GATE EC 2026 Set 1 — Question 2
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Question
The statements (S1), (S2), and (S3) pertain to the scores obtained by students in an exam. The maximum possible marks in the exam is 150.(S1) The highest score is 100.
(S2) The fourth highest score is 76.
(S3) There are at least four students whose scores are within 25 of each other.Which one of the following options is necessarily correct?
(S2) The fourth highest score is 76.
(S3) There are at least four students whose scores are within 25 of each other.Which one of the following options is necessarily correct?
Correct answer
(A) (S1) and (S2) together imply (S3)
Solution
Let the scores of the students in descending order be .
1.Statement (S1) states that the highest score is 100, so .
2.Statement (S2) states that the fourth highest score is 76, so .
3.If both (S1) and (S2) are true, then we have .
4.The range of the scores for the top four students is .
5.Since all four students () have scores between 76 and 100 inclusive, the difference between any two of their scores is at most 24.
6.Since , these four students' scores are necessarily within 25 of each other.
7.This satisfies statement (S3), which says there are at least four students whose scores are within 25 of each other.
Therefore, (S1) and (S2) together imply (S3). Option (A) is correct.Continue learning with Success Tracker
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