Discussion
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.
Answer: C
The necessarily correct option is (S1) and (S3) together imply (S2).
If the average is 25, the four numbers add to 100. If each is at least 20, any three of them add to at least 60, so the fourth is at most \(100 - 60 = 40\). That is (S2).
The others fail. (S1) and (S2) allow 40, 40, 20, 0, which breaks (S3). (S2) and (S3) allow 20, 20, 20, 20, whose average is 20, not 25. And (S1) alone allows 100, 0, 0, 0, so it does not imply (S3).
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