2. 外语
  3. Is xy

Is xy

admin2022-10-18  47
问题 Is xy<6?
(1) x<3andy<2.
(2) 1/22 < 64.
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B
解析 (1)    Given that x < 3 and y < 2, it is not possible to determine whether or not xy < 6. For example, if x = 1 and y = 1, then x < 3, y < 2, and xy=1. However, if x = -3 and y = -3, then x < 3, y < 2, and xy = 9; NOT sufficient.
(2)    Given that y2 < 64, then it easily follows that -8 < y < 8. Thus, we have 1/2 0 and y < 0, it follows that xy ≤ 0 < 6. Case 2: Suppose that 0 < y < 8. Then xy is the product of two positive quantities. Since the product of two positive quantities is greatest when each of the quantities is greatest, it follows that Since xy < 6 in each case, and the two cases include all possible values of x and y, we have xy < 6; SUFFICIENT.
The correct answer is B;
statement 2 alone is sufficient.
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