If x is a positive number, what is the value of x ?

[BTGmoderatorDC]

If x is a positive number, what is the value of x ?

(1) |x – 2| = 1
(2) x^2 = 4x -3


OA E

Source: GMAT Prep

[Brent@GMATPrepNow]

If x is a positive number, what is the value of x ?

(1) |x – 2| = 1
(2) x² = 4x - 3

OA E

Source: GMAT Prep

Given: x is a positive number

Target question: What is the value of x ?

Statement 1: |x – 2| = 1
So, EITHER x - 2 = 1 OR x - 2 = -1
If x - 2 = 1, then x = 3
If x - 2 = -1, then x = 1
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x² = 4x - 3
Rearrange the terms of this quadratic equation so that the equation is set equal to zero: x² - 4x + 3 = 0
Factor to get: (x - 3)(x - 1) = 0, which means either x = 3 or x = 1
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that either x = 3 or x = 1
Statement 2 tells us that either x = 3 or x = 1
So, when we combine the two statements, we still have two possible values of x.
Since we still can’t answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent