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Re: Is integer x prime? [#permalink]
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Bunuel
Is integer x prime?

(1) x is greater than 2
(2) The difference between the two members of any pair of factors of x is even


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1. x is greater than 2. Insufficient. 3 is prime but 4 is not prime.
2. Difference between two members of any pair of factors of x is even. Insufficient. 3 is prime and has factors 1 and 3. Difference is even
15 is not prime and has four factors 1,3,5,15. Difference between any two factors is even.

Using 1 and 2, still both statements are insufficient as x can be 3,5 or 15.
Answer E
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Re: Is integer x prime? [#permalink]
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Bunuel
Is integer x prime?

(1) x is greater than 2
(2) The difference between the two members of any pair of factors of x is even


Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Solution: E.

Statement (1) merely says x > 2; INSUFFICIENT. Statement (2) is more difficult to apply. Since every positive integer has 1 as a factor, any positive integer with an even factor will have a pair of factors whose difference is odd, since (even - 1) = odd. This means that statement (2) says that ALL of x's factors are odd. This is a requirement of every prime number other than 2, but there are many non-prime numbers all of whose factors of odd (take 9, 25, or 49, for instance); INSUFFICIENT. The first statement eliminates no possibilities allowed in statement 2; (E)
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Re: Is integer x prime? [#permalink]
Such an amazing Question from Kaplan
Here is my approach =>
We need to check if x is prime or not
Statement 1 => x can be 3 or 4 or any integer>2 => not sufficient
Statement 2 => here x can never be even because if x is even then 2 must be one of its factor and SINCE ONE IS A FACTOR OF EVERY INTEGER => 2-1=1=> ODD . hence the number must be odd .
Hence it can be 1,3,5,7,,,,=> not suff
Combining the two statements => x can be 9 or a 5 or anything odd>2 => not suff
SMASH THAT E
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Re: Is integer x prime? [#permalink]
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Re: Is integer x prime? [#permalink]
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