Determining the relative height of individuals from comparative statements
Question
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.
Options
The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
The Question can be answered by using either Statement alone
The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
The Question cannot be answered even by using both the Statements together
Explanation
We are given: p + q + r = 50, and q = 16 is the minimum value. Substitute q=16 into the total sum: p + r = 50 - 16 = 34.
Statement I states the cost of p is not more than r, meaning p \le r. Multiple integer solutions satisfy p + r = 34 under this rule (e.g., p=16, r=18 or p=17, r=17). Insufficient.
Statement II states the cost of r is not more than p, meaning r \le p. Similarly, this creates multiple combinations. Insufficient.
Combine both statements: We have both p \le r and r \le p. The only mathematical way both inequalities can hold simultaneously is if the two variables are exactly equal: p = r. Substitute p = r back into the sum equation: p + p = 34 \implies 2p = 34 \implies p = 17. This delivers a single unique value for p, making both statements necessary together.
Answer: (c).
Question details
Year
2024
Paper
CSAT
Question
Q69
Section
Logical & Analytical Reasoning
Sub-topic
Ranking & Order
Type
Factual single
Difficulty
Easy
Source hint
Logical comparison puzzle
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