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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