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# If a ≠ 0, does xa = a ?

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If a ≠ 0, does xa = a ? [#permalink]
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Because to prove xa = a, x must be 1,
per 1st statement, x is a prime number and hence x cannot be 1[Remember that 1 is not a prime number], so enough.
per 2nd statement, x may be or may not be 1, hence out.
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Re: If a ≠ 0, does xa = a ? [#permalink]
Bunuel wrote:
If a ≠ 0, does xa = a ?

(1) x is a single digit prime integer

(2) 0 < a < 10

Kudos for a correct solution.

IMO: A

If a ≠ 0, does xa = a ?
xa-a = 0
a(x-1) = 0 since a ≠ 0, the question is asking if x =1 ?

St 1: x is a single digit prime integer

Thus x = {2,3,5,7}
Thus x ≠ 1. Suff

St 2: 0 < a < 10

Gives nothing whether x = 1 or not
Not Suff
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Re: If a ≠ 0, does xa = a ? [#permalink]
Bunuel wrote:
If a ≠ 0, does xa = a ?

(1) x is a single digit prime integer

(2) 0 < a < 10

Kudos for a correct solution.

Statement 1: x is a single digit prime number i.e x=2,3,5 or 7
Now, is xa=a? This can only be possible if a=0. But a is not equal to 0(given)
Therefore, xa will never be equal to a. Sufficient
Statement 2: 0<a<10
If a=1,x=1, then xa=a
But if x=0, a=1, then , above equation does not hold true. Insufficient
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Re: If a ≠ 0, does xa = a ? [#permalink]
Bunuel wrote:
If a ≠ 0, does xa = a ?

(1) x is a single digit prime integer

(2) 0 < a < 10

Kudos for a correct solution.

PRINCETON REVIEW OFFICIAL SOLUTION:

The question is equivalent to asking “Does x = 1?” For the first statement, x could be 2, 3, 5 or 7. In each case, given that a ≠ 0, the answer to the question “Does xa = a ?” is ‘no’ so the statement is sufficient. Statement (2) on the other hand is no help – x could be 1 for any number chosen for a or x could be some other number. So, the correct answer to this question is (A).

However, anybody who forget that 1 is not prime, would probably think that the first statement could lead to either a ‘yes’ or a ‘no’ answer to the question. That person would most likely pick (E) as their answer.

The moral to the story is that the GMAT test writers employ very precise language when they write questions. In order to avoid the traps, you need to know the precise definitions of the terms employed and you need to take the time to explore all the possibilities implied by those terms.
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Re: If a ≠ 0, does xa = a ? [#permalink]
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Re: If a ≠ 0, does xa = a ? [#permalink]
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