Two Statements S1 and S2 are given below followed by a Question : S1 : There are not more than two figures on any page of a 51-page book. S2 : There is at least one figure on every page. Question : Are there more than 100 figures in that book? Which one of the following is correct in respect of the above Statements and the Question?
- (a) Both S1 and S2 are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.
- (b) S1 alone is sufficient to answer the Question.
- (c) S1 and S2 together are not sufficient to answer the Question. ✓ UPSC's answer
- (d) S2 alone is sufficient to answer the Question.
Why the answer is (c)
• S1 states that no page has more than 2 figures, so the maximum total is 51 pages × 2 figures = 102 figures.
• S2 states that every page has at least 1 figure, so the minimum total is 51 pages × 1 figure = 51 figures.
• Combining S1 and S2, the total number of figures lies between 51 and 102 (inclusive).
• The question asks if there are *more than* 100 figures.
• Since the total could be 101 or 102 (Yes) or 51 to 100 (No), the answer is not uniquely determined.
• Therefore, even together, the statements are not sufficient to answer the question definitively.
Why the other options are wrong
- (a) Both S1 and S2 are sufficient to answer the Question, but neither S1 alone nor S2 alone…
- The statements together do not provide a unique answer because the total could be 100 or less, or 101 or more.
- (b) S1 alone is sufficient to answer the Question.
- S1 alone only gives a maximum of 102 figures but does not specify the minimum, so the total could be 0 to 102, making the answer indeterminate.
- (d) S2 alone is sufficient to answer the Question.
- S2 alone only gives a minimum of 51 figures but does not specify the maximum, so the total could be 51 or much higher, making the answer indeterminate.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.