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GATE 2026 CE (CE2) – Question 5

General Aptitude · Analytical Aptitude: Logical Reasoning and Deduction · 1 mark · Multiple choice

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.

  1. (S1) and (S2) together imply (S3)
  2. (S2) and (S3) together imply (S1)
  3. (S1) and (S3) together imply (S2)
  4. (S1) implies (S3)

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Correct answer: (C) (S1) and (S3) together imply (S2)

Explanation

S1 means the four numbers add up to 100. With S3 each number is at least 20, so any three of them add up to at least 60, which leaves at most 100 - 60 = 40 for the fourth. So every number is at most 40, which is S2, and option C holds. Option A fails for 40, 40, 20, 0. Option B fails for 20, 20, 20, 20, whose average is 20. Option D fails for the same numbers as option A.