Manhattan PS

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Manhattan PS

by scottchapman » Sat Apr 18, 2015 7:06 pm
Two teams are distributing information booklets. Team A distributes 60% more boxes of booklets than Team B, but each box of Team A's has 60% fewer booklets than each box of Team B's. Which of the following could be the total number of booklets distributed by the two groups?

2,000
3,200
4,100
4,800
4,900

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by GMATGuruNY » Sun Apr 19, 2015 2:45 am
Two teams are distributing information booklets. Team A distributes 60% more boxes of booklets than Team B, but each box of Team A's has 60% fewer booklets than each box of Team B's. Which of the following could be the total number of booklets distributed by the two groups?

A)2,000
B)3,200
C)4,100
D)4,800
E)4,900
To determine what COULD be the total number of booklets, test the SMALLEST POSSIBLE CASE.
Since 60% = 3/5, plug in the SMALLEST POSSIBLE VALUE -- 5 -- for the unknowns attributed to team B.

Team B:
Let the number of boxes = 5.
Let the booklets per box = 5.
Total booklets = 5*5 = 25.

Team A:
Since team A distributes 60% more boxes, the number of boxes = 5 + 0.6(5) = 8.
Since each box contains 60% fewer booklets, booklets per box = 5 - 0.6(5) = 2.
Total booklets = 8*2 = 16.

Total booklets for the two teams = 25+16 = 41.
Since 41 is the least possible value for the total number of booklets, the correct answer choice must be a multiple of 41.

The correct answer is C.
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by [email protected] » Sun Apr 19, 2015 9:56 am
Hi scottchapman,

Here's an approach that TESTs VALUES and involves a Number Property:

If...
Team B = 100 boxes
Team A = 160 boxes

And if....
Team B = 100 pamphlets/box
Team A = 40 pamphlets/box

Under these circumstances...
Team A = 40(160) = 6400 pamphlets
Team B = 100(100) = 10,000 pamphlets
Total = 16,400 pamphlets

Now, this answer (16,400) is NOT among the choices, but notice how it's exactly 4 times Answer C???

If you keep the number of boxes as is and change the number of pamphlets by dividing each number by 4....
Team B = 25 pamphlets/box
Team A = 10 pamphlets/box

Then...
Team A = 10(160) = 1600 pamphlets
Team B = 25(100) = 2500 pamphlets
Total = 4100 pamphlets

Final Answer: C

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by scottchapman » Sun Apr 19, 2015 12:47 pm
GMATGuruNY: Thank you for your reply. At first, it looks like a percentage question but after review I suppose its more of a ratio question. I looked back at my "work" to see what I did and made some silly math errors. Additionally, I spent way too much time 4:29 on this question. I just tried to brute force it because it shouldn't have been that difficult to solve. Thank you for your explanation.

Rich.C: Thank you for your reply. As stated above to GMATGuruNY, I took too much time on the question. I attempted to solve it a few different ways including trying to test values, which for whatever reason, I goofed up the math--maybe trying do some work in my head to save time---Obviously, not the best way to do this. Thank you for your explanation--it totally makes sense now. I have to get these questions correct!

Cheers!

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by Matt@VeritasPrep » Sun Apr 19, 2015 10:59 pm
We could also opt for algebra with a touch of number theory thrown in.

Let's say team B has x boxes, each with y booklets.

That means team A has (1.6)x boxes, each with (.4)y booklets.

Hence the total number of booklets = xy + (1.6x)(.4y) = 1.64xy

So we want an answer that's a multiple of 164. 164 = 4 * 41, so 41,000 works. (41,000 = 41 * 4 * 250).

This way seems very quick - I think I'd be done before I was even thinking of which numbers to try or how to backsolve.