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Is x> 0? (1) |x|-x = 0

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Is x> 0? (1) |x|-x = 0  [#permalink]

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New post Updated on: 01 Aug 2015, 10:21
1
5
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A
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E

Difficulty:

  55% (hard)

Question Stats:

52% (01:08) correct 48% (01:00) wrong based on 118 sessions

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Is x> 0?
(1) |x|-x = 0
(2) \(x ^ 3-x ^ 2\) = 0

Originally posted by pirimidin on 01 Aug 2015, 10:08.
Last edited by ENGRTOMBA2018 on 01 Aug 2015, 10:21, edited 3 times in total.
Edited the question and the topic, added the OA and formatted the question
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Is x> 0? (1) |x|-x = 0  [#permalink]

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New post 01 Aug 2015, 10:20
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pirimidin wrote:
Is x> 0?
(1) |x|-x = 0
(2) \(x^3-x^2\) = 0


Please format the question and the topic properly.

Add the OA to complete the question. Read the rules for posting at the location http://gmatclub.com/forum/rules-for-pos ... 33935.html

As for the question,

Question asks : is x>0?

Per statement 1, |x| = x --> x \(\geq\) 0. Thus x = 0 or x >0. This statement is thus not sufficient to answer whether x>0.

Per statement 2, x^3-x^2 = 0 ---> x^2(x-1) = 0 ---> either x = 0 or x =1 . Thus this statement as well is not sufficient to answer whether x>0.

Combining, we see that both x =0 and x =1 satisfy both the equations and give a "yes" and "no" respectively to the question is x>0 . Thus, both the statements are not sufficient as well.

E is the correct answer.
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Re: Is x> 0? (1) |x|-x = 0  [#permalink]

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New post 01 Aug 2015, 12:01
Hi pirimidin,

This question can be solved in a few different ways. While you can approach this conceptually (or by taking an Algebraic approach), it can be handled rather easily by TESTing VALUES.

We're asked if X is greater than 0. This is a YES/NO question.

Fact 1: |X| - X = 0

IF....
X = 0
The answer to the question is NO.

IF....
X = 1
The answer to the question is YES.
Fact 1 is INSUFFICIENT.

Fact 2: X^3 - X^2 = 0

IF....
X = 0
The answer to the question is NO.

IF....
X = 1
The answer to the question is YES.
Fact 2 is INSUFFICIENT.

Combined, we already have a TEST that fits both Facts and gives us a NO answer (X = 0) and one that gives us a YES answer (X = 1). Thus, no more work is needed.
Combined, INSUFFICIENT.

Final Answer:

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

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New post 06 Jun 2019, 04:57
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Is x> 0? (1) |x|-x = 0   [#permalink] 06 Jun 2019, 04:57
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