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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7612
GMAT 1: 760 Q51 V42 GPA: 3.82

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Difficulty:   35% (medium)

Question Stats: 70% (01:13) correct 30% (01:29) wrong based on 94 sessions

### HideShow timer Statistics [Math Revolution GMAT math practice question]

If $$(|x|-2)(x-1)=0$$, then $$x=$$?

1) $$x>0$$
2) $$-1≤x≤1$$

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NUS School Moderator D
Joined: 18 Jul 2018
Posts: 985
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)

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1
The question can be broken down into two parts.
x-1 = 0. therefore x = 1.
|x|-2 = 0. therefore |x| = 2 or x = +2 or -2.
From statement 1: X can be 1 or 2. Hence insufficient.
From statement 2: X can only be 1. Hence sufficient.
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CEO  V
Joined: 12 Sep 2015
Posts: 3851
Re: If (|x|-2)(x-1)=0, then x=?  [#permalink]

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3
Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If $$(|x|-2)(x-1)=0$$, then $$x=$$?

1) $$x>0$$
2) $$-1≤x≤1$$

Target question: What is the value of x?

Given: (|x| - 2)(x - 1) = 0
This tells us that EITHER: |x| - 2 OR x - 1 = 0
If |x| - 2 = 0, then x = 2 OR x = -2
If x - 1 = 0, then x = 1

So, there are 3 possible values of x:
i. x = 2
ii. x = -2
iii. x = 1

Statement 1: x > 0
When we examine the 3 possible values of x, we see that two values are greater than 0
It COULD be the case that x = 2, or it COULD be the case that x = 1,
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: -1 ≤ x ≤ 1
When we examine the 3 possible values of x, we see that only one value satisfies statement 2 (x = 1)
So, it MUST be the case that x = 1
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7612
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If (|x|-2)(x-1)=0, then x=?  [#permalink]

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=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Original condition:
$$(|x|-2)(x-1)=0$$
=> $$|x| = 2$$ or$$x = 1$$
=> $$x = 2, x = -2$$ or $$x = 1$$

Since we have $$1$$ variable ($$x$$) and $$0$$ equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
By condition 1) ($$x > 0$$), the possible solutions are $$x = 1$$ and $$x = 2$$.
Since we don’t have a unique solution, condition 1) is not sufficient.

Condition 2)
By condition 2) ($$-1≤x≤1$$), the only possible solution is $$x = 1$$.
Since we have a unique solution, condition 2) is sufficient.

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Director  G
Joined: 20 Feb 2015
Posts: 790
Concentration: Strategy, General Management
Re: If (|x|-2)(x-1)=0, then x=?  [#permalink]

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MathRevolution wrote:
[Math Revolution GMAT math practice question]

If $$(|x|-2)(x-1)=0$$, then $$x=$$?

1) $$x>0$$
2) $$-1≤x≤1$$

from question we get
$$|x| =2$$
x= +2 or -2
or
x=1

1) $$x>0$$
x can have 2 values +2 or +1
insufficient

2) $$-1≤x≤1$$
x can have only one value +1
sufficient
Manager  G
Joined: 20 Feb 2017
Posts: 164
Location: India
Concentration: Operations, Strategy
WE: Engineering (Other)
Re: If (|x|-2)(x-1)=0, then x=?  [#permalink]

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x can be 2,-2 or 1
From statement 1
x can be 2 or 1, hence we have 2 values for x. Thus insufficient
From Statement 2
We know that x could be 1. Hence sufficient
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If you feel the post helped you then do send me the kudos (damn theya re more valuable than \$) Re: If (|x|-2)(x-1)=0, then x=?   [#permalink] 02 Sep 2018, 11:54
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