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# gmat quant - sets/venn diagram

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Intern
Joined: 08 Mar 2011
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gmat quant - sets/venn diagram [#permalink]

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08 Mar 2011, 01:59
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Question Stats:

67% (04:24) correct 33% (05:00) wrong based on 6 sessions

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Hi Friends,
I am new to gmatclub.
I would like to put across the below question so that you can help me out in solving.

Each of 435 bags contains at least one of the following three items: raisins, 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 only almonds is 20 times the number of bags that contain only raisins and peanuts. The number of bags that contain only peanuts is one-fifth the number of bags that contain only almonds. 210 bags contain almonds. How many bags contain only one kind of item?
256
260
316
320
It cannot be determined from the given information.
[Reveal] Spoiler: OA
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Re: gmat quant - sets/venn diagram [#permalink]

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08 Mar 2011, 02:19
asmit123 wrote:
Hi Friends,
I am new to gmatclub.
I would like to put across the below question so that you can help me out in solving.

Each of 435 bags contains at least one of the following three items: raisins, 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 only almonds is 20 times the number of bags that contain only raisins and peanuts. The number of bags that contain only peanuts is one-fifth the number of bags that contain only almonds. 210 bags contain almonds. How many bags contain only one kind of item?
256
260
316
320
It cannot be determined from the given information.

Let A, R and P denote the bags with only Almond, Raisin and Peanuts
Let AR, RP and AP denote bags containing any two of them
Let ARP denote bags containing all three.

We know $$A+R+P+AR+RP+AP+ARP = 435$$ ..(1)
Also, $$R=10P$$,

$$A=20RP$$,

$$P=1/5*A$$

Also given that $$A+AR+AP+ARP = 210$$ ...(2)

Put 2 in 1 and bring everything in form of A to solve for A and get A = 100, so P = 20 and R = 200

So, A+P+R = 320
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Re: gmat quant - sets/venn diagram [#permalink]

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08 Mar 2011, 03:13
Thanks much.Cheers
Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
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Re: gmat quant - sets/venn diagram [#permalink]

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08 Mar 2011, 06:15
I use concept of factors to avoid straight algebra.
R = only raisins
A - only apricots
P = only peanuts
X = raisins + apricots
Y = apricots + peanuts
Z = raisins + peanuts
RAP = all

R = 10P [raisins is 10 times the number of bags that contain only peanuts]
A = 20Z [almonds is 20 times the number of bags that contain only raisins and peanuts]
P = 1/5A [peanuts is one-fifth the number of bags that contain only almonds]

Z = 0.05 A = 1/20A
P=0.2 A = 1/5A
R = 10 * 0.2 A = 2A
R+A+P = answer = 2A + A + 0.2A = 3.2 A = 16/5 A

Property of answer = multiple of 16
Z = 1/20 A
Property of A = multiple of 20.

Only 320 and 256 left.

Let 16/5A = 320
A = 100. Which is a multiple of 20

Let 16/5A = 256
A = 80. Which is NOT a multiple of 20
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Re: gmat quant - sets/venn diagram [#permalink]

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08 Mar 2011, 07:11
1
KUDOS
gmat1220 wrote:
I use concept of factors to avoid straight algebra.
R = only raisins
A - only apricots
P = only peanuts
X = raisins + apricots
Y = apricots + peanuts
Z = raisins + peanuts
RAP = all

R = 10P [raisins is 10 times the number of bags that contain only peanuts]
A = 20Z [almonds is 20 times the number of bags that contain only raisins and peanuts]
P = 1/5A [peanuts is one-fifth the number of bags that contain only almonds]

Z = 0.05 A = 1/20A
P=0.2 A = 1/5A
R = 10 * 0.2 A = 2A
R+A+P = answer = 2A + A + 0.2A = 3.2 A = 16/5 A

Property of answer = multiple of 16
Z = 1/20 A
Property of A = multiple of 20.

Only 320 and 256 left.

Let 16/5A = 320
A = 100. Which is a multiple of 20

Let 16/5A = 256
A = 80. Which is NOT a multiple of 20

Since when is 80 not a multiple of 20?

I think sometimes it may be good to try and use factor concepts to do it faster, but I personally think that questions of exactly this nature, where two (or more) choices may conform to the boundary conditions based on factors, can result in one spending too much time on backsolving and eventually returning to algebra to get the correct answer. Here, most of the algebra is already done. Now just using the condition on total almonds, we can get direct answer.

Just my 2 cents...
Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
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Re: gmat quant - sets/venn diagram [#permalink]

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08 Mar 2011, 07:17
hey thanks ! I overuse factors too much ! You have a point.
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Re: gmat quant - sets/venn diagram [#permalink]

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08 Mar 2011, 22:57
R -> 10P

A -> 20(RP)

P -> 1/5(A)

A -> 210

A + P + R + AR + PR + AP + APR = 435

So A + P + R = ?

Now we have -> A + AR + AP + APR = 210

So P + R + PR = 435 - 210 = 225

P + 10P + A/20 = 225

11P + A/20 = 225

11A/5 + A/20 = 225 => 44A + A = 225 * 20 => A = 5 * 20 = 100 => P = 20 => R = 200

So answer is 320 (choice D)
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Re: gmat quant - sets/venn diagram   [#permalink] 08 Mar 2011, 22:57
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