UPSC CSE Prelims 2024

Correct Option (B)

The problem provides the following information:

• The sum of the prices of three articles p, q, and r is ₹50: p + q + r = 50.
• The price of article q is ₹16, which is the least among the three: q = 16.

From this, we can deduce:

• Substituting q = 16 into the sum equation: p + 16 + r = 50, which simplifies to p + r = 34.
• Since q = 16 is the least price, it implies that p > q and r > q. Therefore, p > 16 and r > 16.
• Assuming prices are positive integers, the minimum possible integer value for p and r is 17.

Now, let's evaluate each statement:

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

• This can be expressed as p ≤ r.
• We have the conditions: p + r = 34, p ≥ 17, r ≥ 17, and p ≤ r.
• If p = 17, then r = 34 - 17 = 17. This satisfies p ≤ r (17 ≤ 17).
• If p were less than 17, it would violate p ≥ 17.
• If p were greater than 17, then r would be less than 17 (since p + r = 34), which would violate r ≥ 17.
• Thus, the only integer solution satisfying all conditions is p = 17 and r = 17.
• Therefore, Statement I alone is sufficient to determine the price of article p.

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

• This can be expressed as r ≤ p.
• We have the conditions: p + r = 34, p ≥ 17, r ≥ 17, and r ≤ p.
• If r = 17, then p = 34 - 17 = 17. This satisfies r ≤ p (17 ≤ 17).
• If r were less than 17, it would violate r ≥ 17.
• If r were greater than 17, then p would be less than 17 (since p + r = 34), which would violate p ≥ 17.
• Thus, the only integer solution satisfying all conditions is p = 17 and r = 17.
• Therefore, Statement II alone is sufficient to determine the price of article p.

Since both Statement I alone and Statement II alone are sufficient to answer the question, the question can be answered by using either statement alone.

Incorrect Options:

Option A is incorrect because the question can be answered by using either statement alone, not just one but not the other.

Option C is incorrect because the question can be answered by either statement alone; it is not necessary to use both statements together, nor is it true that it cannot be answered by either statement alone.

Option D is incorrect because the question can be definitively answered by using either statement alone, indicating that it is not unanswerable even with both statements.