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
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.
Q1. 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
Explanation:
Statement 1 is incorrect: The passage states that food is lost or wasted throughout the supply chain, from agricultural production to household consumption. This implies that food distribution methods are not solely responsible for the wastage. Therefore, this statement is not fully supported
Statement 2 is correct: The passage mentions that food wastage contributes to land degradation due to deforestation, unsustainable agricultural practices, and groundwater extraction. These factors imply an adverse effect on land productivity, making this statement accurate.
Statement 3 is correct: The passage indicates that food wastage leads to significant carbon dioxide emissions (3.5 billion tonnes per year). Reducing food waste would logically reduce the carbon footprint associated with these emissions, so this statement is valid.
Statement 4 is incorrect: The passage does not address the availability of post-harvest technologies to prevent food loss or wastage. Since there is no information supporting this claim, this statement is invalid.
Q2. 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. 1 only
Explanation:
Assumption 1 is valid according to the passage. The passage highlights that food is lost or wasted throughout the supply chain, indicating a need for improvements in the food distribution mechanism to reduce wastage effectively. Reimagining the food distribution process aligns with this need for efficiency.
Assumption 2 is not valid. While the passage emphasizes the importance of addressing food loss and wastage for sustainability, it does not suggest that reducing food wastage is a social or moral responsibility of all citizens. Therefore, this assumption is not supported by the passage.
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.
Q3. Which of the following statements best reflects/reflect the most logical and rational inference/inferences that can be made from the passage?
Central banks cannot bring down inflation without budgetary backing.
The effects of monetary policy depend on the fiscal policies pursued by the government.
Select the correct answer using the code given below:
A. 1 only B. 2 only C. Both 1 and 2 D. Neither 1 nor 2
Answer: C. Both 1 and 2
Explanation:
Statement 1 is correct: The passage implies that central banks need budgetary support to effectively combat inflation. Without fiscal discipline, governments may end up borrowing more to cover rising debt-service costs, which could counteract the effects of monetary policy. This supports the validity of Statement 1.
Statement 2 is correct: The passage states that higher interest rates impact budget deficits and that monetary policy effectiveness depends on the fiscal policies adopted by the government. This indicates that monetary policy’s effects are indeed influenced by government fiscal actions, making Statement 2 valid.
Q4. Based on the above passage, the following assumptions have been made:
Fiscal policies of governments are solely responsible for higher prices.
Higher prices do not affect the long-term government bonds.
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. Neither 1 nor 2
Explanation:
Assumption 1 is not valid: The passage does not suggest that fiscal policies alone are responsible for higher prices. It explains that inflation and interest rates are affected by both fiscal and monetary policies, meaning that other factors also contribute to higher prices. Therefore, this assumption is not supported.
Assumption 2 is not valid: The passage does not mention the impact of higher prices on long-term government bonds. Since there is no information provided about the effect of inflation on these bonds, this assumption cannot be inferred from the passage.
Q5. What is the least possible number of cuts required to cut a cube into 64 identical pieces?
A. 8 B. 9 C. 12 D. 16
Answer: B. 9
Explanation:
Understanding the Divisions Needed:
To get 64 identical pieces, we need to divide the cube into 4 × 4 × 4 = 64 sections.
This means the cube must be divided into 4 equal sections along each of the 3 dimensions.
Minimum Cuts Calculation:
For each dimension, 3 cuts are required to divide the cube into 4 sections.
Since there are 3 dimensions (length, width, and height), we need 3 cuts per dimension.
3 cuts × 3 dimensions = 9 cuts total.
Therefore, the least possible number of cuts required to cut the cube into 64 identical pieces is 9.
Q6. In the expression 5 * 4 * 3 * 2 * 1, * is chosen from +, -, × each at most two times. What is the smallest non-negative value of the expression?
A. 3 B. 2 C. 1 D. 0
Answer: D. 0
Explanation:
The goal is to minimize the value of the expression by strategically using subtraction and addition while ensuring the result is non-negative.
Approach:
Maximizing Subtraction: Subtraction will reduce the value of the expression. To achieve the smallest result, we want to subtract as much as possible.
Addition Strategy: Add numbers only when necessary to prevent the value from becoming negative.
Calculation:
First, subtract strategically to bring the result to zero: 5 - 4 = 1, 1 - 3 = -2, -2 + 2 = 0, 0 × 1 = 0.
By using subtraction, addition, and multiplication in the correct order, we achieve a result of 0.
Thus, the smallest non-negative value of the expression is 0.
Q7. A certain number of men can complete a piece of work in 6k days, where k is a natural number. By what percent should the number of men be increased so that the work can be completed in 5k days?
A. 10% B. (50/3)% C. 20% D. 25%
Answer: C. 20%
Explanation:
Let the number of men required to complete the work in 6k days be denoted by m. According to the problem, this number of men can complete the work in 6k days.
The relationship between the number of men and the time taken to complete the work can be described by the formula:some text
Men × Time = Work (constant)
So, initially:some text
m × 6k = constant work
Let the new number of men be n. According to the formula, for the work to be completed in 5k days:some text
n × 5k = constant work
Since the work is constant, we can equate the two expressions for the work:some text
m × 6k = n × 5k
Simplifying this:some text
n = 6/5 × m
Percent increase = (n - m) / m × 100 = ((6/5)m - m) / m × 100 = (1/5) × 100 = 20%
Thus, the number of men should be increased by 20% to complete the work in 5k days.
Q8. X, Y, and Z can complete a piece of work individually in 6 hours, 8 hours, and 8 hours respectively. However, only one person at a time can work in each hour and nobody can work for two consecutive hours. All are engaged to finish the work. What is the minimum amount of time that they will take to finish the work?
A. 6 hours 15 minutes B. 6 hours 30 minutes C. 6 hours 45 minutes D. 7 hours
Answer: C. 6 hours 45 minutes
Explanation:
X, Y, and Z can complete the work individually in 6 hours, 8 hours, and 8 hours, respectively. To minimize the total time required to finish the work, we need to utilize the most efficient worker, X, as much as possible. Thus, we will alternate between X and either Y or Z, starting with X.
Work Rates:
X completes the work in 6 hours, so in one hour, X completes 1/6 of the work.
Y (or Z) completes the work in 8 hours, so in one hour, Y (or Z) completes 1/8 of the work.
Work Distribution:
We will alternate between X and Y (or Z) in the following pattern:
First hour: X works, completing 1/6 of the work.
Second hour: Y (or Z) works, completing 1/8 of the work.
Third hour: X works, completing 1/6 of the work.
Fourth hour: Y (or Z) works, completing 1/8 of the work.
Fifth hour: X works, completing 1/6 of the work.
After 6 hours, the total work completed is:
3X + 3Y = 3 × 1/6 + 3 × 1/8 = 1/2 + 3/8 = 7/8
Remaining Work:
After 6 hours, 7/8 of the work is completed, leaving 1/8 of the work remaining. Since it’s now X’s turn to work, we calculate how much time X will need to complete the remaining 1/8 of the work:
X completes 1/6 of the work in 1 hour,
So to complete 1/8, the time required is: (1/8 ÷ 1/6) hours = 3/4 hours = 3/4 × 60 minutes = 45 minutes
Total Time: Thus, the total time to complete the work is:
6 hours (for the first 7/8 of the work) + 45 minutes (for the remaining 1/8) = 6 hours 45 minutes.
Thus, the correct answer is C. 6 hours 45 minutes.
Q9. How many consecutive zeros are there at the end of the integer obtained in the product 12 × 24 × 36 × 48 ×.... × 2550?
A. 50 B. 55 C. 100 D. 200
Answer: D. 200
Explanation:
To find the number of trailing zeros in the product 12 × 24 × 36 × ... × 2550, we need to count the number of times 10 appears in this product. Since each 10 is created by a pair of 2 and 5, and there are always more factors of 2, the number of zeros at the end of the product depends on the number of factors of 5.
Steps:
1. Identify terms that contribute factors of 5: We look at multiples of 5 in the sequence and count their factors of 5:
- 510 contributes 10 factors of 5
- 1020 contributes 20 factors of 5
- 1530 contributes 30 factors of 5
- 2040 contributes 40 factors of 5
- 2550 contributes 100 factors of 5
2. Add up the factors of 5: 10 + 20 + 30 + 40 + 100 = 200
So, the product has **200 trailing zeros**.
Q10. On January 1st, 2023, a person saved Rs 1. On January 2nd, 2023, he saved Rs 2 more than that on the previous day. On January 3rd, 2023, he saved Rs 2 more than that on the previous day and so on. At the end of which date was his total savings a perfect square as well as a perfect cube?
A. 7th January, 2023 B. 8th January, 2023 C. 9th January, 2023 D. Not possible
Answer: B. 8th January, 2023
Explanation:
The person’s savings increase by Rs. 2 each day. This forms a sequence of daily savings: 1, 3, 5, 7, 9, 11, 13, 15, ...
Let’s calculate the total savings day by day and check when it becomes both a perfect square and a perfect cube.
Calculations:
1st January: Savings = 1 Total savings = 1 (1 is both a perfect square and a perfect cube)
2nd January: Savings = 3 Total savings = 1 + 3 = 4 (4 is a perfect square but not a perfect cube)
3rd January: Savings = 5 Total savings = 1 + 3 + 5 = 9 (9 is a perfect square but not a perfect cube)
4th January: Savings = 7 Total savings = 1 + 3 + 5 + 7 = 16 (16 is a perfect square but not a perfect cube)
5th January: Savings = 9 Total savings = 1 + 3 + 5 + 7 + 9 = 25 (25 is a perfect square but not a perfect cube)
6th January: Savings = 11 Total savings = 1 + 3 + 5 + 7 + 9 + 11 = 36 (36 is a perfect square but not a perfect cube)
7th January: Savings = 13 Total savings = 1 + 3 + 5 + 7 + 9 + 11 + 13 = 49 (49 is a perfect square but not a perfect cube)
8th January: Savings = 15 Total savings = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64 (64 is both a perfect square and a perfect cube, as 64 = 82 = 43)
Thus, the total savings amount to 64 on 8th January, 2023, which is both a perfect square and a perfect cube.
Therefore, the correct answer is B. 8th January, 2023.
Directions for the following 4 (four) 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
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 planning curriculum that had its roots in the social sciences, geography and architecture. Planning in India, and its education differ from the West.
Q11. Which one of the following statements best reflects the most logical and rational inference that can be made from the above passage?
A. Curriculum for urban planning courses should have a diverse and interdisciplinary approach. B. In India, city administration is under bureaucracy which lacks formal training in urban planning and management. C. In India, the management of urban areas is a local affair with a chronic problem of insufficient funds. D. With high density of population and widespread poverty in our urban areas, planned development in them is very difficult.
Answer: A. Curriculum for urban planning courses should have a diverse and interdisciplinary approach.
Explanation:
The passage highlights how cities like New York, London, and Paris succeeded in urban planning by using a "systems approach" that integrates various disciplines like mathematics, social sciences, geography, and architecture. It contrasts the planning and education methods in the West with those in India, suggesting that India's approach might not have the same interdisciplinary focus.
Option A is correct because the passage emphasizes the need for an interdisciplinary approach in urban planning education, drawing from fields like social sciences, geography, and architecture.
Option B is incorrect because while it discusses bureaucracy and training, the passage does not specifically mention India's city administration or bureaucracy.
Option C is incorrect as the passage does not mention local management or funding issues related to urban areas.
Option D is incorrect because the passage doesn’t discuss issues like population density or poverty as barriers to urban planning.
Thus, the most logical inference is Option A, which suggests a diverse and interdisciplinary approach to urban planning curricula.
Q12. Based on the above passage, the following assumptions have been made:
India needs a new generation of urban professionals with knowledge relevant to modern urban practice.
Indian universities at present have no capacity or potential to impart training in systems approach.
Which of the assumptions given above is/are correct?
A. 1 only B. 2 only C. Both 1 and 2 D. Neither 1 nor 2
Answer: A. 1 only
Explanation:
Assumption 1 is valid: The passage indicates that India's approach to urban planning and education differs from the West, which utilizes advanced systems approaches, mathematical models, and interdisciplinary techniques. This suggests a gap, implying that India requires a new generation of urban professionals who are equipped with knowledge relevant to modern urban practices.
Assumption 2 is invalid: While the passage contrasts urban planning education in India with the West, it does not claim that Indian universities completely lack the capacity to teach a systems approach. It only suggests that India's urban planning education differs from that in the West, without asserting an absolute lack of potential.
Therefore, Assumption 1 is correct, while Assumption 2 is not. The correct answer is A. 1 only.
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 may be.
Q13. Which one of the following statements best reflects the central idea of the above passage?
A. Constructed as a marketplace of views, social media ensures instant access to information. B. Social media are not ideal or moral institutions but the products built by companies to make profits. C. Social media have been created to strengthen democracies. D. In today's world, social media are inevitable for well-informed social life.
Answer: B. Social media are not ideal or moral institutions but the products built by companies to make profits.
Explanation:
Option A is incorrect: The passage does not focus on the role of social media in providing instant access to information but rather discusses how social media platforms amplify voices based on capital and user engagement.
Option B is correct: The passage emphasizes that social media are platforms created by companies driven by profit motives, which can lead to a degradation of political discourse, reflecting that social media are not ideal or moral institutions.
Option C is incorrect: The passage does not suggest that social media are created to strengthen democracies. Instead, it critiques how social media can harm the quality of political discourse.
Option D is incorrect: The passage critiques social media’s influence on politics, implying that they are not necessarily indispensable for well-informed social life.
Q14. Based on the above passage, the following assumptions have been made:
Internet is not inclusive enough.
Internet can adversely affect the quality of policies in a country.
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: C. Both 1 and 2
Explanation:
Assumption 1 is valid: The passage implies that the internet, particularly social media, is not inclusive. It points out that entities with high capital can amplify their voices, overshadowing others. This creates an imbalance, suggesting that the internet is not equally accessible or inclusive to all.
Assumption 2 is valid: The passage suggests that when social media platforms prioritize content that generates user engagement (often sensational or inflammatory), it degrades the quality of political discourse. This can adversely affect policy quality because such discourse influences political decisions, leading to a detrimental effect on policies.
Q15. 222333 + 333222 is divisible by which of the following numbers?
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 37
Answer: B. 3 and 37 but not 2
Explanation:
Step 1: Check divisibility by 2
222 is even, so 222333 is even.
333 is odd, so 333222 is odd.
The sum of an even number (222333) and an odd number (333222) is odd.
Thus, 222333 + 333222 is not divisible by 2.
Step 2: Check divisibility by 3
Using the property of divisibility by 3, a number is divisible by 3 if the sum of its digits is divisible by 3.
Sum of digits of 222 = 2 + 2 + 2 = 6, so 222 is divisible by 3. Therefore, 222333 is divisible by 3.
Sum of digits of 333 = 3 + 3 + 3 = 9, so 333 is divisible by 3. Therefore, 333222 is divisible by 3.
Since both terms 222333 and 333222 are divisible by 3, their sum is also divisible by 3.
Thus, 222333 + 333222 is divisible by 3.
Step 3: Check divisibility by 37
To check divisibility by 37, use modular arithmetic:
222 mod 37 = 222 - 37 × 6 = 222 - 222 = 0.
Hence, 222 ≡ 0 mod 37, and 222333 ≡ 0 mod 37.
333 mod 37 = 333 - 37 × 9 = 333 - 333 = 0.
Hence, 333 ≡ 0 mod 37, and 333222 ≡ 0 mod 37.
Since both terms are divisible by 37, their sum is also divisible by 37.
Thus, 222333 + 333222 is divisible by 37.
Final Answer: The expression 222333 + 333222 is divisible by 3 and 37 but not 2.
Q16. What percent of water must be mixed with honey so as to gain 20% by selling the mixture at the cost price of honey?
A. 20% B. 10% C. 5% D. 4%
Answer: A. 20%
Explanation:
Let:
C be the cost price per unit of honey.
The amount of honey used is 100 units.
The total cost price of the honey is C × 100.
Step 1: Selling Price Calculation
We want to sell the mixture at a 20% profit, so the selling price of the mixture should be: 1.20 × C × 100
Step 2: Total Selling Price of Mixture
The total selling price is also given by: (100 + W) × C
Where W is the amount of water.
Step 3: Set the Selling Prices Equal
1.20 × C × 100 = (100 + W) × C
Step 4: Simplify the Equation
1.20 × 100 = 100 + W
120 = 100 + W
Step 5: Solve for W
W = 120 - 100 = 20
So, the amount of water to mix is 20 units.
Step 6: Calculate the Percentage of Water
The percentage of water is: (20 / 100) × 100 = 20%
Conclusion:
The percentage of water to mix is 20%.
Q17. What is the rightmost digit preceding the zeros in the value of 3030?
A. 1 B. 3 C. 7 D. 9
Answer: D. 9
Explanation:
To find the rightmost digit preceding the zeros in 3030, we focus on 330 since
3030 = 330 × 1030,
Since 1030 results in a 31-digit number with 30 zeros at the end, the rightmost digit preceding the zeros will be the unit digit of 330.
1. Step 1: Last digits of powers of 3
The last digits of powers of 3 repeat in a cycle of 4:
- 31 = 3 (last digit is 3)
- 32 = 9 (last digit is 9)
- 33 = 27 (last digit is 7)
- 34 = 81 (last digit is 1)
The last digits of powers of 3 repeat in a cycle: 3, 9, 7, 1. This cycle has a length of 4.
2. Step 2: Find the remainder when 30 is divided by 4
Since 30 ÷ 4 = 7 remainder 2
We have, 330 = 3(4*7+2)
Therefore, the last digit of 330 corresponds to the second position in the cycle, which is 9.
3. Conclusion:
The rightmost digit preceding the zeros in 3030 is 9.
Q18. 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. 3
Explanation:
We are given the numbers 421 and 427. Subtracting 1 from both, we get 420 and 426.
Step 1: Find the prime factors:
- 420 = 2 × 2 × 3 × 5 × 7
- 426 = 2 × 3 × 71
Step 2: Determine common factors:
The common factors between 420 and 426 are 2 and 3, and their multiple, 6.
Therefore, the divisors that can give the same remainder 1 are 2, 3, and 6, resulting in 3 possible divisors.
Q19. 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 the whole petrol and diesel are separately bottled. The bottle capacity (in litres) is an integer. How many different bottle sizes are possible?
A. 3 B. 4 C. 5 D. 6
Answer: B. 4
Explanation:
To solve this, we need to find the common divisors of 399 (the amount of petrol) and 532 (the amount of diesel). The common divisors will give us the possible bottle sizes.
Step 1: Find the prime factors of 399 and 532
399 = 1 × 3 × 7 × 19
532 = 1 × 2 × 2 × 7 × 19
Step 2: Determine common divisors
The common factors between 399 and 532 are 1, 7 and 19, and their multiple, 133.
The possible bottle sizes are the common divisors of 399 and 532, which are 1, 7, 19, and 133.
Therefore, there are 4 possible bottle sizes.
Q20. 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:
The unit digit of S can be 0.
The unit digit of S can be 9.
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. 1 and 3 only
Explanation:
The distinct prime numbers less than 10 are: 2, 3, 5, and 7.
We will check all possible sums of three distinct primes to find all the possible value of unit digit.
2 + 3 + 5 = 10 (unit digit is 0)
2 + 3 + 7 = 12 (unit digit is 2)
2 + 5 + 7 = 14 (unit digit is 4)
3 + 5 + 7 = 15 (unit digit is 5)
Therefore, the unit digit of S can be 0 and 5 but not 9.
Direction 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 all 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 families, 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.
Q21. Based on the above passage, the following assumptions have been made:
For effective school education, parents have greater role than the governments.
School curriculum that conforms to today’s requirements and is uniform for the entire country may address the issues brought out.
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. Neither 1 nor 2
Explanation:
Assumption 1 is invalid: The passage does not mention that parents have a greater role than the government in school education. It focuses on the academic challenges children face, but it does not discuss the relative roles of parents and government in education.
Assumption 2 is invalid: The passage does not suggest that a uniform curriculum will solve the educational issues. It highlights the gap between expectations and outcomes, but does not advocate for a uniform national curriculum as a solution.
Q22. Which one of the following statements best reflects the central idea conveyed by the passage?
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. Public policy should ensure that competencies and achievements of young people are aligned with their expectations.
Explanation:
Option A is incorrect: The passage does not link eradicating poverty with solving the under-performance of school children. It talks about the gap between academic expectations and actual outcomes, but not poverty as a direct solution.
Option B is incorrect: The passage does not mention any monetary incentives for parents or teachers to improve academic performance.
Option C is correct: The central idea of the passage is about the gap between students' academic performance and the expectations families have for their future. It suggests that public policy should align these competencies and achievements with their expectations.
Option D is incorrect: The passage does not discuss students returning to agriculture or its effect on India’s demographic dividend. It focuses on academic performance and expectations.
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 sense further back, because we nurse the illusion that the industrial revolution ended a golden age.
Q23. Which one of the following statements best reflects the thinking of the author about science?
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. Science must pursue truth but be responsible for social welfare.
Explanation:
Option A is incorrect: The passage does not focus on the commitment of scientists; it emphasizes the evolving role of science and its responsibility to society.
Option B is incorrect: The passage mentions science as a social enterprise, but it does not discuss using science to promote scientific awareness in people.
Option C is incorrect: The passage does not suggest that science made the industrial revolution possible. It focuses on the evolution of science’s social responsibility.
Option D is correct: The passage highlights how science, while initially focused on truth, has now evolved to include social responsibility. Therefore, science must pursue truth but also be responsible for social welfare.
Q24. Consider the sequence:
A_BCD_BBCDABC_DABC_D
Which one of the following completes the sequence?
A. B, A, D, C B. B, A, C, D C. A, A, C, D D. A, A, D, C
Answer: C. A, A, C, D
Explanation:
Given Sequence: A_BCD_BBCDABC_DABC_D
Breaking it down:
Let's divide the sequence in groups of 5:
We can see a repetition of string of 'ABCD' with doubling one alphabet in each string starting A in first string, B in second string, C in third string and D is fourth string.
Complete Sequence: AABCDABBCDABCCDABCDD
Thus, the missing letters are A, A, C, D.
Q25. Two persons P and Q enter into a business. P puts ₹ 14,000 more than Q, but P has invested for 8 months and Q has invested for 10 months. If P's share is ₹ 400 more than Q's share out of the total profit of ₹ 2,000, what is the capital contributed by P?
A. ₹ 30,000 B. ₹ 26,000 C. ₹ 24,000 D. ₹ 20,000
Answer: A. ₹ 30,000
Explanation:
Let's solve this step-by-step.
Step 1: Set Up the Variables
Let Q's investment be ₹ X, which was invested for 10 months.
P invested ₹ (X + 14,000) for 8 months.
Step 2: Determine the Shares of Profit
The total profit from the business is ₹ 2,000.
We are given that P's share is ₹ 1,200.
Q's share is then ₹ 800 (since 2,000 - 1,200 = 800).
Step 3: Set Up the Profit-Sharing Ratio Equation
Since profit is divided in the ratio of each person’s contribution (capital × time), we can set up the following equation:
8 × (X + 14,000) ÷ (10 × X) = 1,200 ÷ 800
Step 4: Simplify the Equation
8 × (X + 14,000) ÷ (10 × X) = 3 ÷ 2
2 × 8 × (X + 14,000) = 3 × 10 × X
16X + 224,000 = 30X
Step 5: Solve for X
30X - 16X = 224,000
14X = 224,000
X = 16,000
Thus, Q’s investment is ₹ 16,000.
Step 6: Calculate P’s Investment
Since P invested ₹ 14,000 more than Q:
P = X + 14,000 = 16,000 + 14,000 = 30,000
The capital contributed by P is ₹ 30,000.
Q26. P’s salary is 20% lower than Q’s salary, which is 20% lower than R’s salary. By how much percent is R’s salary more than P’s salary?
A. 48.75% B. 56.25% C. 60.50% D. 62.25%
Answer: B. 56.25%
Explanation:
Assume R's salary is 100.
Q’s salary is 20% lower than R’s, so Q’s salary = 100 - 20 = 80.
P’s salary is 20% lower than Q’s, so P’s salary = 80 - (20% of 80) = 80 - 16 = 64.
Now, to find by how much R’s salary is more than P’s:
Difference = 100 - 64 = 36.
Percentage difference = (36 / 64) × 100 = 56.25%.
So, R’s salary is 56.25% more than P’s salary.
Q27. A number is mistakenly divided by 4 instead of multiplying by 4. What is the percentage change in the result due to this mistake?
A. 25% B. 50% C. 72.75% D. 93.75%
Answer: D. 93.75%
Explanation:
Assume the number is 100.
Correct operation (multiplying by 4): 100 × 4 = 400.
Mistaken operation (dividing by 4): 100 / 4 = 25.
Calculate the difference between the correct and mistaken results:
Difference = 400 - 25 = 375.
To find the percentage change:
Percentage change = (375 / 400) × 100 = 93.75%.
So, the percentage change in the result is 93.75%.
Q28. In an examination, 80% of students passed in English, 70% of students passed in Hindi, and 15% failed in both subjects. What is the percentage of students who failed in only one subject?
A. 15% B. 20% C. 25% D. 35%
Answer: B. 20%
Explanation:
Assume the total number of students is 100.some text
Students who passed in English = 80%.
Students who passed in Hindi = 70%.
Students who failed in both subjects = 15%.
To find the percentage of students who passed in at least one subject:
Students passing at least one subject = 100 - 15 = 85%.
Next, we find those who passed both subjects:
Students passing both subjects = 80 + 70 - 85 = 65%.
Finally, the percentage of students who failed in only one subject:
Students failing in only one subject = 85 - 65 = 20%.
So, the percentage of students who failed in only one subject is 20%.
Q29. A father said to his son, “n years back I was as old as you are now. My present age is four times your age n years back.” If the sum of the present ages of the father and the son is 130 years, what is the difference of their ages?
A. 30 years B. 32 years C. 34 years D. 36 years
Answer: A. 30 years
Explanation:
Let the father's present age be X and the son's present age be Y.
From the problem, we have two equations:
Equation 1: X - Y = n (The father’s age n years ago was equal to the son’s present age).
Equation 2: X = 4(Y - n) (The father’s current age is four times the son’s age n years ago).
Substitute n from Equation 1 into Equation 2:some text
Rearranging and simplifying, we find the ratio of their ages: X/Y = 8/5.
Assume the father’s age X = 8k and the son’s age Y = 5k.
The sum of their ages is 130:some text
8k + 5k = 130,
13k = 130,
k = 10.
Therefore:
Father's age X = 8k = 80 years,
Son's age Y = 5k = 50 years,
The difference in age = 80 - 50 = 30 years.
Thus, the difference in their ages is 30 years.
Q30. Consider the following:
1000 litres = 1m³
1 metric ton = 1000 kg
1 hectare = 10000 m²
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. 1, 2 and 3
Explanation:
Statement 1: 1000 litres = 1m³
This is correct. 1 cubic meter (m³) is equal to 1000 liters.
Statement 2: 1 metric ton = 1000 kg
This is correct. 1 metric ton is equal to 1000 kilograms.
Statement 3: 1 hectare = 10000 m²
This is correct. 1 hectare is defined as 10,000 square meters.
Thus, all the statements are correct.
Answer: D. 1, 2 and 3
Directions for the following 4 (four) Items :
Read the following two passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.
Passage—1
“The 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 has 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?
Q31. Which of the following is/are emphatically conveyed by the author of the passage?
Without science, mankind could not have continued to exist till today.
It is the science that will ultimately determine the destiny of mankind.
Select the correct answer using the code given below:
A. 1 only B. 2 only C. Both 1 and 2 D. Neither 1 nor 2
Answer: D. Neither 1 nor 2
Explanation:
Statement 1 is incorrect: The passage does not emphasize that mankind could not have continued to exist without science. It highlights the relationship between science and mankind but does not assert that survival depends entirely on science.
Statement 2 is incorrect: The passage does not suggest that science will ultimately determine the destiny of mankind. Instead, it raises a question about whether science's progress is the cause of international conflict or if the fault lies elsewhere.
Q32. Based on the above passage, the following assumptions have been made:
The horrors of modern life are the inevitable result of the progress of science.
The aspect of truth likely to be overlooked is that science is what man has made it.
Which of the assumptions given above is/are correct?
A. 1 only B. 2 only C. Both 1 and 2 D. Neither 1 nor 2
Answer: B. 2 only
Explanation:
Assumption 1 is invalid: The passage does not claim that the horrors of modern life are the inevitable result of the progress of science. It questions whether science is responsible or if the fault lies elsewhere.
Assumption 2 is valid: The passage emphasizes that science cannot be treated as an abstract entity, and its relationship with mankind is shaped by human actions, which aligns with the idea that science is what man has made it.
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.
Q33. When we meet other people while we travel, we learn to differentiate between
A. imagination and understanding B. communities and nationalities C. local values and universal values D. friends and foes
Answer: C. local values and universal values
Explanation:
Option A is incorrect: The passage does not discuss imagination versus understanding, but rather focuses on the differences between local and universal values encountered during travel.
Option B is incorrect: The passage does not make a distinction between communities and nationalities, but rather addresses how values are shaped and understood in different cultures.
Option C is correct: The passage highlights how universal values like justice, love, and honor are shaped differently in different cultures, emphasizing the learning of local versus universal values during travel.
Option D is incorrect: The passage does not discuss the differentiation between friends and foes, but rather focuses on values in different cultural contexts.
Q34. With reference to the above passage, the following assumptions have been made:
Travel leads to an understanding of humans.
Travel helps those who wish to learn fundamental common values.
A person with long experience in travel can resolve differences amongst people.
Which of the assumptions given above are valid?
A. 1 and 2 only B. 2 and 3 only C. 1 and 3 only D. 1, 2 and 3
Answer: A. 1 and 2 only
Explanation:
Assumption 1 is valid: The passage implies that travel leads to a better understanding of humans, particularly how values like justice, love, and honor are experienced differently in various cultures.
Assumption 2 is valid: The passage explicitly states that one of the greatest gains of travel is the learning of fundamental common values, which aligns with assumption 2.
Assumption 3 is invalid: The passage does not suggest that a person with long experience in travel can resolve differences amongst people, but rather emphasizes the understanding of values and their differences across cultures.
Q35. 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?
A. 2 B. 4 C. 6 D. 8
Answer: D. 8
Explanation:
Let the two-digit number X be represented as 10a + b, where a is the tens digit and b is the ones digit.
The number Y, formed by interchanging the digits of X, will be 10b + a.
The sum X + Y = (10a + b) + (10b + a) = 11a + 11b = 11(a + b).
We are told that X + Y is the greatest two-digit number, which is 99. So, 11(a + b) = 99.
This simplifies to a + b = 9.
Now, a and b are digits (ranging from 0 to 9) and must satisfy a + b = 9. The possible pairs for (a, b) are:some text
(1, 8)
(2, 7)
(3, 6)
(4, 5)
(5, 4)
(6, 3)
(7, 2)
(8, 1)
Thus, there are 8 possible values for X.
Q36. Consider the following:
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?
A. 40 kg B. 42 kg C. 45 kg D. 63 kg
Answer: B. 42 kg
Explanation:
We are given that:
Weight of 6 boys = Weight of 7 girls = Weight of 3 men = Weight of 4 women.
The average weight of women is 63 kg.
First, calculate the total weight of the 4 women:
Total weight of women = 4 × 63 = 252 kg.
Now, the weight of 6 boys equals the weight of 4 women, which is 252 kg.
Thus, the total weight of 6 boys is 252 kg, and the average weight of the boys is:
Average weight of boys = 252 ÷ 6 = 42 kg.
Q37. How many times do the hour hand and the minute hand coincide in a clock between 10:00 a.m. and 2:00 p.m. (same day)?
A. 3 times B. 4 times C. 5 times D. 6 times
Answer: A. 3 times
Explanation:
The hour hand and minute hand coincide approximately once every hour and 5 minutes (or 65 minutes).
Between 10:00 a.m. and 2:00 p.m., the coincidences occur at the following times:
Between 10:00 a.m. and 11:00 a.m.
Between 11:00 a.m. and 1:00 p.m.
Between 1:00 p.m. and 2:00 p.m.
Thus, the hands coincide 3 times during this period.
Answer: A. 3 times
Q38. The calendar for the year 2025 is the same for:
A. 2029 B. 2030 C. 2031 D. 2033
Answer: C. 2031
Explanation:
To determine which year shares the same calendar as 2025, we calculate the total number of odd days from 2025 onward until they sum to 7, resetting the day alignment.
Step 1: Odd days for each year
Year
Type
Odd Days
2025
Common
1
2026
Common
1
2027
Common
1
2028
Leap Year
2
2029
Common
1
2030
Common
1
Total Odd Days = 1 + 1 + 1 + 2 + 1 + 1 = 7.
When the total odd days equal 7, the day alignment resets, and the same calendar repeats.
The year 2031 has the same calendar as 2025.
Answer: C. 2031
Q39. Let p, q, r and s be distinct positive integers. Let p, q be odd and r, s be even. Consider the following statements:
1. (p-r)2(qs) is even.
2. (q-s)q2s is even.
3. (q + r)2(p + s) is odd.
Which of the statements given above are correct?
A. 1 and 2 only B. 2 and 3 only C. 1 and 3 only D. 1, 2 and 3
Answer: D. 1, 2 and 3
Explanation:
We are given that:
p, q are odd.
r, s are even.
Let's evaluate each statement:
Statement 1: (p - r)2 (q * s) is even.
Since p is odd and r is even, (p - r) is odd. Squaring an odd number gives an odd result.
q is odd and s is even, so q * s is even.
An odd number times an even number is even, so this statement is true.
Statement 2: (q - s) * q2 * s is even.
q is odd and s is even, so q - s is odd.
q^2 is odd (since odd * odd = odd), and s is even.
An odd number multiplied by an odd number and then by an even number is even, so this statement is true.
Statement 3: (q + r)2 (p + s) is odd.
q is odd and r is even, so (q + r) is odd (odd + even = odd).
p is odd and s is even, so (p + s) is odd (odd + even = odd).
An odd number squared gives an odd result, and multiplying two odd numbers gives an odd result. Therefore, this statement is true.
Since all three statements are correct, the answer is: D. 1, 2 and 3
Q40. What is the angle between the minute hand and hour hand when the clock shows 4:25 hours?
A. 12.5° B. 15° C. 17.5° D. 20°
Answer: C. 17.5°
Explanation:
To find the angle between the minute hand and the hour hand at 4:25, follow these steps:
Minute Hand Position:
The minute hand moves 360° in 60 minutes, so it moves 6° per minute.
At 25 minutes, the minute hand has moved:
25 × 6° = 150° from the 12 o'clock position.
Hour Hand Position:
The hour hand moves 360° in 12 hours, so it moves 30° per hour.
At 4:00, the hour hand is at 4 × 30° = 120°.
In the next 25 minutes, the hour hand moves further. It moves 0.5° per minute (since 30° per hour ÷ 60 minutes).
In 25 minutes, the hour hand moves: 25 × 0.5° = 12.5°.
So, at 4:25, the hour hand is at: 120° + 12.5° = 132.5°.
Angle Between the Hands:
The difference between the minute hand and hour hand is:
150° - 132.5° = 17.5°.
Thus, the angle between the minute hand and hour hand is 17.5°.
Directions for the following 4 (four) 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
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.
Q41. Which of the following statements best reflects/reflect the most logical and rational inference/inferences that can be made from the passage?
In conventional classroom learning, the central goal is duration of learning rather than attainment of competency.
Conventional classrooms encourage a one-size-fits-all approach and stamp out all differentiation.
Select the correct answer using the code given below:
A. 1 only B. 2 only C. Both 1 and 2 D. Neither 1 nor 2
Answer: C. Both 1 and 2
Explanation:
Statement 1 is correct: The passage emphasizes that conventional classrooms focus on "fixed duration over learning effectiveness," indicating that the system prioritizes time spent over actual competency or skill development.
Statement 2 is correct: The passage mentions that every learner receives the "same set of lectures in the same way for the same duration," implying a one-size-fits-all approach that disregards individual learning needs and abilities.
Q42.Based on the above passage, the following assumptions have been made:
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.
Even with its present conventional classroom system of education, India produces a sufficient number of skilled workers to fully realize the benefits of the demographic dividend.
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. Neither 1 nor 2
Explanation:
Assumption 1 is invalid: The passage critiques the conventional classroom system, highlighting its ineffectiveness in achieving high employability. It implies the need for change, not that India should retain the current system due to unorganized sector employment.
Assumption 2 is invalid: The passage indicates low employability (10 percent) despite years of education, suggesting that the conventional system is insufficient for producing a skilled workforce, hence contradicting the idea of "sufficient skilled workers."
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.
Q43. Based on the above passage, the following assumptions have been made:
The adolescent does not feel comfortable with his parents because they tend to be dominating and assertive.
The adolescent of modern times does not have much respect for parents.
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. 1 only
Explanation:
Assumption 1 is valid: The passage suggests that parents can be "dominating and assertive," as their "parental solicitude" often disguises a "love of power," making adolescents feel uncomfortable.
Assumption 2 is invalid: The passage does not indicate a lack of respect by adolescents toward parents. It only highlights a communication gap due to parental assertiveness, leading adolescents to act independently rather than openly disrespecting them.
Q44. Which one of the following statements best reflects the central idea of the above passage?
A. Parents in general may not be of much help when children are on their way to becoming adults. B. When children reach adolescence, involvement of parents in their lives is unnecessary. C. Modern-day nuclear families are not capable of bringing up children properly. D. In modern societies, adolescents tend to be stubborn, disobedient, and careless.
Answer: A. Parents in general may not be of much help when children are on their way to becoming adults.
Explanation:
Option A is correct: The passage suggests that as children reach adolescence, the dominant and assertive attitudes of parents may not be helpful, and that adolescents often prefer to manage their affairs independently.
Option B is incorrect: The passage does not imply that parental involvement is entirely unnecessary, only that it can be problematic if it becomes too assertive or controlling.
Option C is incorrect: The passage does not discuss family structures like nuclear families or suggest any inability to bring up children properly.
Option D is incorrect: There is no mention of adolescents being stubborn, disobedient, or careless; rather, it highlights the conflict that arises due to parental attitudes.
Q45. What is the number of fives used in numbering a 260-page book?
A. 55 B. 56 C. 57 D. 60
Answer: B. 56
Explanation:
To find the number of times the digit "5" appears in numbering a 260-page book, we need to count the occurrences of "5" in both the tens and units places across all page numbers from 1 to 260.
Units place: Pages with 5 in the units place appear once every 10 pages (e.g., 5, 15, 25, ..., 255), giving us 26 occurrences (one for each set of 10 up to 260).
Tens place: Pages with 5 in the tens place are from 50 to 59, 150 to 159, and 250 to 259. Each of these ranges has 10 occurrences of "5" in the tens place, resulting in 30 occurrences.
Adding both:
26 (units place) + 30 (tens place) = 56 times.
Q46. 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, ......
A. 83 B. 84 C. 85 D. 86
Answer: B. 84
Explanation:
The first 28 terms contain these groups:
First group: 1 term (1)
Second group: 2 terms (1, 2)
Third group: 3 terms (3, 2, 1)
Fourth group: 4 terms (4, 3, 2, 1)
Fifth group: 5 terms (5, 4, 3, 2, 1)
Sixth group: 6 terms (6, 5, 4, 3, 2, 1)
Seventh group: 7 terms (7, 6, 5, 4, 3, 2, 1)
Counting up to the 28th term, we find the sum of these terms is 84.
Q47. A person buys three articles P, Q, and R for ₹ 3,330. If P costs 25% more than R and R costs 20% more than Q, then what is the cost of P?
A. ₹ 1,000 B. ₹ 1,200 C. ₹ 1,250 D. ₹ 1,350
Answer: D. ₹ 1,350
Explanation:
Let the cost of article Q be ₹ x.
Since R costs 20% more than Q:some text
Cost of R = x + 0.2x = 1.2x
P costs 25% more than R:some text
Cost of P = 1.2x + 0.25(1.2x) = 1.5x
Total cost of P, Q, and R is ₹ 3,330:some text
x + 1.2x + 1.5x = 3,330
3.7x = 3,330
x = 3,330 / 3.7 = 900
Cost of P = 1.5 × 900 = ₹ 1,350.
Answer: D. ₹ 1,350
Q48. If the sum of the two-digit numbers AB and CD is the three-digit number 1CE, where the letters A, B, C, D, E denote distinct digits, then what is the value of A?
A. 9 B. 8 C. 7 D. Cannot be determined due to insufficient data
Answer: A. 9
Explanation:
Let AB and CD represent two-digit numbers, where A and C are the tens digits and B and D are the units digits, respectively. This gives:
AB = 10A + B
CD = 10C + D
Their sum is a three-digit number, 1CE, where "1" is the hundreds digit:
10A + B + 10C + D = 100 + 10C + E
Since 1CE is a three-digit number starting with "1," and the sum of two two-digit numbers typically results in a number around 100, A must be 9 to reach the hundreds place in the sum.
Answer: A. 9
Q49. Three numbers x, y, z are selected from the set of the first seven natural numbers such that x > 2y > 3z. How many such distinct triplets (x, y, z) are possible?
A. One triplet B. Two triplets C. Three triplets D. Four triplets
Answer: D. Four triplets
Explanation:
We are given the set of the first seven natural numbers: {1, 2, 3, 4, 5, 6, 7}. We need to find the number of distinct triplets (x, y, z) such that:
x > 2y
2y > 3z
Let's analyze each possible value of z and find corresponding values of y and x.
Case 1: z = 1
For 2y > 3z → 2y > 3 → y > 1.5, so y ≥ 2.
For x > 2y → x > 2y, so possible values of x are greater than 2y.
For x > 2y → x > 2y, so possible values of x are greater than 2y.
Checking for possible values:
y = 4 → x > 8 (no possible x)
Total triplets: None for z = 2.
Case 3: z = 3
For 2y > 3z → 2y > 9 → y > 4.5, so y ≥ 5.
For x > 2y → x > 2y, so possible values of x are greater than 2y.
Checking for possible values:
y = 5 → x > 10 (no possible x)
Total triplets: None for z = 3.
Conclusion: From the calculations above, the possible triplets are:
(5, 2, 1)
(6, 2, 1)
(7, 2, 1)
(7, 3, 1)
Thus, there are 4 distinct triplets.
Answer: D. Four triplets
Q50. The total cost of 4 oranges, 6 mangoes, and 8 apples is equal to twice the total cost of 1 orange, 2 mangoes, and 5 apples. Consider the following statements:
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.
The total cost of one orange and one mango is equal to the cost of one apple.
Which of the statements given above is/are correct?
A. 1 only B. 2 only C. Both 1 and 2 D. Neither 1 nor 2
Answer: C. Both 1 and 2
Explanation:
Let's assume the cost of one orange is O, one mango is M, and one apple is A.
Given:
The total cost of 4 oranges, 6 mangoes, and 8 apples is twice the total cost of 1 orange, 2 mangoes, and 5 apples. This translates to the equation
4O + 6M + 8A = 2 × (O + 2M + 5A)
Now, let's simplify this equation:
4O + 6M + 8A = 2(O + 2M + 5A)
4O + 6M + 8A = 2O + 4M + 10A
4O + 6M + 8A - 2O - 4M - 10A = 0
2O + 2M - 2A = 0
O + M = A
This means the cost of 1 orange and 1 mango is equal to the cost of 1 apple.
Now, let's evaluate 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.
3O + 5M + 9A = 4O + 6M + 8A
Using the relation O + M = A, substitute A in both sides:
3O + 5M + 9(O + M) = 4O + 6M + 8(O + M)
Simplifying both sides gives us the same expression, so Statement 1 is correct.
Statement 2: The total cost of 1 orange and 1 mango is equal to the cost of 1 apple.
From the equation we derived earlier, Statement 2 is correct.
Conclusion: Both statements are correct.
Directions for the following 3 (three) items :
Read the following three passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.
Passage-1
When an international team of 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.
Q51. 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 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. This can be used as one of the methods of carbon sequestration.
Explanation:
Option A is incorrect: The passage does not suggest that this method is used to produce limestone for commercial building purposes.
Option B is correct: The method described in the passage is a form of carbon sequestration, where carbon dioxide is captured and turned into solid stone, preventing its release into the atmosphere.
Option C is incorrect: While calcium and magnesium are dissolved from the basalt, the purpose described in the passage is not to make these minerals available for extraction but rather to convert carbon dioxide into a stable form (limestone).
Option D is incorrect: The passage does not focus on creating rock-dissolving acid, but rather on a chemical process that uses an acid mixture for carbon sequestration.
Passage 2
Geographers analyzed 175 satellite images of ocean colour, 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.
Q52. Based on the above passage, the following assumptions have been made:
Giant icebergs have a bearing on primary productivity and food chains of the Southern Ocean.
Melting of giant icebergs can produce climate change effects and impact world fisheries.
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. 1 only
Explanation:
Assumption 1 is valid: The passage indicates that giant icebergs increase primary productivity by promoting phytoplankton growth, which forms the base of the ocean's food chain.
Assumption 2 is invalid: Although the passage highlights carbon storage and primary productivity, it does not suggest a direct link between iceberg melting and global climate change effects or the impact on world fisheries.
Passage-3
Evolution has endowed caterpillars that feed on corn with a unique ability, they can induce the plant to turn off its defence against insect predators. This helps caterpillars to eat more and grow faster. The agent that causes this effect is the caterpillar's faeces or frass. The find could throw new light on compounds associated with plant response to pathogens like fungi or bacteria.
Q53. Which one of the following statements best reflect the most logical and 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. This finding can help in the development of organic, ecologically sustainable pesticides.
Explanation:
Option A is incorrect: The passage does not suggest that caterpillars could be used to control weeds.
Option B is incorrect: While the passage mentions insights into plant responses, it does not directly relate to developing antimicrobial compounds.
Option C is correct: The finding could inspire the creation of ecologically sustainable pesticides that mimic the caterpillar-induced defense suppression, aligning with organic farming practices.
Option D is incorrect: There is no mention of genetically modifying caterpillars for pest control.
Q54. 325 + 227 is divisible by which of the following?
A. 3 B. 7 C. 10 D. 11
Answer: C. 10
Explanation:
Rewrite the expression:
We know that 32 = 25, so: 325 = (25)5 = 225. Thus, the expression becomes: 325 + 227 = 225 + 227.
Divisibility by 3: 225 × 5 is not divisible by 3, as it doesn't contain a factor of 3.
Divisibility by 7: 225 × 5 is not divisible by 7, as it doesn't contain a factor of 7.
Divisibility by 10: 225 × 5 is divisible by 10, because it contains both 2 and 5 as factors.
Divisibility by 11: 225 × 5 is not divisible by 11, as it doesn't contain a factor of 11.
Conclusion: The expression 325 + 227 is divisible by 10.
Q55. Let p and q be positive integers satisfying p < q and p + q = k. What is the smallest value of k that does not determine p and q uniquely?
A. 3 B. 4 C. 5 D. 6
Answer: C. 5
Explanation:
For k = 3: The only valid pair satisfying p < q is p = 1 and q = 2. Thus, k = 3 uniquely determines p and q.
For k = 4: The possible pairs are (1, 3) and (2, 2). However, since p < q is required, only the pair (1, 3) is valid. Hence, k = 4 also uniquely determines p and q.
For k = 5: The valid pairs satisfying p < q are (1, 4) and (2, 3). Here, k = 5 does not uniquely determine p and q, because there are two possible pairs.
The smallest value of k that does not determine p and q uniquely is k = 5.
Q56. A person walks 100 m straight from his house, turns left and walks 100 m, again turns left and walks 300 m, then turns right and walks 100 m to reach his office. In which direction does he walk initially from his house if his office is exactly in the North-East direction?
A. North-West B. West C. South D. South-West
Answer: C. South
Explanation:
For the office to be in the North-East direction, the initial direction must be South.
Q57. A person walks 100 m Westward, then turns left and walks 100 m. He then takes a 225° turn clockwise. In which direction is he walking now?
A. South-West B. South-East C. North-West D. North-East
Answer: D. North-East
Explanation:
To calculate the direction:
A 90-degree turn clockwise from South brings him to West.
A further 90-degree turn (total 180 degrees) brings him to North.
Finally, a 45-degree turn (total 225 degrees) brings him to North-East.
Q58. A statement is given followed by two conclusions numbered I and II. Consider the statement and the conclusions.
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. Neither Conclusion-I nor Conclusion-II follows
Explanation:
Conclusion I does not follow: The statement mentions that India is the largest producer of milk, but it does not provide any information regarding India's status as the largest exporter of milk. The fact that India is the largest producer does not necessarily imply it is the largest exporter.
Conclusion II does not follow: The statement only indicates that India is the largest producer of milk. It does not state anything about whether India imports milk. Therefore, being the largest producer does not imply that India does not import milk.
Q59. A Question is given followed by two Statements I and II. Consider the Questions and the Statements.
Question: 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.
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. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
Explanation:
Statement-I:
m + n > mn and m > n
For m = 2, n = 1: 2 + 1 = 3 > 2 × 1 = 2, and 2 > 1, which satisfies both conditions.
For m = 3, n = 1: 3 + 1 = 4 > 3 × 1 = 3, and 3 > 1, which satisfies both conditions. This gives multiple possible pairs for m and n, so it is not sufficient to uniquely determine m and n.
Statement-II:
mn = 24
Possible pairs are:
1 × 24 = 24
2 × 12 = 24
3 × 8 = 24
4 × 6 = 24
This also gives multiple possible pairs, so it is not sufficient alone.
Combining Statement-I and Statement-II:
From Statement-II, m and n must be pairs where the product is 24. Using Statement-I, we check:
(24, 1): 24 + 1 = 25 > 24, and 24 is greater than 1, so this pair satisfies all the conditions.
Other pairs like (2, 12), (3, 8), and (4, 6) fail to meet the condition m + n > mn.
Hence, both statements together provide the unique solution (m, n) = (24, 1).
Q60. A Question is given followed by two Statements I and II. Consider the Questions and the Statements.
Question: What is the time required to download the software?
Statement-I: The size of the software is 12 megabytes. Statement-II: The transfer rate is 2.4 kilobytes per second.
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. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
Explanation:
Using Statement-I alone: This gives us the size of the software but does not provide any information about the transfer rate, which is necessary to calculate the download time. Hence, this statement alone is not sufficient.
Using Statement-II alone: This tells us the transfer rate but does not provide the size of the software. Without knowing the size, we cannot calculate the time required to download. Hence, this statement alone is not sufficient.
Combining Statement-I and Statement-II:
From Statement-I, we know the software size is 12 megabytes.
From Statement-II, we know the transfer rate is 2.4 kilobytes per second. We can calculate the time required to download the software using the formula:
Download Time = Size of the Software / Transfer Rate
We need to convert the size to the same unit as the transfer rate:
Time = 12288 kilobytes / 2.4 kilobytes per second = 5120 seconds.
Thus, combining both statements gives us the unique solution for the download time.
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.
Q61. Which one of the following statements best reflects the crux of the above passage?
A. Responsible media should not distort the real in an ideal democracy. B. Fake news seems inherent in the life of an ideal democracy. C. There should not be any kind of restrictions on the freedom of expression in an ideal democracy. D. Irresponsible media and political leaders cannot be effectively controlled in an ideal democracy.
Answer: A. Responsible media should not distort the real in an ideal democracy.
Explanation:
Option A is correct: The passage emphasizes that a responsible media must circulate reality without distortion in a democracy. This aligns directly with the key message of the passage.
Option B is incorrect: The passage does not suggest that fake news is inherent in an ideal democracy. Instead, it highlights the importance of responsible media to prevent distortion.
Option C is incorrect: While the passage emphasizes free expression, it does not discuss restrictions or lack thereof on freedom of expression.
Option D is incorrect: The passage does not discuss the inability to control irresponsible media or political leaders.
Passage – 2: Now-a-days there is a growing trend to use interconnected home devices. As consumers increasingly network their homes, the 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". Corporate marketers will have powerful incentives to observe consumer behaviour to understand the buying needs and preferences of the device owners.
Q62. Which one of the following statements best reflects the most logical, rational and practical message implied by the passage?
A. Knowledge of consumer behaviour leads to more capital expenditure in the manufacturing sector. B. Knowledge of consumer behaviour stimulates the growth of commerce and trade and thus helps in the overall economic development of the country. C. Interconnected devices give a lot of comfort to home users and improve the overall quality of life. D. Interconnected devices can be at security risk and home users may have privacy risk.
Answer: D. Interconnected devices can be at security risk and home users may have privacy risk.
Explanation:
Option A is incorrect: The passage does not discuss capital expenditure in the manufacturing sector.
Option B is incorrect: While understanding consumer behavior may aid commerce and trade, the passage does not focus on economic development. Instead, it emphasizes privacy concerns.
Option C is incorrect: Although interconnected devices may improve comfort and quality of life, this is not the central focus of the passage. The passage warns about privacy and security risks instead.
Option D is correct: The passage explicitly mentions privacy risks and the potential for interconnected devices to turn homes into corporate storefronts. This reflects the logical and practical message implied.
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 a resource-constrained world. Resource 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.
Q63. Which one of the following statements best reflects the crux of the above passage?
A. Environmental sustainability is inimical to our objective of achieving a high rate of GDP growth. B. Poverty eradication is not possible without rapid economic growth and the consequent environmental degradation. C. Maintaining high environmental standards is now a prerequisite for achieving steady, sufficient and inclusive growth. D. With large populations, rampant poverty and limited resources of today's world, environmental degradation cannot be prevented and inequalities are inevitable.
Answer: C. Maintaining high environmental standards is now a prerequisite for achieving steady, sufficient and inclusive growth.
Explanation:
Option A is incorrect: The passage does not suggest that environmental sustainability conflicts with achieving GDP growth. Instead, it highlights the need to integrate sustainability into growth strategies.
Option B is incorrect: The passage does not argue that poverty eradication requires environmental degradation. It suggests the opposite: that sustainable, resource-efficient.
Option C is correct: The passage explicitly states the importance of maintaining high environmental standards to ensure steady, sufficient, and inclusive growth. This aligns with the crux of the passage.
Option D is incorrect: The passage does not claim that environmental degradation is unavoidable or that inequalities are inevitable. It proposes solutions to prevent such outcomes.
Q64. 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.
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. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
Explanation:
Using Statement-I alone: Statement-I tells us that x/y is odd, meaning the quotient of x and y is an odd number. For this to be true, x must be an odd multiple of y. However, without knowing any specific values for x and y, we cannot conclude the exact values of x and y. Therefore, Statement-I alone is insufficient to answer the question.
Using Statement-II alone: Statement-II states that xy = 12. The factors of 12 are (1, 12), (2, 6), (3, 4), (12, 1), (6, 2), (4, 3). These are the only possible pairs of x and y that satisfy the equation xy = 12. However, we still need more information to determine the unique values of x and y. Therefore, Statement-II alone is insufficient to answer the question.
Combining Statement-I and Statement-II: From Statement-II, we know the possible pairs of (x, y) that satisfy xy = 12 are (1, 12), (2, 6), (3, 4), (12, 1), (6, 2), (4, 3).some text
Only for the pair (6, 2), x/y = 6/2 = 3 is odd.
Thus, the only pair that satisfies both the condition xy = 12 and x/y being odd is (6, 2). Therefore, combining both statements, we can conclude that the unique values of x and y are 6 and 2.
Q65. A question is given followed by two Statements I and II. Consider the Question and the Statements.
A certain amount was distributed among X, Y, and Z.
Question: Who received the least amount?
Statement-I: 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?
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. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
Explanation:
Using Statement-I alone: From Statement-I, we have X = (4/5) × (Y + Z), or X = 4k and (Y + Z) = 5k. This gives us the relationship between X, Y, and Z but does not allow us to determine who received the least. Thus, Statement-I alone is insufficient.
Using Statement-II alone: From Statement-II, we have Y = (2/7) × (X + Z), or Y = 2k and (X + Z) = 7k. This gives us the relationship between Y, X, and Z but does not directly provide the least amount. Hence, Statement-II alone is insufficient.
Combining Statement-I and Statement-II: From both equations:some text
From Statement-I: X = 4k and (Y + Z) = 5k
From Statement-II: Y = 2k and (X + Z) = 7k
Solving these gives:
Y + Z = 5k
2k + Z = 5k, so Z = 3k
Now we know X = 4k, Y = 2k, and Z = 3k. Hence, X : Y : Z = 4 : 2 : 3. Clearly, Y received the least amount.
Q66. 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?
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: D. The Question cannot be answered even by using both the Statements together.
Explanation:
Using Statement-I alone: Statement-I provides the highest marks (70) and the lowest marks (50) but does not give information about the total number of students or their individual marks. Hence, it is not sufficient to determine the number of students in the class. Therefore, Statement-I alone is insufficient.
Using Statement-II alone: Statement-II tells us that excluding the highest and lowest marks does not change the average, which means the average of the remaining marks is also 60. However, this alone does not provide enough information to calculate the total number of students. Therefore, Statement-II alone is insufficient.
Combining Statement-I and Statement-II: From Statement-II, we know that excluding the highest (70) and lowest (50) marks does not change the average, so the average of the remaining marks is still 60. Let the number of students in the class be n, and the total sum of marks be S. The average marks are given by:
S/n = 60, so S = 60n.
After excluding the highest and lowest marks, the sum of the remaining marks is (S - 70 - 50) = S - 120, and the number of students is (n - 2).
Thus, the new average is: (S - 120) / (n - 2) = 60.
Substituting S = 60n: (60n - 120) / (n - 2) = 60.
Simplifying:
60n - 120 = 60(n - 2),
60n - 120 = 60n - 120.
This equation holds true for any value of n, indicating that no specific number of students can be determined. Therefore, both statements together still do not give a unique answer.
Q67. 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-I: 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?
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: A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
Explanation:
Using Statement-I alone: Statement-I tells us that the sum of the three distinct prime numbers is less than 23. The possible prime numbers less than 23 are: 2, 3, 5, 7, 11, 13, 17, 19. The only triplet that satisfies this condition is (3, 5, 11), with the sum 3 + 5 + 11 = 19, which is less than 23 and is prime. Hence, Statement-I alone is sufficient to answer the question.
Using Statement-II alone: Statement-II tells us that one of the numbers is 5.
(5, 7, 11) has the sum 5 + 7 + 11 = 23, which is prime.
(5, 11, 13) has the sum 5 + 11 + 13 = 29, which is prime.
With Statement-II, we have multiple possible sets of prime numbers (5, 7, 11) and (5, 11, 13), so Statement-II alone does not provide a unique answer.
Q68. A question is given followed by two Statements I and II. Consider the Question and the Statements.
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?
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: D. The Question cannot be answered even by using both the Statements together.
Explanation:
Using Statement-I alone: Statement-I tells us that (2x + y) is an integer. This means that the sum of 2x and y is an integer. However, this does not provide any direct information about whether (x + y) is an integer. Hence, Statement-I alone is insufficient to answer the question.
Using Statement-II alone: Statement-II tells us that (x + 2y) is an integer. This means that the sum of x and 2y is an integer, but it does not directly provide information about (x + y). Therefore, Statement-II alone is insufficient to answer the question.
Combining Statement-I and Statement-II:some text
From Statement-I, we know (2x + y) is an integer, and from Statement-II, we know (x + 2y) is an integer.
However, even when combining these two, we still cannot directly conclude whether (x + y) is an integer, as there is no clear relationship that would lead to (x + y) being an integer.
Thus, both statements together do not provide enough information to answer the question.
Q69. A question is given followed by two Statements I and II. Consider the Question and the Statements.
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?
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. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
Explanation:
Using Statement-I alone: Statement-I tells us that the cost of p is not more than that of r. This means p ≤ r, but it does not provide a unique relationship between p, q, and r to determine the exact price of p. Therefore, Statement-I alone is insufficient.
Using Statement-II alone: Statement-II tells us that the cost of r is not more than that of p. This means r ≤ p, but again, it does not provide enough information to determine the exact price of p. Thus, Statement-II alone is also insufficient.
Combining both Statements:
From Statement-I, we know p ≤ r, and from Statement-II, we know r ≤ p.
This means p = r, and together with the information that the total cost of p, q, and r is ₹50, we can solve for p.
Let p = r, and since q costs ₹16, the total cost equation is: p + q + r = 50, p + 16 + p = 50, 2p = 34, p = ₹17.
Thus, combining both statements gives us a unique solution for the price of p.
Q70. 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?
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: D. The Question cannot be answered even by using both the Statements together.
Explanation:
Using Statement-I alone: Statement-I tells us that P + Q = R + S. However, this provides no direct information about the relationship between P and Q's individual scores. Hence, Statement-I alone is insufficient to answer the question.
Using Statement-II alone: Statement-II tells us that P + S > Q + R. While this indicates a relationship between the total scores of P and S and Q and R, it does not directly answer whether P scored more than Q. Therefore, Statement-II alone is insufficient.
Combining both Statements: From Statement-I, we know that P + Q = R + S, and from Statement-II, we know that P + S > Q + R. Combining these, we still cannot determine the individual scores of P and Q, nor establish if P scored more than Q.
Thus, even using both statements together, the question cannot be answered.
Passage-1
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.
Q71. Which one of the following statements best reflects the most logical and rational message conveyed by the above passage?
A. It is the poetry, not science or religion, which recognizes and accepts imperfections in humans. B. Truth is revealed through science or religion and poetry is anathema to truth. C. Poetry is romantic, imaginary and is about feeling whereas science and religion are about truth. D. In a world of violence, tyranny and bigotry, poetry is a form of dynamic resistance.
Answer: A. It is the poetry, not science or religion, which recognizes and accepts imperfections in humans.
Explanation:
Option A is correct: The passage emphasizes that poetry recognizes and embraces the plurality, contradictions, and imperfections in life, unlike science or religion, which pursue absolute, unitarian truths. This makes Option A the most logical choice.
Option B is incorrect: The passage does not suggest that poetry is against truth or sees it as anathema. It highlights that poetry thrives on contradictions and plurality, which science and religion often disregard.
Option C is incorrect: This misrepresents poetry as merely romantic or emotional, whereas the passage portrays it as a medium that upholds pluralistic realities and challenges tyranny.
Option D is incorrect: While the passage does suggest that poetry resists tyranny and bigotry, it primarily focuses on poetry’s role in embracing the pluralistic and contradictory aspects of life. This option oversimplifies the broader argument.
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.
Q72. Based on the above passage, the following assumptions have been made:
The author of the passage believes that flowers are creations of Nature's luxury.
The author of the passage does not believe in the usefulness of flowers except as things of beauty.
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. Neither 1 nor 2
Explanation:
Assumption 1 is invalid: The author does not describe flowers as creations of Nature's luxury. Instead, the passage explains that flowers serve a practical purpose — to attract insects for pollination. The concept of luxury is not mentioned or implied.
Assumption 2 is invalid: The passage clearly states that the beauty of flowers (both their appearance and fragrance) is a by-product of their primary function, which is to attract insects for pollination. The author does not suggest that flowers are merely things of beauty; instead, their beauty is incidental to their actual role in nature.
Therefore, neither of the assumptions is valid.
Q73. A question is given followed by two Statements I and II. Consider the Question and the Statements.
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?
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: A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
Explanation:
Using Statement-I alone: Statement-I tells us that the age of P is greater than the age of Q, i.e., P > Q. However, this does not give a unique solution, as there are multiple possible combinations of P and Q where P is greater than Q. For example:some text
If P = 81, Q = 18, the condition holds.
If P = 72, Q = 27, the condition holds.
Therefore, Statement-I alone is not sufficient to determine the exact difference in their ages.
Using Statement-II alone: Statement-II provides a mathematical relationship between the sum and difference of their ages:
The sum of their ages is 11/6 times their difference:
P + Q = (11/6) × (P - Q)
Substituting the values of P and Q (P = 10x + y and Q = 10y + x), we can simplify the equation:
Given that x and y must be digits (i.e., between 0 and 9), the only solution that satisfies this equation is when y = 1 and x = 5. Therefore, P = 51 and Q = 15.
The difference in their ages is:
P - Q = 51 - 15 = 36
Thus, Statement-II alone is sufficient to answer the question.
Q74. Main Statement is followed by four Statements labelled P, Q, R and S. Choose the ordered pair of the Statements where the first Statement implies the second, and the two Statements are logically consistent with the Main Statement.
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.
Select the correct answer.
A. SP only B. RQ only C. Both SP and RQ D. Neither SP nor RQ
Answer: C. Both SP and RQ
Explanation:
The main statement says: "Pradeep becomes either a Director or a Producer." This means that Pradeep cannot be both a Director and a Producer simultaneously, nor can he be neither. He must be one of the two.
If Statement S (Pradeep is not a Producer) is true, it implies Statement P (Pradeep is a Director), because Pradeep must be either a Director or a Producer, and if he is not a Producer, he must be a Director.
Thus, SP is logically consistent with the main statement.
If Statement R (Pradeep is not a Director) is true, it implies Statement Q (Pradeep is a Producer), because if he is not a Director, he must be a Producer.
Thus, RQ is logically consistent with the main statement.
Conclusion: Both SP and RQ are logically consistent with the main statement and satisfy the condition that the first statement implies the second.
Q75. a + b means a – b; a – b means a x b; a x b 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)
A. 15
B. 0
C. –15
D. –25
Answer: D. –25
Explanation:
The expression to evaluate is: 10 + 30 – 100 × 50 ÷ 25
Step 1: Replace operations based on their new definitions:
Q76. 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:
If 2x(S)3y and 3x(T)4z, then 9y(P)8z.
If x(Q)2y and y(R)z, then x(R)z.
Which of the statements given above is/are correct?
A. 1 only
B. 2 only
C. Both 1 and 2
D. Neither 1 nor 2
Answer: D. Neither 1 nor 2
Explanation:
Statement 1: If 2x ≥ 3y and 3x = 4z, then 9y > 8z.
Interpretation:
2x ≥ 3y
3x = 4z ⟹ x = 4z/3
Substituting x = 4z/3 in 2x ≥ 3y:some text
2(4z/3) ≥ 3y
8z/3 ≥ 3y ⟹ 8z ≥ 9y
This implies 9y ≤ 8z, which contradicts 9y > 8z.
Conclusion: Statement 1 is incorrect.
Statement 2: If x < 2y and y ≤ z, then x ≤ z.
Interpretation:
x < 2y
y ≤ z
From the above, x < 2y does not guarantee x ≤ z because z depends on y, and x could still be greater than z.
Conclusion: Statement 2 is incorrect.
Q77. If in a certain code, ‘ABCD’ is written as 24 and ‘EFGH’ is written as 1680, then how is ‘IJKL’ written in that code?
A. 11880
B. 11240
C. 7920
D. 5940
Answer: A. 11880
Explanation:
Step 1: Determine the alphabetical positions of the letters.
A = 1, B = 2, C = 3, D = 4
E = 5, F = 6, G = 7, H = 8
I = 9, J = 10, K = 11, L = 12
Step 2: For 'ABCD,' the product is: 1 × 2 × 3 × 4 = 24. The code for 'ABCD' is 24
Step 3: For 'EFGH,' the product is: 5 × 6 × 7 × 8 = 1680. The code for 'EFGH' is 1680.
Step 4: For 'IJKL,' the product is: 9 × 10 × 11 × 12 = 11880. The code for 'IJKL' is 11880.
Q78. If in a certain code, ‘POT’ is written as ATOP and ‘TRAP’ is written as APART, then how is ‘ARENA’ written in that code?
A. AARENA
B. AANREA
C. AANEAR
D. AANERA
Answer: D. AANERA
Explanation:
The given pattern involves adding an 'A' at the beginning and rearranging the letters of the word in reverse order.
For 'POT': Reverse the word → TOP. Add 'A' at the beginning → ATOP.
For 'TRAP': Reverse the word → PART. Add 'A' at the beginning → APART.
For 'ARENA': Reverse the word → ANERA. Add 'A' at the beginning → AANERA.
Q79. What will come in place of * in the sequence 3, 14, 39, 84, *, 258?
A. 150
B. 155
C. 160
D. 176
Answer: B. 155
Explanation:
Given sequence: 3, 14, 39, 84, *, 258
The pattern follows a cubic relation:
For 1: 1³ + 1² + 1 = 3
For 2: 2³ + 2² + 2 = 14
For 3: 3³ + 3² + 3 = 39
For 4: 4³ + 4² + 4 = 84
For 5: 5³ + 5² + 5 = 155
For 6: 6³ + 6² + 6 = 258
Thus, the missing number is 155.
Q80. In some code, letters P, Q, R, S, T represent numbers 4, 5, 10, 12, 15. It is not known which letter represents which number. If Q – S = 2S and T = R + S + 3, then what is the value of P + R – T?
A. 1
B. 2
C. 3
D. Cannot be determined due to insufficient data
Answer: B. 2
Explanation:
We have two conditions:
Q – S = 2S, which simplifies to Q = 3S.
T = R + S + 3.
Step 1: Analyze the possible values for S and Q
From Q = 3S, we can deduce that Q must be a multiple of 3.some text
If S = 5, then Q = 15.
If S = 4, then Q = 12.
Step 2: Case (1) S = 4 and Q = 12
T = R + S + 3 => T = R + 7
T = 12 and R = 5, which contradicts with Q = 12. So, this case is invalid.
Case (2) S = 5 and Q = 15
From T = R + S + 3, we substitute S = 5:some text
T = R + 5 + 3 = R + 8.
Now, the possible values for T and R are 4, 10, 12, and 15.some text
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