Vincen wrote:What is the value of x?

(1) 4 < x < 6
(2) |x| = 4x − 15

Target question: What is the value of x?

Statement 1: 4 < x < 6
ASIDE: Some students will assume that x is an integer and incorrectly conclude that x must equal 5. This is a common mistake on the GMAT.
The truth of the matter is that there are infinitely many values of x that satisfy statement 1.
For example x could equal 4.1, or x could equal 4.132 or 4.54 or 5 or 5.4211 etc
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: |x| = 4x − 15
There are 3 steps to solving equations involving ABSOLUTE VALUE:
1. Apply the rule that says: If |x| = k, then x = k and/or x = -k
2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots

Given: |x| = 4x − 15
So, there are two possible cases to examine:
Case a: x = 4x − 15. When we solve this equation, we get: x = 5
Case b: x = -(4x − 15). When we solve this equation, we get: x = 3
At this point, it LOOKS LIKE there are two possible values of x. However, we haven't performed step 3 yet: Plug solutions into original equation to check for extraneous roots

Let's do that.
Case a: Plug x = 5 into original equation to get: |5| = 4(5) − 15
Simplify right side of equation to get: |5| = 5
This works, so x = 5 IS a possible value of x

Case b: Plug x = 3 into original equation to get: |3| = 4(3) − 15
Simplify right side of equation to get: |3| = -3
This DOES NOT work, so x = 3 is NOT a possible value of x

Since there is only ONE possible value of x (x = 5), statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent