Number Properties 4th Edition pg 118 : DIVISIBILITY & PRIMES

[charleslm.king]

Data sufficiency example: -

is N divisible by 7?
(1) N = x - y, x and y are integers
(2) x is divisible by 7, and y is not divisible by 7

The answer given is BOTH TOGETHER are SUFFICIENT but NEITHER ALONE is sufficient. N is not divisible by 7 because y is not divisible by 7 AND x - y = N.

However, for y = 0, N = x and thus is divisible by 7 (meaning neither alone are sufficient nor are they sufficient together). Am I missing something?

[jnelson0612]

Data sufficiency example: -

is N divisible by 7?
(1) N = x - y, x and y are integers
(2) x is divisible by 7, and y is not divisible by 7

The answer given is BOTH TOGETHER are SUFFICIENT but NEITHER ALONE is sufficient. N is not divisible by 7 because y is not divisible by 7 AND x - y = N.

However, for y = 0, N = x and thus is divisible by 7 (meaning neither alone are sufficient nor are they sufficient together). Am I missing something?

Yes, 0 is divisible by 7; in fact, it is divisible by all positive integers. :-)