Is x < 0 ? (1) |x - 5| = 7x + 2 (2) |x + 5| = |4x + 5|

Is x < 0?


(1) |x - 5| = 7x + 2

If x <= 5, then x - 5 <= 0, thus |x - 5| = -(x - 5). So, in this case we'd have -(x - 5) = 7x + 2 --> x = 3/8.

If x > 5, then x - 5 > 0, thus |x - 5| = x - 5. So, in this case we'd have x - 5 = 7x + 2 --> x = -7/6. Discard this root because it is not in the range we are considering (x > 5).

Thus, x = 3/8. Sufficient.


(2) |x + 5| = |4x + 5|.

Square (we can safely do that since both sides are non-negative): x^2 + 10x + 25 = 16x^2 + 40x + 25 --> x(x + 2) = 0 --> x = 0 or x = -2. Not sufficient.

Technically answer should be A, as statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

But even though formal answer to the question is A, this is not a realistic GMAT question, as: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. But the statements above contradict each other:
From (1) x = 3/8 and from (2) x = 0 or x = -2. The statements clearly contradict each other.

So, the question is flawed. You won't see such a question on the test.