题目信息
Is xy < 6 ?
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.
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正确答案：
B:Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Algebra Inequalities
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. Given that y2 < 64, then it easily follows that −8 < y < 8. Thus, we have
and −8 < y < 8. We consider two cases, according to the sign of y. Case 1: Suppose that −8 < y ≤ 0. Since x > 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 xy < 
< 6.
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.
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. Given that y2 < 64, then it easily follows that −8 < y < 8. Thus, we have
and −8 < y < 8. We consider two cases, according to the sign of y. Case 1: Suppose that −8 < y ≤ 0. Since x > 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 xy < < 6.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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