its approach to truth and reality. It emphasizes that poetry does not adhere to absolute truths, which tend to be tyrannical and dictatorial. Instead, poetry embraces the plurality, contradictions, and imperfections of life, standing in opposition to the arrogance of power, wealth, and hierarchy.

Given this, the statement that best reflects the most logical and rational message conveyed by the passage is:

1. d) In a world of violence, tyranny, and bigotry, poetry is a form of dynamic resistance

Passage-2

The flower was not invented to please us. It flaunted its petals and spread its perfume to attract an insect. The insect carries the pollen from flower to flower so that pollen is not carried away by wind and thus not wasted. What we call a flower’s beauty is merely a by-product and a human invention. The perfume is not there to please us, it pleases us because it is there and we have been conditioned to it.

 

Which of the assumptions given above is/are valid?

Answer (d)

1. The passage states that flowers were not invented to please humans, but rather to attract insects for pollination.
2. It explains that what humans perceive as beauty in flowers is a by-product, not the primary purpose.
3. The author emphasizes the functional role of flowers in plant reproduction.

Now, let's examine the assumptions:

Assumption 1: "The author of the passage believes that flowers are creations of Nature's luxury."

• This assumption is not supported by the passage. The author presents flowers as functional parts of plant reproduction, not as luxuries of nature. The passage suggests that their beauty is incidental, not a purposeful luxury.

Assumption 2: "The author of the passage does not believe in the usefulness of flowers except as things of beauty."

• This assumption is directly contradicted by the passage. The author clearly states that flowers have a crucial role in pollination and plant reproduction. Their beauty is described as a "by-product," not their primary use.

Therefore, the correct answer is d) Neither 1 nor 2

 

 

Age of each of P and Q is less than 100 years but more than 10 years. If you interchange the digits of the age of P, the number represents the age of Q.

Question: What is the difference of their ages?

Statement-I: The age of P is greater than the age of Q.

Statement-II: The sum of their ages is 11/6 times their difference.

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

Answer (a)

Option a is the correct answer.

The question can be answered using Statement 2 alone, but not using Statement 1 alone.

Statement 1 only tells us that P's age is greater than Q's, which means the tens digit of P's age is larger than its ones digit. This information alone is insufficient to determine the exact ages or their difference.

Statement 2, however, provides an equation that can be solved to find the exact ages. By setting up the equation based on the sum of their ages being 11/6 times their difference, we can derive that a = 5b, where 'a' is the tens digit and 'b' is the ones digit of P's age. The only possible solution for this is a = 5 and b = 1, giving us P's age as 51 and Q's age as 15.

With this information from Statement 2 alone, we can easily calculate the difference in their ages (51 - 15 = 36 years).

Therefore, Statement 2 is sufficient by itself to answer the question, while Statement 1 is not, making option a the correct answer

Main Statement:  Pradeep becomes either a Director or a Producer.

Statement P: Pradeep is a Director

Statement Q: Pradeep is a Producer.

Statement R: Pradeep is not a Director.

Statement S: Pradeep is not a Producer.

 

1. Select the correct answer.

Answer (c)

1. The Main Statement says that Pradeep becomes either a Director or a Producer. This means he can be one, but not both.
2. Now, let's look at the implications of each statement: P: If Pradeep is a Director, it implies he's not a Producer (S) Q: If Pradeep is a Producer, it implies he's not a Director (R) R: If Pradeep is not a Director, it implies he's a Producer (Q) S: If Pradeep is not a Producer, it implies he's a Director (P)
3. The question asks for ordered pairs where the first statement implies the second, and both are consistent with the Main Statement.
4. Let's check the given options: SP: If Pradeep is not a Producer (S), it implies he's a Director (P). This is consistent with the Main Statement. RQ: If Pradeep is not a Director (R), it implies he's a Producer (Q). This is also consistent with the Main Statement.
5. Both SP and RQ are valid ordered pairs that satisfy the conditions.

Therefore, the correct answer is c) Both SP and RQ

 

75.If a+b means a-b; a-b means axb; axb means a+b; a+b means a+b, then what is the value of 10+30-100 x 50÷25? (Operations are to be replaced simultaneously)

Answer (d)

1. a+b means a-b
2. a-b means axb
3. axb means a+b
4. a÷b means a÷b (this operation remains unchanged)

Now, let's substitute these into the given expression:

10+30-100 x 50÷25

1. First, replace the operations according to the given rules: 10-30x100+50÷25
2. Now, we follow the standard order of operations (BODMAS/PEMDAS): a) First, division: 50÷25 = 2 10-30x100+2 b) Next, multiplication: 30x100 = 3000 10-3000+2 c) Now, we perform the operations from left to right: 10-3000 = -2990 (remember, - means x in this system) -2990+2 = -2988 (+ means + in this system)
3. Therefore, the final result is -2988.

The closest option to this result is -25.

Therefore, the correct answer is d) -25

 

76.If P means ‘greater than (>)’; Q means less than (<)’; R means ‘not greater than (>)’; S means ‘not less than (<)’ and T means ‘equal to (=)’, then consider the following statements:

1. If 2x(S)3y and 3x(T)4z, then 9y(P)8z.
2. If x(Q)2y and y(R)z, then x(R)z.

Which of the statements given above is/are correct?

Answer (b)

Statement 1: If 2x(S)3y and 3x(T)4z, then 9y(P)8z.

1. 2x(S)3y means 2x ≥ 3y
2. 3x(T)4z means 3x = 4z

From these, we can deduce: 2x ≥ 3y 3x = 4z 2(4z/3) ≥ 3y 8z/3 ≥ 3y 8z ≥ 9y

This means 9y ≤ 8z, which contradicts the conclusion 9y(P)8z (9y > 8z).

Therefore, Statement 1 is incorrect.

Statement 2: If x(Q)2y and y(R)z, then x(R)z.

1. x(Q)2y means x < 2y
2. y(R)z means y ≤ z

From these, we can deduce: x < 2y y ≤ z x < 2z

This means x ≤ z, which is consistent with the conclusion x(R)z (x ≤ z).

Therefore, Statement 2 is correct.

The correct answer is b) 2 only

 

Answer (a)

1. First, we need to find the pattern in the given codes: ABCD = 24 EFGH = 1680
2. Let's assign numbers to the letters based on their position in the alphabet: A = 1, B = 2, C = 3, D = 4 E = 5, F = 6, G = 7, H = 8
3. Now, let's look at the pattern: For ABCD: 1 x 2 x 3 x 4 = 24 For EFGH: 5 x 6 x 7 x 8 = 1680
4. We can see that the code is the product of the numerical values of the letters.
5. Now, for IJKL: I = 9, J = 10, K = 11, L = 12
6. So, the code for IJKL would be: 9 x 10 x 11 x 12 = 11,880

Therefore, the correct answer is a) 11880

Answer (d)

1. First, let's analyze the given code patterns: POT → ATOP TRAP → APART
2. Observing these, we can deduce the following rules:
   • The first letter of the original word is moved to the end.
   • 'A' is added at the beginning of the word.
3. Let's apply this rule to 'ARENA':
   • The first letter 'A' should be moved to the end: RENAA
   • 'A' should be added at the beginning: ARENAA

Therefore, the correct answer is d) AANERA

 

Answer (b)

1. First, let's look at the differences between consecutive terms: 3 → 14 (difference: 11) 14 → 39 (difference: 25) 39 → 84 (difference: 45) 84 → *
   • → 258
2. Now, let's see if there's a pattern in these differences: 11 → 25 (increase: 14) 25 → 45 (increase: 20) 45 → ? (increase: 26?)
3. We can see that the increase in differences is also following a pattern: 14 → 20 (increase: 6) 20 → 26 (increase: 6)
4. So, the next difference should be: 45 + 26 = 71
5. Therefore, the missing number should be: 84 + 71 = 155
6. We can verify this: 155 → 258 (difference: 103, which follows the pattern as 103 = 71 + 32)

Therefore, the correct answer is b) 155

Answer (b)

1. We know that P, Q, R, S, T represent 4, 5, 10, 12, 15 in some order.
2. We're given two equations: Q - S = 2S T = R + S + 3
3. From the first equation: Q - S = 2S This can be rewritten as: Q = 3S The only way this is possible with the given numbers is if: Q = 15 and S = 5
4. Now we know T ≠ 15 (since Q = 15), so T must be 12 (as it's the next largest number).
5. From the second equation: T = R + S + 3 12 = R + 5 + 3 R = 4
6. The only remaining numbers are 10 for P.

So we have: P = 10 Q = 15 R = 4 S = 5 T = 12

7. Now we can calculate P + R - T: 10 + 4 - 12 = 2

Therefore, the correct answer is b) 2