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If xyz=x, is x=0?

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by Max@Math Revolution » Fri Jun 08, 2018 1:31 am

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Answers

A

B

C

D

E

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Difficulty—

[GMAT math practice question]

If xyz=x, is x=0?

1) yz=0
2) xy=0
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Source: — Data Sufficiency |
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by GMATGuruNY » Fri Jun 08, 2018 2:58 am
Max@Math Revolution wrote:[GMAT math practice question]

If xyz=x, is x=0?

1) yz=0
2) xy=0
Statement 1:
Substituting yz=0 into xyz = x, we get:
x*0 = x
0 = x.
Thus, the answer to the question stem is YES.
SUFFICIENT.

Statement 2:
Substituting xy=0 into xyz = x, we get:
0*z = x
0 = x.
Thus, the answer to the question stem is YES.
SUFFICIENT.

The correct answer is D.
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by Max@Math Revolution » Sun Jun 10, 2018 5:17 pm
=>

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.

Since we have xyz-x=0 or x(yz-1)=0 from the original condition, either x = 0 or yz = 1. Since yz = 0 by condition 1), we must have x = 0. Thus, condition 1) is sufficient.

Condition 2) tells us that xy = 0. This implies that xyz = 0. Since xyz= x, we must have x = 0. Thus, condition 2) is also sufficient.

Therefore, D is the answer.
Answer: D
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