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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.

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.

PLEASE HELP

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
_________________

Your attitude determines your altitude Smiling wins more friends than frowning

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.

Last edited by mrsmarthi on 09 Feb 2009, 19:06, edited 1 time in total.

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.

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
_________________

Your attitude determines your altitude Smiling wins more friends than frowning

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