BTGmoderatorDC wrote: ↑Tue Mar 15, 2022 6:22 pm
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
Brent Hanneson - Creator of GMATPrepNow.com
