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Gmat Paper Test-Overlapping Sets- very tough

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by khurram » Wed Jun 04, 2008 12:36 pm
The question below is one of the toughest I have seen.

Total bags are 453. Each bag contains at least one of the following: raisin, almonds and peanuts. The number of bags that contain only raisins is 10 times the number of bags that contain only peanuts. The number of bags that contain almonds is 20 times the number of bags that contain only raisins and peanuts. The number of bags that contain only peanuts is 1/5 the number of bags that contain only almonds. 210 bags contain almonds. How many bags cotain only one kind of item

Ans is 320.


This is how I have solved.

bags only Raisins= 10 times bags contain only peanuts.
bags only Almonds= 20 times the bags that contain raisins and peanuts.
bags that contain only peanuts=1/5 the number of bags that contain only almonds.

r=10p
r+P=y name Y
A=20(r+P) or same as (20Y)
p=1/5 A or 1/5 (20Y) or 4y

so P =4y
A =20Y
R=10p or 40Y

so 64Y What Then.

How do you get 320.

Thanks
Khurram
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Re: Gmat Paper Test-Overlapping Sets- very tough

by Ian Stewart » Wed Jun 04, 2008 1:37 pm
khurram wrote:The question below is one of the toughest I have seen.

Total bags are 453. Each bag contains at least one of the following: raisin, almonds and peanuts. The number of bags that contain only raisins is 10 times the number of bags that contain only peanuts. The number of bags that contain almonds is 20 times the number of bags that contain only raisins and peanuts. The number of bags that contain only peanuts is 1/5 the number of bags that contain only almonds. 210 bags contain almonds. How many bags cotain only one kind of item

Ans is 320.
What may make it tough is that there's a problem with the question:
  • 210 bags contain almonds.
    The number of bags that contain almonds is 20 times the number of bags that contain only raisins and peanuts.
You can't divide 210 by 20.

Ignoring that, you know that 210 bags contain almonds. Thus, the other kinds of bags add to 453-210 = 243. These are the bags containing Peanuts only (P), Raisins only (R), and Peanuts+Raisins (PR).

-From the statement I quoted above, we ought to be able to calculate PR (it's 210/20 = 10.5, which doesn't make any sense, but that's what the questions says!).
-We're also told that R = 10P
-Thus, P + 10P + 10.5 = 243.
-From that, you can find P.
-The number of 'almonds only' bags is 5P, from the info in the question. The question asks us, finally, to find P + R + A = P + 10P + 5P, so with P we can find the answer.
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by netigen » Wed Jun 04, 2008 1:49 pm
Are you sure you typed the question right:

The number of bags that contain almonds is 20 times the number of bags that contain only raisins and peanuts = 210

number of bags that contain only raisins and peanuts = 210/20 != an integer?
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by khurram » Wed Jun 04, 2008 5:13 pm
yep, just checked it.

Maybe it is a misprint on the paper test.

Khurram
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by scooby » Sun Feb 13, 2011 8:04 pm
i think the question says the bag that contains ONLY almondsis 20 times the number of bags that contains only raisins and peanuts,
so we have to keep in mind that the bags that contains almonds and the bag that contains only almonds are two different things!
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