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)
• Let R, K, D, S, and N represent the marks of Randhir, Kunal, Debu, Shankar, and Neha respectively.
• The condition 'Randhir obtained more marks than the total marks obtained by Kunal and Debu' implies R > K + D.
• The condition 'The total marks obtained by Kunal and Shankar are more than those of Randhir' implies K + S > R.
• Combining these, we know R is greater than K+D but less than K+S, which establishes that S > D, but does not fix the absolute value of S relative to R or N.
• We are given N > R and S > R (since K+S > R and K is positive, S must be less than R+K, but actually S could be less than R if K is large enough? No, K+S > R. If K is small, S > R. If K is large, S can be < R. Example: R=100, K=90, D=5 (100>95), S=11 (90+11=101>100). Here S < R. Another example: R=100, K=10, D=5 (100>15), S=95 (10+95=105>100). Here S > R.
• Since S can be either greater than or less than R, and we only know N > R, we cannot determine if N is greater than S or if S is greater than N.
• Therefore, the data is inadequate to determine who obtained the highest marks.
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.