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Is N divisible by 7? Question about zero

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Is N divisible by 7? Question about zero

by nbalow » Sat Mar 14, 2015 10:11 am
Question that may have been answered before:

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

Now, I understand that 1 could be yes or no depending on what integers you put in for x and y so that's insufficient. 2 is obviously insufficient because it doesn't talk about N. Every post I have seen says c is the answer but my question is what if you put 0 (an integer) in for y? Does the answer become e? Is zero technically divisible by 7 (or any number for that matter) because the remainder is zero? I suppose if 0 is divisible by 7 then that wouldn't satisfy 2 as a value for y and then the answer would indeed be c.

Thanks in advance for the help!
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by GMATGuruNY » Sat Mar 14, 2015 10:22 am
nbalow wrote: Is zero technically divisible by 7 (or any number for that matter) because the remainder is zero?
0 is considered a multiple of every positive integer.
That said, the GMAT does not typically test this concept.
On the GMAT, problems about divisibility are generally constrained to POSITIVE VALUES.
If the problem above were to appear on the GMAT, it would almost certainly be made clear that x and y are positive integers and that x>y.
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by Matt@VeritasPrep » Sun Mar 22, 2015 11:05 pm
Another way to do this:

S1 is insufficient because we could have N = 14 - 7 or N = 3 - 2.
S2 is insufficient because we don't know what N is.

Together, we have

x = 7k, where k is some integer (we don't care which)
y = 7m + r, where m is some integer (we don't care which), and r is a REMAINDER (1, 2, 3, 4, 5, or 6).

So x - y =
7k - (7m + r) =
7k - 7m - r =
7(k - m) - r

So x - y = 7(k-m) - r, or a multiple of 7 minus 1, 2, 3, 4, 5, or 6. That won't divide by 7, so we're done: N is NOT divisible by 7.
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