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GATE 2026 MT – Question 5

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 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 fixes the sum of the four numbers at $4\times25=100$. Under S3, any three sum to at least $3\times20=60$, so the remaining number is at most $100-60=40$. Thus S1 and S3 imply S2, **C**.

The other implications fail. For A and D, the numbers 40, 40, 20, 0 satisfy S1 and S2 but violate S3. For B, four numbers equal to 20 satisfy S2 and S3 but have average 20.