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# Is the positive integer n an odd integer?

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Re: Is the positive integer n an odd integer? [#permalink]
Here is what i did =>
we need to see whether or not integer n is odd .
Statement 1 => n+4 = prime and it must be a prime greater than 2 hence it must be odd as all the primes greater than 2 are odd
hence n+4=odd => n=odd=> sufficient
Statement 2 => n+3=20=> n=odd or n+3=15=> n=even => not suff

Smash that A
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Re: Is the positive integer n an odd integer? [#permalink]
Quote:
Is the positive integer n an odd integer?

(1) n+4 is a prime number.
(2) n+3 is not a prime number

We know that n is positive. Side note: It can't be zero which is neither positive nor negative.

(1) First consider: By definition, a prime number has exactly two divisors, 1 and itself. So the only even prime number is two. Every other even number has at least three divisors 1, 2, and itself. We therefore know that n+4 is odd.

For addition the following rules apply:

odd+odd=even
even+even=even
odd+even=odd

We can conclude that n must be odd. Therefore (1) is sufficient.

Note that we know at this point that the possible answers are a or e. If (2) is n.s. we pick a. If (2) is sufficient we pick e. Even if we can't figure out if (2) is sufficient we have a 50% chance.

(2) First consider. There is an infinite amount of non-prime numbers (both even and odd). So there is an infinite number of possible values for n.

Examples:
If n=1 (which is odd) then n+3=4 (which is not prime)
If n=6 (which is even) then n+3=9 (which is not prime)

So n could be odd or even and therefore (2) is not sufficient.

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Re: Is the positive integer n an odd integer? [#permalink]
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Re: Is the positive integer n an odd integer? [#permalink]
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