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If -|x| = b, where b is a non-zero integer, which of the following statements can be true?

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by BTGmoderatorDC » Fri May 01, 2020 1:21 am

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B

C

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E

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Difficulty—

If -|x| = b, where b is a non-zero integer, which of the following statements can be true?

I. b < 0

II. x < -b

III. x > b


A) I only
B) II only
C) III only
D) I & II only
E) I, II & III


OA E

Source: e-GMAT
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Re: If -|x| = b, where b is a non-zero integer, which of the following statements can be true?

by Jay@ManhattanReview » Fri May 01, 2020 4:34 am
BTGmoderatorDC wrote: ↑
Fri May 01, 2020 1:21 am
 If -|x| = b, where b is a non-zero integer, which of the following statements can be true?

I. b < 0

II. x < -b

III. x > b

A) I only
B) II only
C) III only
D) I & II only
E) I, II & III

OA E

Source: e-GMAT
So, we have –|x| = b. Since |x| is a non-negative number and it is, –|x| must be a non-positive number. However since b is a non-zero integer, we have –|x| a negative integer. This implies that b is a negative integer.

Let's take each statement one by one.

I. b < 0: This a must be true statement.

II. x < –b: This can be true. Say for example x = b = –1; thus, –b = 1, so we have –1 < 1. A valid result.

III. x > b: This can be true. Say for example x = 1 and b = –1; thus, 1 > –1. A valid result.

So all statements can be true.

The correct answer: E

Hope this helps!

-Jay
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Re: If -|x| = b, where b is a non-zero integer, which of the following statements can be true?

by Scott@TargetTestPrep » Sun May 03, 2020 5:23 am
BTGmoderatorDC wrote: ↑
Fri May 01, 2020 1:21 am
 If -|x| = b, where b is a non-zero integer, which of the following statements can be true?

I. b < 0

II. x < -b

III. x > b


A) I only
B) II only
C) III only
D) I & II only
E) I, II & III


OA E

Source: e-GMAT
Since b is a non-zero integer, x is also a non-zero integer. In that case, |x| is positive and -|x| is negative. Since b = -|x|, b is also negative. So statement I is true.

Now, if x = -1, then b = -1, and -b = 1. Since -1 < 1, we see that II can be true. If x = 1, then b = -1 and x > b. We see that Statement III can be true as well.

Answer: E

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