If a ≠ 0, does xa = a ?

Question

(1) x is a single digit prime integer

(2) 0 < a < 10

Kudos for a correct  solution .

D3N0 · Answer

Ans: A

Solution: because a ≠ 0 : we can say xa-a=0 a(x-1)= 0 so x=1
we need to see that is x=1 or not?
1) x is a prime number means x can not be 1 so it gives us the ans  
2) this statement talks about the values of a but nothing about x so

lipsi18 · Answer

Reframe the question; xa=a when x=1 or a=1, otherwise xa is not = a.
1. x = 2,3,5,7; hence xa will never = a; sufficient
2. a = 1,2,3,4...9 so xa may = a or xa may not =a, Not sufficient.

Hence A.

Thanks

dav90 · Answer

A should be the answer,
Because to prove xa = a, x must be 1,
per 1st statement, x is a  prime  number and hence x cannot be 1   , so enough.
per 2nd statement, x may be or may not be 1, hence out.

VenoMfTw · Answer

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

KS15 · Answer

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
Answer A

Bunuel · Answer

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.

bumpbot · Answer

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If a ≠ 0, does xa = a ?

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