What is the value of $x?$

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Thu Jul 30, 2020 11:38 am

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What is the value of $x?$

(1) $|x+2|=2|x−2|$
(2) $x>2$

[spoiler]OA=C[/spoiler]

Source: Princeton Review

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Source: Beat The GMAT — Data Sufficiency | Thu Jul 30, 2020 11:38 am

terminator12: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Tue Jul 28, 2020 9:01 pm

Re: What is the value of $x?$

by terminator12 » Thu Jul 30, 2020 5:48 pm

Statement 1:
We see 2 important points here: -2 and 2
let's make ranges about these points:
1) x < -2
- x - 2 = 2(-x + 2)
x = 6

2) -2 < x < 2
x + 2 = 2(-x + 2)
x = $\frac{2}{3}$

3) x + 2 = 2(x - 2)
x = 6

Hence, we have 2 different values of x. Hence, insufficient.

Statement 2:
Says x > 2
Clearly insufficient.

Statement 1 + 2:
We get x = 6
Hence, both statements are needed to find x.

Hope this helps!

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