GATE 2026 XH2 (English) – Question 24
In a cricket match amongst 7 friends, named P1 – P7, P1 scored maximum individual runs of 25 and P7 scored minimum individual run of 0. No two friends had the same score. The median and average runs scored were 15 and 12.57, not necessarily in that order. Two players, P2 and P3, who scored more than median but less than maximum, scored less than 40 runs together. One player scored double the sum of non-zero scores of two players.
What could be the possible value(s) of the second highest score?
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Correct answer: (B) 20; (C) 21
Explanation
The median of 7 scores is a score, so the median is 15 and the average is $12.57 = 88/7$, which makes the total 88. The scores in order are $0 < a < b < 15 < c < d < 25$ with $a + b + c + d = 48$. P2 and P3 are $c$ and $d$, with $c + d < 40$, so $a + b > 8$. A score that is twice the sum of two non-zero scores is at most 25, so those two scores add to at most 12; they must be $a$ and $b$ with $9 \le a + b \le 12$, and the doubled score is $c$ or $d$. For $a + b = 9$ the doubled score is 18 and then $c + d = 39$ gives 18 and 21. For $a + b = 10$ it is 20 and $c + d = 38$ gives 18 and 20. For $a + b = 11$ or 12 the other score would be 15 or 12, which is not allowed. So the second highest score is 21 or 20.