Consider the following statements about four numbers: (S1) The average of the…
2026
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. (S1) and (S3) together imply (S2) — Let the four numbers be a, b, c, and d. Statement (S1) gives a+b+c+d=100. If (S3) also holds, then each number is at least 20. For any one number, such as a,…
- A.
(S1) and (S2) together imply (S3)
- B.
(S2) and (S3) together imply (S1)
- C.
(S1) and (S3) together imply (S2)
- D.
(S1) implies (S3)
Attempted by 33 students.
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Correct answer: C
Let the four numbers be a, b, c, and d. Statement (S1) gives a+b+c+d=100. If (S3) also holds, then each number is at least 20. For any one number, such as a, we have a = 100-(b+c+d) <= 100-3(20)=40, so each number is at most 40. Thus (S1) and (S3) together imply (S2). The remaining implications require additional assumptions beyond the stated conditions.