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.
_________________

New to the Math Forum?

Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:

GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:

PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.

What are GMAT Club Tests?

Extra-hard Quant Tests with Brilliant Analytics