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# Is |x|>2? 1) x>2 2) x(x-2)>0

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8017
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Is |x|>2? 1) x>2 2) x(x-2)>0  [#permalink]

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03 Nov 2016, 01:30
3
2
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:05) correct 33% (01:09) wrong based on 132 sessions

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Is |x|>2?

1) x>2
2) x(x-2)>0

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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Re: Is |x|>2? 1) x>2 2) x(x-2)>0  [#permalink]

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03 Nov 2016, 01:41
1) x>2

so |x| will be greater than 2.
Sufficient

2) x(x-2)>0

x<0 & x>2

x<0, say x = -1, |x|<2
x<0, say x = -3, |x|>2
x>0, say x =2.5, |x|>2

Not Sufficient.

Option A
Intern
Joined: 23 Oct 2016
Posts: 32
Re: Is |x|>2? 1) x>2 2) x(x-2)>0  [#permalink]

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03 Nov 2016, 03:27
1
MathRevolution wrote:
Is |x|>2?

1) x>2
2) x(x-2)>0

Basically, we have to know if x>2 or x<-2

Statement1: x>2 => sufficient

Statement2: for x(x-2) to be positive, we have 2 different scenarios:

Scenario1: x>0 and x>2 => x>2 => sufficient
Scenario2: x<0 and x<2 => x<0 => x can be -1, then lxl is not greater than 2 and x can be -5, then lxl>2
=> not sufficient.

IF YOU'RE GOING THROUGH HELL. KEEP GOING.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Is |x|>2? 1) x>2 2) x(x-2)>0  [#permalink]

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07 Nov 2016, 00:52
==>In the case of the inequality, if the range of the question includes the range of the condition, it is important that the condition is sufficient. In the original condition, you get 1 variable(x), so D is highly likely to be the answer. The question is x<-2 or 2<x?
In the case of 1), from x>2, the range of the question includes the range of the condition, hence sufficient.
In the case of 2), from x<0 or 2<x, the range of the question does not include the range of the condition, hence not sufficient. The answer is A.

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Re: Is |x|>2? 1) x>2 2) x(x-2)>0  [#permalink]

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01 Feb 2018, 21:58
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Re: Is |x|>2? 1) x>2 2) x(x-2)>0   [#permalink] 01 Feb 2018, 21:58
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