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Is integer x prime?

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Bunuel
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Is integer x prime? [#permalink] New post   23 Apr 2015, 03:44
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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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E
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Harley1980
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Is integer x prime? [#permalink] New post   23 Apr 2015, 08:44
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Bunuel wrote:
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.



1) x can be 3 - prime or can be 4 not prime
Insufficient
2) x can be 3 and has factors 3 and 1 and difference will be even or x can be 9 and has factors 9, 3 and 1 all pair will give us even difference.
In first case x is prime and in second case x is not prime.
Insufficient

1+2) in second statement we already took numbers that more than 2, so even when we combine statements it's insufficient.

Answer is E
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Re: Is integer x prime? [#permalink] New post   23 Apr 2015, 20:56
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clearly statement 1 not enoguh

Statement 2 -
consider prime number 3= 3*1 .. difference betwn factors = 3-1=2 even
non prime number = 8 = 8*1 ..difference 8-1=7.. odd also 8=4*2 difference is 2 even
So statement 2 alone not enough

Combining them we can have , 3 or 8 as examples so that is also not enough
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Re: Is integer x prime? [#permalink] New post   25 Apr 2015, 08:41
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Bunuel wrote:
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.



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] New post   27 Apr 2015, 02:34
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Bunuel wrote:
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] New post   24 Aug 2016, 07:35
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] New post   22 Jun 2021, 23:42
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Re: Is integer x prime? [#permalink]
22 Jun 2021, 23:42
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