UPSC PREVIOUS-YEAR QUESTIONS

Data Sufficiency

Practise the original questions with answers and explanations.

2 questions

Question 12024 · CSAT

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

Explanation

We need to find unique natural numbers m and n.

**Statement I: m + n > mn and m > n.**
Let’s test some natural number pairs where m > n:
– If m=2, n=1: 2+1 = 3, 2*1 = 2. Since 3 > 2, (2,1) is a possible pair.
– If m=3, n=1: 3+1 = 4, 3*1 = 3. Since 4 > 3, (3,1) is a possible pair.
Since there are multiple possibilities, Statement I alone is insufficient.

**Statement II: The product of m and n is 24 (mn = 24).**
Possible pairs of natural numbers (m,n):
– (1,24), (2,12), (3,8), (4,6), (6,4), (8,3), (12,2), (24,1).
Since there are multiple possibilities, Statement II alone is insufficient.

**Combining Statement I and Statement II:**
We need to find a pair (m,n) from the list in Statement II that satisfies m + n > mn and m > n.
From Statement II, mn = 24. So the condition m + n > mn becomes m + n > 24.
Let’s check the pairs from Statement II that also satisfy m > n:
1. (24,1): m+n = 25. Is 25 > 24? Yes. So (24,1) is a solution.
2. (12,2): m+n = 14. Is 14 > 24? No.
3. (8,3): m+n = 11. Is 11 > 24? No.
4. (6,4): m+n = 10. Is 10 > 24? No.
Only the pair (24,1) satisfies both conditions. Thus, m=24 and n=1 are uniquely determined.
Therefore, both statements together are sufficient to answer the question. This question tests data sufficiency and number properties.

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Question 22024 · CSAT

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

Explanation

To calculate the time required to download software, we need two pieces of information: the total size of the software and the rate at which it can be transferred.

– **Statement I alone**: Provides only the size of the software (12 megabytes). Without knowing the transfer rate, we cannot determine the time. Thus, Statement I alone is insufficient.
– **Statement II alone**: Provides only the transfer rate (2.4 kilobytes per second). Without knowing the size of the software, we cannot determine the time. Thus, Statement II alone is insufficient.

– **Combining both statements**: We have the software size (12 megabytes) and the transfer rate (2.4 kilobytes per second). To calculate the time, we need to convert units to be consistent. Assuming 1 megabyte = 1000 kilobytes (a common simplification in CSAT, though technically 1024 KB):
Software size = 12 MB = 12 * 1000 KB = 12000 KB.
Transfer rate = 2.4 KB/s.
Time = Total Size / Transfer Rate = 12000 KB / 2.4 KB/s = 5000 seconds.

Since a unique time can be calculated using both statements together, but not individually, option (C) is correct. This question tests data sufficiency in a practical context.

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