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If a ≠ 0, does xa = a?

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by VJesus12 » Wed Jun 20, 2018 2:28 am

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B

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E

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Difficulty—

If a ≠ 0, does xa = a?

(1) x is a single digit prime integer

(2) 0 < a < 10

The OA is the option A.

Why is sufficient the first statement? I think the answer should be E. Could anyone help me? Please.
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Source: — Data Sufficiency |
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by Vincen » Wed Jun 20, 2018 3:34 am
Hello Vjesus12.

Here we are asked if ax=a. This is equivalent to ask: x=1?

Because since a ≠ 0 we can divide both sides of the equation and get x=1.

First Statement
(1) x is a single digit prime integer
Here we know that x is a single digit prime number, then x=2, 3, 5 or 7. Hence x ≠ 1.
Therefore, the answer to the question is NO. So, this statement is sufficient.

Second Statement
(2) 0 < a < 10
Here we don't know anything about x. Therefore, this statement is not sufficient.

So, the correct answer is the option A.

I hope it helps you. <i class="em em-smiley"></i>
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