UPSC CSE 2024 · PYQ · Data Sufficiency / Logic · medium
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 in ₹ 50. The cost of article q is ₹ 16 which is the least. Question: What is the cost of article p? Statement-I: The cost of p is not more than the cost of r. Statement-II: The cost of r is not more than the cost 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✓ Correct
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
Explanation
Total cost of p, q, r is ₹50; q = ₹16 (least), so p + r = ₹34, with p, r > 16 each (since q is least and presumably amounts are positive integers or simply that q is strictly the least). Statement I: p ≤ r. With p + r = 34 and p > 16 and p ≤ r, possible values: p = 17, r = 17 (but then p = r); if amounts must be distinct, p ≤ r with p > 16 gives p in {17}, r = 17. Hmm, but if equal, both 17 satisfy p ≤ r. So p = 17. Statement II: r ≤ p. With p + r = 34, r > 16, r ≤ p gives r = 17, p = 17. So p = 17. Each statement alone yields p = 17 (since both p and r exceed 16, and their sum is 34, forcing both = 17). Hence either statement alone is sufficient. The answer is (b).
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