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# DRY FRUITS

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Manager
Joined: 20 May 2008
Posts: 54

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09 Feb 2009, 04:55
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?

(A) 256
(B) 260
(C) 316
(D) 320
(E) It cannot be determined from the given information.

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SVP
Joined: 07 Nov 2007
Posts: 1728
Location: New York
Re: DRY FRUITS  [#permalink]

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09 Feb 2009, 05:45
LoyalWater wrote:
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?

(A) 256
(B) 260
(C) 316
(D) 320
(E) It cannot be determined from the given information.

R+A+P+RA+PA+RP+RAP=435 -->(1)

R=10P
A=20RP
P=1/5*A
A+RA+PA+RAP=210 -->(2)

FROM 1 AND 2

R+P+RP =435-210 = 225

10P+P+1/4*P = 225
-->P=20

R+A+P = 200+100 +20 =320
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Manager
Joined: 27 May 2008
Posts: 192
Re: DRY FRUITS  [#permalink]

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09 Feb 2009, 06:01
D

Same explanation as that of Suresh.
Senior Manager
Joined: 30 Nov 2008
Posts: 478
Schools: Fuqua
Re: DRY FRUITS  [#permalink]

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Updated on: 09 Feb 2009, 19:06
Let R be the number of bags containing Raisins.
Let A be the number of bags containing Almonds.
Let P be the number of bags containing Peanuts.
Let PR be the number of bags containing Peanuts and Raisins
Let OR be the number of bags containing only Raisins.
Let OA be the number of bags containing only Almonds.
Let OP be the number of bags containing only Peanuts.

From the given information we can draw the following facts.

Total no of bags containing Almonds ie A = 210.
OP = 1/5 OA --> eq 1
OA = 20 PR --> Eq 2
OR = 10 OP --> Eq 3

From Eq 1 and 2,

OP = 1/5 * 20 * (PR) = 4 * (PR) --> Eq 4

From Eq 4 and Eq 3,

OR = 10 * 4 * (PR) --> Eq 5

The question is asking for " How bags contains only one of the items"

ie OA + OP + OR = ?

Using Venn diagram Notation, we can say that

A + OP+ PR + OR = 485. (Now Substituting the values of OP, OR, PR from 4 and 5 in the below)

210 + 4(PR) + PR + 40(PR) = 485.

Solving it, we get PR = 5.

OA = 20 PR = 20 * 5 = 100
OP = 4 * PR = 4 * 5 = 20
OR = 40* O r= 40 * 5 = 200

OA + OR + OP = 320.

Edited the post.

Originally posted by mrsmarthi on 09 Feb 2009, 13:55.
Last edited by mrsmarthi on 09 Feb 2009, 19:06, edited 1 time in total.
Senior Manager
Joined: 30 Nov 2008
Posts: 478
Schools: Fuqua
Re: DRY FRUITS  [#permalink]

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09 Feb 2009, 15:23
x2suresh wrote:
R+A+P+RA+PA+RP+RAP=435 -->(1)

R=10P
A=20RP
P=1/5*A
A+RA+PA+RAP=210 -->(2)

FROM 1 AND 2

R+P+RP =435-210 = 225

10P+P+1/4*P = 225
-->P=20

R+A+P = 200+100 +20 =320

I think you misinterpretted the questions.

There can be bags that contain only one item, cobination of any two items, or combination all three items.

So when Number of bags containing almonds = 210 means, it can be number of bags containing ONLY ALMONDS, and number of bags having a mixture of 2 or 3 items where Almonds can be one of the items.

Can you interpret the problem like this?
SVP
Joined: 07 Nov 2007
Posts: 1728
Location: New York
Re: DRY FRUITS  [#permalink]

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09 Feb 2009, 18:16
mrsmarthi wrote:
x2suresh wrote:
R+A+P+RA+PA+RP+RAP=435 -->(1)

R=10P
A=20RP
P=1/5*A
A+RA+PA+RAP=210 -->(2)

FROM 1 AND 2

R+P+RP =435-210 = 225

10P+P+1/4*P = 225
-->P=20

R+A+P = 200+100 +20 =320

I think you misinterpretted the questions.

There can be bags that contain only one item, cobination of any two items, or combination all three items.

So when Number of bags containing almonds = 210 means, it can be number of bags containing ONLY ALMONDS, and number of bags having a mixture of 2 or 3 items where Almonds can be one of the items.

Can you interpret the problem like this?

I believe I interpreted correctly
A+RA+PA+RAP=210 -->(2)
A = No. of Bags with only almonds
RA = No. of Bags with almonds and Raisins
PA = No. of Bags with almonds and peanuts
RAP = No. of Bags with almonds,raisins and peants
_________________

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Senior Manager
Joined: 30 Nov 2008
Posts: 478
Schools: Fuqua
Re: DRY FRUITS  [#permalink]

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09 Feb 2009, 19:06
Oops....I was confused with the calc. Sorry.
VP
Joined: 18 May 2008
Posts: 1176
Re: DRY FRUITS  [#permalink]

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10 Feb 2009, 02:35
Agree with suresh.
Intern
Joined: 07 Jan 2009
Posts: 16
Location: Boston/Cleveland
Re: DRY FRUITS  [#permalink]

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10 Feb 2009, 13:43
x2suresh wrote:
mrsmarthi wrote:
x2suresh wrote:
R+A+P+RA+PA+RP+RAP=435 -->(1)

R=10P
A=20RP
P=1/5*A
A+RA+PA+RAP=210 -->(2)

FROM 1 AND 2

R+P+RP =435-210 = 225

10P+P+1/4*P = 225
-->P=20

R+A+P = 200+100 +20 =320

I think you misinterpretted the questions.

There can be bags that contain only one item, cobination of any two items, or combination all three items.

So when Number of bags containing almonds = 210 means, it can be number of bags containing ONLY ALMONDS, and number of bags having a mixture of 2 or 3 items where Almonds can be one of the items.

Can you interpret the problem like this?

I believe I interpreted correctly
A+RA+PA+RAP=210 -->(2)
A = No. of Bags with only almonds
RA = No. of Bags with almonds and Raisins
PA = No. of Bags with almonds and peanuts
RAP = No. of Bags with almonds,raisins and peants

Isn't it just A=20(R+P), thats the way I read it

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Re: DRY FRUITS &nbs [#permalink] 10 Feb 2009, 13:43
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# DRY FRUITS

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