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 ✓ UPSC's answer
- (d) The Question cannot be answered even by using both the Statements together
Why the answer is (c)
• The total cost of articles p, q, and r is ₹50, and the cost of q is given as ₹16.
• Subtracting the cost of q from the total gives the combined cost of p and r as ₹34 (50 - 16 = 34).
• Statement I states that the cost of p is not more than r (p ≤ r), which allows multiple possibilities such as p=10, r=24 or p=17, r=17, so it is insufficient alone.
• Statement II states that the cost of r is not more than p (r ≤ p), which also allows multiple possibilities such as r=10, p=24 or r=17, p=17, so it is insufficient alone.
• Combining both statements implies that p ≤ r and r ≤ p, which mathematically means p = r.
• Since p + r = 34 and p = r, we get 2p = 34, resulting in p = 17, making the question answerable only when both statements are used together.
Why the other options are wrong
- (a) The Question can be answered by using one of the Statements alone, but cannot be answered…
- Neither statement alone provides a unique value for p, as both allow for a range of possible prices for p and r that sum to 34.
- (b) The Question can be answered by using either Statement alone
- Using either statement alone results in multiple valid pairs for (p, r), so the price of p cannot be uniquely determined by just one statement.
- (d) The Question cannot be answered even by using both the Statements together
- The question can be answered by combining both statements, which together imply p = r, allowing the calculation of p as 17.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.