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If a ≠ 0, does xa = a ? [#permalink]
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24 Aug 2015, 22:51
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60% (00:58) correct 40% (01:00) wrong based on 179 sessions
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Re: If a ≠ 0, does xa = a ? [#permalink]
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24 Aug 2015, 23:38
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Bunuel wrote: If a ≠ 0, does xa = a ?
(1) x is a single digit prime integer
(2) 0 < a < 10[/i] Ans: A Solution: because a ≠ 0 : we can say xaa=0 a(x1)= 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 [Sufficient] 2) this statement talks about the values of a but nothing about x so [Not sufficient]
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Re: If a ≠ 0, does xa = a ? [#permalink]
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25 Aug 2015, 09:42
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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.
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If a ≠ 0, does xa = a ? [#permalink]
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25 Aug 2015, 18:11
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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 [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]
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25 Aug 2015, 21:58
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: AIf a ≠ 0, does xa = a ? xaa = 0 a(x1) = 0 since a ≠ 0, the question is asking if x =1 ? St 1: x is a single digit prime integerThus x = {2,3,5,7} Thus x ≠ 1. Suff St 2: 0 < a < 10Gives nothing whether x = 1 or not Not Suff
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Re: If a ≠ 0, does xa = a ? [#permalink]
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25 Aug 2015, 23:17
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 Answer A



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Re: If a ≠ 0, does xa = a ? [#permalink]
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30 Aug 2015, 08:17
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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