Numbers

[knight247]

If k and n are integers, is n divisible by 7?
(1) n-3=2k
(2) 2k-1 is divisible by 7

This is a problem from the OG. The OA is C. And i got the idea from there. But here is where i have a problem with statement 1

(1) n-3=2k
2k is even. To get an even sum/difference the numbers have to be both odd or both even. Can't have a mix of odd and even. Now, if one odd number i.e. 3 is already there then n has to be odd. Coz if n is even then u can't get an even sum of 2k. So if this statement says n is odd then how could it be divisible by 7. So statement 1 says clearly that n is not divisible by 7(Sufficient). Statement 2 gives no indication by itself of n's divisibility by 7 hence insufficient. Should be A according to me

[Frankenstein]

Hey,
No.. n is odd. That is fine. But n can be an odd multiple of 7 right.
Consider n = 21
n-3 = 18 =2k -> n is divisible by 7
Consider n = 19
n-3 = 16 = 2k -> n is not divisible by 7
See, we can't say n is divisible by 7 or not for certain using statement(1) alone. Hence, the answer is not A