# Question

Why must *1*2*N*/5 be divisible by *12*? I understand that the total population of the school would be 12*N*/5. I also understand that because the question involves people, the answer must be a whole number. However, for the answer to be a whole number, it is my understanding that *N* must be divisible by 5. If 12*N*/5 were divided by 12 we would still end up with *N*/5.

# Answer

We see that *N* must be divisible by 5, but the question doesn't ask about *N*. The question asks about 12*N*/5. Well, clearly, 12*N*/5 must be divisible by 12, so this question really boils down to "which of these five numbers is divisible by 12"? That's the real question-inside-the-question, the actual mathematical task at hand.

So you're right that it's not a given that 12*N*/5 will be an integer—*that's why* we are looking for an answer choice that *is* divisible by 12. The equation that we're trying to solve, 12(*N*/5), is the total 2004 population. However if you'll recall, *N* is only equal to the 2003 girl OR boy population. So, we are not solving for *x*, per se, but we are solving for the total student population at Jefferson High in 2004 (12(*N*/5)). This is why we are not looking for a number that is divisible by 5, but a number that is divisible by 12. If we were looking for a number that was divisible by 5, we would get an answer only for *N*, which would be an answer to the 2003 girl or boy population, and not the total 2004 population (which is what the question is asking for).

# Link

http://gre.magoosh.com/questions/41

## Comments