题目信息
Is x less than y ?
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：
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Algebra Inequalities
Determine if x < y is true.
If x − y + 1 < 0, then x < y − 1. Since y − 1 < y, it follows that x < y; SUFFICIENT. If x = 1 and y = 2, then x − y − 1 = − 2 < 1 and x < y is true. However, if x = 1.5 and y = 1, then x − y − 1 = −0.5 < 1 and x < y is not true; NOT sufficient.
The correct answer is A;statement 1 alone is sufficient.
Tip In (1), manipulating the given inequality leads to x < y − 1, which leads directly to x < y since y − 1 < y. This is not the case in (2), where manipulating the given inequality leads to x < y + 1 but not to x < y since y + 1 > y. Examples can then be used to verify that x < y can be, but doesn't have to be, true.
Determine if x < y is true.
If x − y + 1 < 0, then x < y − 1. Since y − 1 < y, it follows that x < y; SUFFICIENT. If x = 1 and y = 2, then x − y − 1 = − 2 < 1 and x < y is true. However, if x = 1.5 and y = 1, then x − y − 1 = −0.5 < 1 and x < y is not true; NOT sufficient.
The correct answer is A;statement 1 alone is sufficient.
Tip In (1), manipulating the given inequality leads to x < y − 1, which leads directly to x < y since y − 1 < y. This is not the case in (2), where manipulating the given inequality leads to x < y + 1 but not to x < y since y + 1 > y. Examples can then be used to verify that x < y can be, but doesn't have to be, true.
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