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  3. Of the numbers q, r, s, and t, which is greatest?(1) The average (arithmetic me

Of the numbers q, r, s, and t, which is greatest?(1) The average (arithmetic me

游客2025-02-27  26
问题 Of the numbers q, r, s, and t, which is greatest?
(1) The average (arithmetic mean) of q and r is s.
(2) The sum of q and r is t.
选项 A、Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B、Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C、BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D、EACH statement ALONE is sufficient.
E、Statements (1) and (2) TOGETHER are NOT sufficient.
答案 E
解析 Determine which of the numbers q, r, s, and t is the greatest.
(1)    Given that (q+r)/2= s, then s is halfway between q and r and q ≤ s ≤ r or r ≤ s ≤ q. So it is possible that q is the greatest, it is possible that r is the greatest, and it is possible that t is the greatest since no information is given about t, NOT sufficient.
(2)    Given that t = q + r, it is not possible to determine which of q, r, s, and t is greatest. For example, if q - 1, r - 5, s = 3, and t = 6, then t is the greatest, but if q = 1, r = -5, s = -2, and t = -4, then q is the greatest; NOT sufficient.
Taking (1) and (2) together, it is still not possible to determine which of q, r, s, and t is greatest because the examples used to show that (2) is not sufficient satisfy (1) also.
The correct answer is E;
both statements together are still not sufficient.
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