GATE CE 2026 Set 2 — Question 5
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General Aptitude → Analytical Aptitude → Deduction & Induction
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Question
Consider the following statements about four numbers:
(S1) The average of the four numbers is 25
(S2) Each number is at most 40
(S3) Each number is at least 20
Choose the option that is necessarily correct.
(S1) The average of the four numbers is 25
(S2) Each number is at most 40
(S3) Each number is at least 20
Choose the option that is necessarily correct.
Correct answer
(C) (S1) and (S3) together imply (S2)
Solution
Let the four numbers be .
(S1)
(S2)
(S3) Evaluating the options:
(A) If (S1) and (S2) are true, can we violate (S3)? Yes. If , then , which is not .
(B) If (S2) and (S3) are true, the average can be any value between 20 and 40. It is not necessarily 25.
(C) If (S1) and (S3) are true, then for any number, say :
. Since , their sum is at least 60. Thus, . This applies to all four numbers, so (S2) is necessarily true.
(D) (S1) alone does not restrict the numbers to be .Therefore, (S1) and (S3) together imply (S2).
(S1)
(S2)
(S3) Evaluating the options:
(A) If (S1) and (S2) are true, can we violate (S3)? Yes. If , then , which is not .
(B) If (S2) and (S3) are true, the average can be any value between 20 and 40. It is not necessarily 25.
(C) If (S1) and (S3) are true, then for any number, say :
. Since , their sum is at least 60. Thus, . This applies to all four numbers, so (S2) is necessarily true.
(D) (S1) alone does not restrict the numbers to be .Therefore, (S1) and (S3) together imply (S2).
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