Sunita cuts a sheet of paper into three pieces. Length of first piece is equal to the average of the three single digit odd prime numbers. Length of the second piece is equal to that of the first plus one-third the length of the third. The third piece is as long as the other two pieces together. The length of the original sheet of paper is
- (a) 13 units
- (b) 15 units
- (c) 16 units
- (d) 30 units ✓ UPSC's answer
Why the answer is (d)
• The single-digit odd prime numbers are 3, 5 and 7; their average is 5, so the first piece is 5 units long.
• Let the third piece be t units; the second piece is 5 + t/3.
• The third piece equals the other two together: t = 5 + 5 + t/3, so 2t/3 = 10 and t = 15.
• The pieces are 5, 10 and 15 units, so the original sheet was 30 units long, option (d).
Why the other options are wrong
- (a) 13 units
- 13 units is incorrect because the calculated lengths of the pieces are 5, 10, and 15, which sum to 30, not 13.
- (b) 15 units
- 15 units is incorrect because it equals only the length of the third piece, not the total length of the original sheet.
- (c) 16 units
- 16 units is incorrect because it does not match the sum of the derived piece lengths (5 + 10 + 15 = 30).
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2019, held on 2 June 2019. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.