A certain shipment of identical cans of soup...

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SOURCE: PrincetonReview

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: D

I have PrincetonReview's official explanation and will post later - its explanation doesn't make sense to me.
Source: — Data Sufficiency |

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by maihuna » Wed Apr 06, 2011 8:18 am
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.
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by VivianKerr » Wed Apr 06, 2011 8:37 am
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.
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by giovanni.gastone » Wed Apr 06, 2011 7:14 pm
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.

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by Ian Stewart » Fri Apr 08, 2011 5:30 am
Yes, you're absolutely right; this is a catastrophically bad question and solution. I posted about the many, many problems with this question and solution in more detail here:

www.beatthegmat.com/pr-adv-inequalities ... 62862.html

It's another example of a prep company solution which completely misapplies an n equations/n unknowns 'shortcut', but if you aren't interested in the details, just move on to better material.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by giovanni.gastone » Fri Apr 08, 2011 6:07 am
Thank you Ian. I just read your other post and will just disregard this problem and move on now.