san2009 wrote:there seems to me that there is something wrong with the solution here. i've bolded the part of the solution that I think misinterprets what the question is saying. pls help!


A certain shipment of identical cans of soup can be packed either into cartons that hold 15 cans each or into cartons that hold 25 cans each. If all cartons will be completely filled regardless of the size chosen, and there will be an equal number of small and large cartons used, how many of the larger cartons would be needed to for the entire shipment?
(1) Forty fewer cartons would be needed if the shipment were packed in the larger cartons than if it were packed in the smaller cartons.
(2) If the cans were packed into the smaller cartons, 100 cartons would be needed.

OA is D

PR Solution:

Yes. Remember that when you are dealing with unknown quantities on a Data Sufficiency problem, you should think of the information in terms of algebraic equations. The problem tells you that the total number of cans to be packed in 15-can cartons is equal to the number of cans to be packed in 25-can cartons. 15x = 25y. Statement 1 tells you that the difference in the number of cartons required is 40, or x - y = 40. Combined with the problem, this yields enough information to solve for each variable (two independent equations, two variables); eliminate BCE. Statement 2 specifies one of the variables (x = 100), and so is sufficient for the same reason. Eliminate A.


The question is saying, that NUMBER of large and small cartons will be the same....NOT the number of cans. Pls advise.

You're absolutely right. The wording of the question is very awkward, so I don't care for it to begin with - it's not like a real GMAT question - and there's a clearly an error in the solution as well. If the number of small and large cartons is equal, then we have x of each type, and thus 15x + 25x = 40x cans in total. We don't get an equation 15x = 25y; that's just nonsense. They seem to be answering a completely different question in the solution (the question says you have an equal number of cartons of each type, whereas the solution says you have an equal number of cans in each type of carton), but even with that reinterpretation, the second equation they give in the solution (x-y = 40) is still nonsense; the x and y in this equation are not the same x and y as in the equation 15x = 25y. There's even a third problem with the question that I'll point out below.

This is not a two equation/two unknown problem at all. I'd find it easiest to let n be the number of cans. Then Statement 1 tells you that n/25 + 40 = n/15, which we can solve to find the number of cans (you'd find n=1500). Similarly, Statement 2 tells you that there are 1500 cans. If we can find the number of cans, we can answer the question, so the answer is D.

There's a problem though, if we need to use an equal number of each type of carton. We saw above that if x is the number of cartons of each type, then 40x is the number of cans. So using either statement we find that 40x = 1500, or x = 37.5, so we need 37.5 cartons of each type. Clearly x needs to be an integer, so the numbers in the question don't even make sense. Now, if what they really meant was that the number of cans in each type of carton is equal, then the numbers do make sense; we can have 50 of the smaller cartons and 30 of the larger ones. Notice that the difference in these numbers is not 40; the second equation they give in their solution, x-y=40 is obviously not correct.

All in all, not worth your time!