题目信息
If y = 2x + 1, what is the value of y − x ?
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：
D:EACH statement ALONE is sufficient.
Algebra Equations; Exponents
Given that 22x + 2 = 64 = 26, it follows that 2x + 2 = 6. Therefore, x = 2 and y − x = 22 + 1 − 2 = 6; SUFFICIENT. From the given information we have y = 2x + 1 and from (2) we have y = 22x−1. Therefore, 2x + 1 = 22x−1, and hence x + 1 = 2x − 1. Solving for x gives x = 2, and thus y − x = 22 + 1 − 2 = 6; SUFFICIENT.
The correct answer is D;each statement alone is sufficient.
Given that 22x + 2 = 64 = 26, it follows that 2x + 2 = 6. Therefore, x = 2 and y − x = 22 + 1 − 2 = 6; SUFFICIENT. From the given information we have y = 2x + 1 and from (2) we have y = 22x−1. Therefore, 2x + 1 = 22x−1, and hence x + 1 = 2x − 1. Solving for x gives x = 2, and thus y − x = 22 + 1 − 2 = 6; SUFFICIENT.
The correct answer is D;each statement alone is sufficient.
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