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GMAT - Quant problem

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GMAT - Quant problem

by JSgmat » Sat Aug 09, 2014 3:54 pm
Hello everyone, I wonder if you can help me with this problem.

Which of the following inequalities is equivalent to - 2 < x < 4 ?

(A) lx−2l <4
(B) lx−1l <3
(C) lx+1l<3
(D) lx+2l <4
(E) None of the above


The answer is B.

I do not get however why the answer could not be A as well.

Do you have an example that would make A false?

Thank you
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by Brent@GMATPrepNow » Sat Aug 09, 2014 4:03 pm
JSgmat wrote:
Which of the following inequalities is equivalent to - 2 < x < 4 ?

(A) |x − 2| < 4
(B) |x − 1| < 3
(C) |x + 1| < 3
(D) |x + 2| < 4
(E) None of the above
(A) |x − 2| < 4
This means that -4 < x - 2 < 4
Add 2 to all 3 parts to get: -2 < x < 6
Doesn't match. ELIMINATE A

Aside: You asked for a value that makes A an incorrect answer.
Well, x = 5 satisfies the answer choice A inequality |x − 2| < 4, but x = 5 does NOT satisfy the given inequality - 2 < x < 4

(B) |x − 1| < 3
This means that -3 < x - 1 < 3
Add 1 to all 3 parts to get: -2 < x < 4
Perfect match!

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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