GATE ME 2026 Set 1 — Question 5
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General Aptitude → Analytical Aptitude → Numerical Relations & Reasoning
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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 20Choose the option that is necessarily correct.
(S2) Each number is at most 40
(S3) Each number is at least 20Choose the option that is necessarily correct.
Correct answer
(C) (S1) and (S3) together imply (S2)
Solution
Let the four numbers be .
(S1) .
(S2) .
(S3) .To check if (S1) and (S3) imply (S2):
If , then to maximize one number (say ), we must minimize the others. Let .
From (S1), .
Since the maximum possible value for any number is 40, it follows that all numbers must be , which is statement (S2). Thus, (S1) and (S3) together imply (S2).
(S1) .
(S2) .
(S3) .To check if (S1) and (S3) imply (S2):
If , then to maximize one number (say ), we must minimize the others. Let .
From (S1), .
Since the maximum possible value for any number is 40, it follows that all numbers must be , which is statement (S2). Thus, (S1) and (S3) together imply (S2).
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