nave 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 etcSince we cannot answer the

target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: |x| = 4x − 15There are 3 steps to solving equations involving ABSOLUTE VALUE:

1. Apply the rule that says:

If |x| = k, then x = k and/or x = -k2. 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 = 5Case 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:

Cheers,

Brent

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Brent Hanneson – Founder of gmatprepnow.com