## Isn't 0 divisible by any non zero number?

Math questions from any Manhattan Prep GMAT Computer Adaptive Test.
nash.avi

Posts: 23
Joined: Wed Jul 16, 2008 10:04 am

### Isn't 0 divisible by any non zero number?

Here is the question and the answer(explaination). The Answer is C, if 0 is not divisible by 3, else the answer should be E. My question is isnt 0 divisible by 3, because it leaves a reminder of 0. So shouldnt the answer be E.

Please advise.

Thanks in advance

If x is a positive integer, is x - 1 a factor of 104?

(1) x is divisible by 3.

(2) 27 is divisible by x

The factors of 104 are {1, 2, 4, 8, 13, 26, 52, 104}. If x - 1 is definitely one of these factors, OR if x - 1 is definitely NOT one of these factors, then the statement is sufficient.

(1) INSUFFICIENT: x could be any one of the infinite multiples of 3. If x = 3, x - 1 would equal 2, which is a factor of 104. If x = 6, x - 1 would equal 5, which is not a factor of 104.

(2) INSUFFICIENT: The factors of 27 are {1, 3, 9, 27}. Subtracting 1 from each of these values yields the set {0, 2, 8, 26}. The non-zero values are all factors of 104, but 0 is not.

(1) AND (2) SUFFICIENT: Given that x is a factor of 27 and also divisible by 3, x must equal one of 3, 9 or 27. x - 1 must therefore equal one of 2, 8, or 26 - all factors of 104.

The correct answer is C.
nash.avi

Posts: 23
Joined: Wed Jul 16, 2008 10:04 am

### Re: Isn't 0 divisible by any non zero number?

PLEASE IGNORE THIS QUESTION.
RonPurewal
Students

Posts: 19747
Joined: Tue Aug 14, 2007 8:23 am

### Re: Isn't 0 divisible by any non zero number?

for any other posters out there reading this post:

you don't have to consider the issue of whether x can be 0, because the problem statement stipulates that x must be a positive integer.
rajivmgmat
Students

Posts: 5
Joined: Wed Sep 15, 2010 1:28 am

### Re: Isn't 0 divisible by any non zero number?

I answered B because I did not consider 1 as a possible divisor of 27, since 1 is a universal divisor.
I am curious to know if GMAT official testers would consider such problems. Could you share a similar problem from the OG or Quant guide, in which if 1 is not considered as a divisor the solution would be incorrect?

Also I thought this problem is confusing enough to deserve a 700-800 category.
tim
ManhattanGMAT Staff

Posts: 5665
Joined: Tue Sep 11, 2007 9:08 am
Location: Southwest Airlines, seat 21C

### Re: Isn't 0 divisible by any non zero number?

i don't have a specific question in mind, but the GMAT's math is always correct, so you can assume they would consider 1 a divisor of any integer.. :)
Tim Sanders
Manhattan GMAT Instructor

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