When |x|>1 and |x-3|>1, which of the following is contained in the sco : Problem Solving (PS)

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When |x|>1 and |x-3|>1, which of the following is contained in the sco

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Math Revolution GMAT Instructor

Joined: 16 Aug 2015

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When |x|>1 and |x-3|>1, which of the following is contained in the sco [#permalink]

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21 Jul 2017, 01:08

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Difficulty:

35% (medium)

Question Stats:

70% (01:40) correct

30% (01:57) wrong

based on 250 sessions

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When |x|>1 and |x-3|>1, which of the following is contained in the scope of x?

A. -0.5
B. 0
C. 0.5
D. 1.5
E. 2.5

Spoiler: OA

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Re: When |x|>1 and |x-3|>1, which of the following is contained in the sco [#permalink]

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21 Jul 2017, 01:15

Going by the answer options, Only x = 1.5(Option D) is contained in the scope of x

When x=1.5, |x| = 1.5 > 1 and |x-3| = |1.5 - 3| = |-1.5| > 1
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Intern

Joined: 06 May 2014

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Re: When |x|>1 and |x-3|>1, which of the following is contained in the sco [#permalink]

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21 Jul 2017, 02:23

by simplifying modulus, x has following solutions:

X >1
X< -1
X<2
X>4

choice D satisfies 2nd and 3rd solution, so D.
try number line and plot if solutions make it messy.
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Math Revolution GMAT Instructor

Joined: 16 Aug 2015

Posts: 7236

GMAT 1: 760 Q51 V42

GPA: 3.82

Re: When |x|>1 and |x-3|>1, which of the following is contained in the sco [#permalink]

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23 Jul 2017, 18:29

==> |x|>1 becomes x<-1 or 1<x, and for |x-3|>1, you get x-3<-1 or 1<x-3 --> x<2 or 4<x. Then, what satisfies both becomes 1<x<2 or 4<x.

The answer is D.
Answer: D
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