Let x is the no of cartoon needed. x/2 each is of large and small. so there are cans 25*x/2 in large and 15x/2 cans in small cartoons i.e. 20x.

For 20x cans, no of smaller cartoon = 20x/15 = 4x/3
For 20x cans, no of larger cartoon = 20x/25 = 4x/5

40 cartoons less if all are large one

so 4x/5 - 4x/3 = 40
=> 8x/15 = 40
=> x = 600/8 = 75

So A is suff.

Similarly using B, 100 smaller cartoons = 100*15 cans = 20x => x = 100*15/20 = 75
SO B is suff.

So D is OK. What issue do u have.

I think what you're missing is the importance of "all cartons will be completely filled" and "there will be an equal number of small and large cartons used" - that's a lot of info just from the question stem!

From those statements just in the question stem we can set up a primary equation. Each individual statement allows us to set up a secondary relationship. It goes back to the "n equations with n variables" rule. Two equations with two variables. We can substitute and solve.

Thanks guys for your input. What I don't yet understand is why in the stem, we have "there will be an equal number of small and large cartons used", yet when I carry out the calculation using 15x = 25y and x-y = 40, I have...

100 small cartons
65 large cartons

It might be the language that I am having difficulty with. Can anyone help me?

Gio

======================================
PrincetonReview's Official Explanation
======================================

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 answer is D.

Thank you Ian. I just read your other post and will just disregard this problem and move on now.