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

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Math Revolution GMAT Instructor
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If (|x|-2)(x-1)=0, then x=?  [#permalink]

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New post 20 Aug 2018, 02:39
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

70% (01:00) correct 30% (01:12) wrong based on 82 sessions

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[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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If (|x|-2)(x-1)=0, then x=?  [#permalink]

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New post 20 Aug 2018, 02:55
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.
B is the answer.
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Re: If (|x|-2)(x-1)=0, then x=?  [#permalink]

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New post 20 Aug 2018, 05:50
2
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

Answer: B

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Brent
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Re: If (|x|-2)(x-1)=0, then x=?  [#permalink]

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New post 22 Aug 2018, 00:42
=>

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.

Therefore, B is the answer.
Answer: B
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Re: If (|x|-2)(x-1)=0, then x=?  [#permalink]

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New post 02 Sep 2018, 10:36
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
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Re: If (|x|-2)(x-1)=0, then x=?  [#permalink]

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New post 02 Sep 2018, 10:54
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
Answer : B
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Re: If (|x|-2)(x-1)=0, then x=? &nbs [#permalink] 02 Sep 2018, 10:54
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