2024 CSAT, all questions
UPSC Prelims 2024 · CSAT
Question 59: Data Interpretation
A Question is given followed by two Statements I and II. Consider the Question and the Statements.
- QuestionWhat are the values of m and n, where m and n are natural numbers?
- Statement–Im + n > mn and m > n.
- Statement–IIThe product of m and n is 24.
Which one of the following is correct in respect of the above Question and the Statements?
aThe Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
bThe Question can be answered by using either Statement alone
cThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
dThe Question cannot be answered even by using both the Statements together
AnswerUPSC’s answer is (c).
Statement I: m + n > mn means (m − 1)(n − 1) < 1, which for natural numbers means m = 1 or n = 1; with m > n, n = 1 and m is any number above 1, so the pair is not unique. Statement II: mn = 24 has several pairs. Together: n = 1 and mn = 24 give m = 24. So both statements are needed, and neither alone is enough.
Why each option is right or wrong
- (a) Wrong. Neither statement alone fixes m and n.
- (b) Wrong. Statement I leaves m open and statement II gives many pairs.
- (c) Right. Together n = 1 and m = 24.
- (d) Wrong. Together they give a unique answer.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2024, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.