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

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by Max@Math Revolution » Mon Aug 20, 2018 2:33 am

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[Math Revolution GMAT math practice question]

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

$$1)\ x>0$$
$$2)\ -1\le x\le1$$
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Mon Aug 20, 2018 5:49 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

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

$$1)\ x>0$$
$$2)\ -1\le x\le1$$
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

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Wed Aug 22, 2018 12:37 am
=>

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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