BTGModeratorVI wrote: ↑Mon Sep 14, 2020 8:39 am
If (x - 2.5)(x + 0.5) = 4, what is the value of x?
(1) (x+1.5)(x−1.5)=0
(2) (x−3.5)(x+1.5)=0
Answer: [spoiler]A
[/spoiler]Source: Economist GMAT
Target question: What is the value of x?
Given: (x−2.5)(x+0.5) = 4
This information is HUGE, since
it tells us the only 2 possible values of x
Given: (x−2.5)(x+0.5) = 4
Expand and simplify to get: x² - 2x - 1.25 = 4
Subtract 4 from both sides: x² - 2x - 5.25 = 0
Multiply both sides by 4 to get: 4x² - 8x - 21 = 0
Factor to get: (2x + 3)(2x - 7) = 0
If 2x + 3 = 0, then x = -3/2 = -1.5
If 2x - 7 = 0, then x = 7/2 = 3.5
So,
EITHER x = -1.5 OR x = 3.5
So, which value is it?
Statement 1: (x+1.5)(x−1.5) = 0
This tells us that EITHER x = -1.5 OR x = 1.5
Since we already know that
EITHER x = -1.5 OR x = 3.5, we can be certain that
x = -1.5
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: (x − 3.5)(x+1.5) = 0
This tells us that EITHER x = -1.5 OR x = 3.5
Since we already knew that
EITHER x = -1.5 OR x = 3.5,
this statement provides no new information.
So, all we can conclude from this is that
EITHER x = -1.5 OR x = 3.5
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
