In a test, Randhir obtained more marks than the total marks obtained by Kunal and Debu. The total marks obtained by Kunal and Shankar are more than those of Randhir. Sonal obtained more marks than Shankar. Neha obtained more marks than Randhir. Who amongst them obtained highest marks?
- (a) Randhir
- (b) Neha
- (c) Sonal
- (d) Data are inadequate ✓ UPSC's answer
Why the answer is (d)
• From the first two statements, Kunal + Debu < Randhir < Kunal + Shankar, so Shankar > Debu. Neha > Randhir and Sonal > Shankar.
• Nothing fixes Sonal against Neha. For example, Randhir 100, Kunal 90, Debu 5, Shankar 11, Sonal 12, Neha 101 makes Neha the highest; Randhir 100, Kunal 10, Debu 5, Shankar 95, Sonal 120, Neha 101 makes Sonal the highest.
• Both cases satisfy every condition, so the data are inadequate, option (d).
Why the other options are wrong
- (a) Randhir
- Neha obtained more marks than Randhir, so Randhir cannot have the highest marks.
- (b) Neha
- Sonal's marks relative to Neha are unknown; Sonal could have fewer marks than Neha.
- (c) Sonal
- Neha's marks relative to Sonal are unknown; Neha could have fewer marks than Sonal.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2017, held on 18 June 2017. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.