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# If -|x| = b, where b is a non-zero integer, which of the following sta

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Manager
Joined: 13 May 2017
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Location: Finland
Concentration: Accounting, Entrepreneurship
GMAT 1: 530 Q42 V22
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WE: Account Management (Entertainment and Sports)
If -|x| = b, where b is a non-zero integer, which of the following sta  [#permalink]

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27 Nov 2018, 14:11
6
00:00

Difficulty:

95% (hard)

Question Stats:

33% (01:02) correct 67% (01:15) wrong based on 126 sessions

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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 and II only
E. I, II, and III
Senior Manager
Joined: 15 Feb 2018
Posts: 256
Re: If -|x| = b, where b is a non-zero integer, which of the following sta  [#permalink]

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27 Nov 2018, 18:57
Substitute in numbers
-|2|=-2 or -|-2|=-2. We can't use 0 as x or b due to the original condition.

I) The negative sign is outside of the absolute value sign. Thus, the negative is applied to a positive number. B is negative. b<0.
II) 2<--2(x) as they are equal; -2<--2 (o)
III) 2>-2(o); -2>-2(x) as they are equal
Manager
Joined: 14 Jun 2018
Posts: 223
If -|x| = b, where b is a non-zero integer, which of the following sta  [#permalink]

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27 Nov 2018, 22:51
b can be any integer other than 0.
Case 1 : If x > 0 , b is < 0
Case 2 : If x < 0 , b is < 0

Statement I is always true.
Statement II can be true in case 2 but not in case 1
Statement III can be true in case 1 but not in case 2

Manager
Joined: 27 Nov 2015
Posts: 95
Re: If -|x| = b, where b is a non-zero integer, which of the following sta  [#permalink]

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07 Dec 2018, 20:25
3 conditions

1. b obviously can take any value
2. b=-1, x=-1 results in -|x|=b, -1=-1 and satisfies x<-b
3. b=-1, x=1 results in -|x|=b, -1=-1 and satisfies x>b
Re: If -|x| = b, where b is a non-zero integer, which of the following sta   [#permalink] 07 Dec 2018, 20:25
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