An uphill problem

[Shib]

Source: IMS GMAT

[deleted because problem is from a banned source - see below]

[JadranLee]

First, we rephrase the question. We are asked whether it is possible to divide up n students into m equal groups. In other words, we are being asked "Is n divisible by m?".

We can analyze this question further in terms of prime factors. A number n is divisible by a number m if, and only if, the prime box for n contains all of the numbers in the prime box for m. Thus 60 is divisible by 12 because the prime box for 60 [2,2,3,5] contains all of the members of the prime box for 12 [2,2,3]. And 70 is not divisible by 4 because the prime box for 70 [2,5,7] does not contain all of the members of the prime box for 4 [2,2] - the prime box for 4 has an extra 2 that isn't in the prime box for 70.

So we are really being asked: "Does the prime box for n contain all of the members of the prime box for m?"

(1) INSUFFICIENT. If 3n is divisible by m, the prime box for 3n contains all of the prime factors of m. This doesn't imply that n is divisible by m, however. If m is a multiple of 3, such as 6, any number that is divisible by m must have a 3 in its prime box. 3n clearly has a 3 in its prime box, but we cannot be certain that n does. (Imagine, for instance that n=20 and m=6. 3n would be divisible by 6, but n would not be.]

(2) SUFFICIENT. If 13n is divisible by m, the prime box for 13n contains all of the prime factors of m. Since m is less than 13, we know that 13 cannot be a prime factor of m. Therefore, the prime box for n, which is just the prime box for 13n without the extra 13, will also have all of the prime factors of m. Thus n itself must be divisible by m.

The answer is B.

(For more on prime boxes, see the ManhattanGMAT "Number Properties" study guide.)

[GMAT 2007]

Great Explanation Jad.

GMAT 2007

[davetzulin]

hi, i found it a bit odd that in the OG answer explanation used n= 9 as an example.

the problem states

3< m < 13 < n

where m = classrooms, n = students

so although statement 1 rephrased says: 3n/m,
why would they choose "n" as 9? Yes 3*9 is > 13, but 3*n is not the number of students, it's n right?

[tim]

I deleted the original question. OG is a banned source; it is illegal to post OG questions anywhere on the web. If you are in one of our classes, please ask OG questions during office hours or before/after class..

To answer the most recent question, there are several possible values the OG could have chosen. As long as they chose something that works, it's a valid number to use.. :)