Is the postive integer n an odd integer

[BeatGMAT]

Is the positive integer 'n' an odd integer

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

It feels like this might be an easy problem and I get
(1) as:
We are given n + 4 is a prime number. We know that all prime numbers greater starting with 5 (as n is a positive integer, it has to start with 1) are odd, and an odd number - 4 is odd, hence sufficient

(2) I tested this statement with 2 values, 3 & 6, where both n + 3 are not prime numbers, hence insufficient

Is there a better way to test (2) ?

[Guest]

Isn't statement 2 sufficient because if we test it with 3, we get n equals 0? But according to the stem of the question, n is a positive integer

[Guest]

Isn't statement 2 sufficient because if we test it with 3, we get n equals 0? But according to the stem of the question, n is a positive integer

I am sorry I forgot to include the answer - ONLY 1 is sufficient, 2 is not

[Kamlesh]

we can eliminate such statement that say sumthin is not equal 2 sumthing .......... it might be equal to infinity :lol:

[RonPurewal]

Isn't statement 2 sufficient because if we test it with 3, we get n equals 0? But according to the stem of the question, n is a positive integer

you can't use irrelevant cases to test for sufficiency. if the stem states that n must be a positive integer, then you must ignore all cases in which n turns out NOT to be a positive integer.
or:
since statement (2) is about n + 3, not n, you only need to think about cases in which n + 3 is at least 4 (because n is at least 1).

--

since it's data sufficiency, the question of whether n is odd is equivalent to the question of whether n + 3 is odd (they're just opposites: if one is odd, the other is even, and vice versa).
so, just pick two NON-prime numbers for n + 3 - one even, one odd - and that will show insufficiency.
if n + 3 = 10 (not prime), then n = 7. odd.
if n + 3 = 9 (not prime), then n = 6. not odd.
insufficient.