题目信息
Is −3 ≤ x ≤ 3 ?
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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已选答案：
正确答案：
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Algebra Properties of numbers; Inequalities
Given that x2 + y2 = 9, if x < −3 or if x > 3, then x2 > 9 and y2 < 0, which is not possible. Therefore, −3 ≤ x ≤ 3; SUFFICIENT. Given that x2 + y ≤ 9, if x = 0 and y = 4, then x2 + y ≤ 9, and −3 ≤ x ≤ 3 is true. However, if x = 4 and y = −7, then x2 + y ≤ 9, and −3 ≤ x ≤ 3 is not true; NOT sufficient.
The correct answer is A;
statement 1 alone is sufficient.
Given that x2 + y2 = 9, if x < −3 or if x > 3, then x2 > 9 and y2 < 0, which is not possible. Therefore, −3 ≤ x ≤ 3; SUFFICIENT. Given that x2 + y ≤ 9, if x = 0 and y = 4, then x2 + y ≤ 9, and −3 ≤ x ≤ 3 is true. However, if x = 4 and y = −7, then x2 + y ≤ 9, and −3 ≤ x ≤ 3 is not true; NOT sufficient.
The correct answer is A;
statement 1 alone is sufficient.
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