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Each of 435 bags contains at least one of the following [#permalink]

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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?

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. 350

Fill the diagram step by step:

Also given that there are total of 435 bags and 210 bags contain almonds.

From the diagram 20y=5x; y = x/4.

Now, Total = 435 = {Almonds} + 10x + y + x; 435 = 210 + 10x + x/4 + x; x = 20.

The number of bags that contain only one kind of item is the sum of yellow segments: 10x + x + 5x = 16x = 320.

Re: Each of 435 bags contains at least one of the following [#permalink]

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12 Aug 2013, 06:59

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docabuzar 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. 350

My shortcut solution:

Attachments

ratio application.png [ 36.31 KiB | Viewed 15601 times ]

Re: Each of 435 bags contains at least one of the following [#permalink]

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14 Aug 2013, 09:57

Bunuel wrote:

docabuzar 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. 350

Fill the diagram step by step:

Attachment:

Raisins, almonds, and peanuts.PNG

Also given that there are total of 435 bags and 210 bags contain almonds.

From the diagram 20y=5x --> y=x/4. Now, Total=435={Almonds}+10x+y+x --> 435=210+10x+x/4+x --> x=20 --> # of bags that contain only one kind of item is the sum of yellow segments: 10x+x+5x=16x=320.

Answer: D.

Hi Bunuel,

I am unable to understand. Can you please elaborate?

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. 350

Fill the diagram step by step:

Attachment:

Raisins, almonds, and peanuts.PNG

Also given that there are total of 435 bags and 210 bags contain almonds.

From the diagram 20y=5x --> y=x/4. Now, Total=435={Almonds}+10x+y+x --> 435=210+10x+x/4+x --> x=20 --> # of bags that contain only one kind of item is the sum of yellow segments: 10x+x+5x=16x=320.

Answer: D.

Hi Bunuel,

I am unable to understand. Can you please elaborate?

Please tell me what exactly didn't you understand. Thank you.
_________________

Re: Each of 435 bags contains at least one of the following [#permalink]

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14 Aug 2013, 10:42

Diipz wrote:

Bunuel wrote:

docabuzar 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. 350

Fill the diagram step by step:

Attachment:

Raisins, almonds, and peanuts.PNG

Also given that there are total of 435 bags and 210 bags contain almonds.

From the diagram 20y=5x --> y=x/4. Now, Total=435={Almonds}+10x+y+x --> 435=210+10x+x/4+x --> x=20 --> # of bags that contain only one kind of item is the sum of yellow segments: 10x+x+5x=16x=320.

Answer: D.

Hi Bunuel,

I am unable to understand. Can you please elaborate?

The value of almonds from the venn diagram. 20y=5x. Also the explanation leading to the target. Thanks.

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. 350

Fill the diagram step by step:

Attachment:

Raisins, almonds, and peanuts.PNG

Also given that there are total of 435 bags and 210 bags contain almonds.

From the diagram 20y=5x --> y=x/4. Now, Total=435={Almonds}+10x+y+x --> 435=210+10x+x/4+x --> x=20 --> # of bags that contain only one kind of item is the sum of yellow segments: 10x+x+5x=16x=320.

Answer: D.

Hi Bunuel,

I am unable to understand. Can you please elaborate?

The value of almonds from the venn diagram. 20y=5x. Also the explanation leading to the target. Thanks.

The number of bags that contain only almonds is 20 times the number of bags that contain only raisins and peanuts --> {only raisins and peanuts} = y --> {only almonds}=20y;

The number of bags that contain only peanuts is one-fifth the number of bags that contain only almonds --> {only peanuts}=x --> {only peanuts}={only almonds}/5 --> x={only almonds}/5 --> {only almonds}=5x.

Re: Each of 435 bags contains at least one of the following [#permalink]

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23 Oct 2013, 16:08

Asifpirlo wrote:

docabuzar 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. 350

My shortcut solution:

I really liked your method but 256 is also divisible by 16? Why wouldnt that we an answer?//
_________________

“Confidence comes not from always being right but from not fearing to be wrong.”

Re: Each of 435 bags contains at least one of the following [#permalink]

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17 Nov 2013, 19:49

Bunuel,

I would really appreciate your help. When I read this: "The number of bags that contain only almonds is 20 times the number of bags that contain only raisins and peanuts. ". I thought that the number of bags that only contain almonds is equal to the number of bags that contain raisins and the number of bags that only contain peanuts. So I said A=20*(10x+x)=20*(11x). Rather than what you had which is the 20y, where y is the number of bags that are a mixtures of both raisins and peanuts.

This is more of an english question but how is "only" used in word problems on the GMAT. When I get question with an "only A & B" is this equal to ("only" A) & ("only" B). Or should I interpret it as "only" (A&B)

I would really appreciate your help. When I read this: "The number of bags that contain only almonds is 20 times the number of bags that contain only raisins and peanuts. ". I thought that the number of bags that only contain almonds is equal to the number of bags that contain raisins and the number of bags that only contain peanuts. So I said A=20*(10x+x)=20*(11x). Rather than what you had which is the 20y, where y is the number of bags that are a mixtures of both raisins and peanuts.

This is more of an english question but how is "only" used in word problems on the GMAT. When I get question with an "only A & B" is this equal to ("only" A) & ("only" B). Or should I interpret it as "only" (A&B)

Interpretation usually depends on the context. 'Bag containing only A and B' means the bag has A and B only, not say C. If the question wants to imply only A and only B, it will clarify as such. The bag containing only A and the bag containing only B.

Note that here you have assumed that the statement implies this: The number of bags that contain only almonds is 20 times the sum of the number of bags that contain only raisins and the number of bags that contain only peanuts. If number of bags of almonds is 20 times the sum of 2 other numbers, they will specify it as such. In the question they only give number of bags of almonds is 20 times the number of bags of only raisins and peanuts (which means that the intersection of all 3 in not included). So one number of bags is equal to another number of bags, not sum of two other numbers of bags.
_________________

Re: Each of 435 bags contains at least one of the following [#permalink]

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28 Oct 2014, 23:52

Asifpirlo wrote:

docabuzar 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. 350

My shortcut solution:

I dont think there is any logic for this answer, cause option [A] i.e. 256 is also divisible by 16, so please verify your findings...

Re: Each of 435 bags contains at least one of the following [#permalink]

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28 Oct 2016, 06:19

It has to be 320. The process given until now is correct... now... Answer choice D: R+P+A = 320 Since 320/64 = 5, the multiplier for R : P : A = 40:4:20 is 5: R : P : A = 5(40:4:20) = 200:20:100. Here, R=200, P=20, A=100.

Since R+P+RP = 225, and in the ratio above R+P = 220, RP = 5. If D is the correct answer, the value of A will be 20 times the value of RP: A/RP = 100/5 = 20.

Re: Each of 435 bags contains at least one of the following [#permalink]

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26 Nov 2017, 08:03

Bunuel wrote:

docabuzar 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. 350

Fill the diagram step by step:

Also given that there are total of 435 bags and 210 bags contain almonds.

From the diagram 20y=5x; y = x/4.

Now, Total = 435 = {Almonds} + 10x + y + x; 435 = 210 + 10x + x/4 + x; x = 20.

The number of bags that contain only one kind of item is the sum of yellow segments: 10x + x + 5x = 16x = 320.

I dont get why 435 = Almonds + 10x + y + x? as it is 3 sets overlap formula. So i think we need to know 2 more variables: bags that contain raisin & almonds and bags that contain almonds & peanuts?

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. 350

Fill the diagram step by step:

Also given that there are total of 435 bags and 210 bags contain almonds.

From the diagram 20y=5x; y = x/4.

Now, Total = 435 = {Almonds} + 10x + y + x; 435 = 210 + 10x + x/4 + x; x = 20.

The number of bags that contain only one kind of item is the sum of yellow segments: 10x + x + 5x = 16x = 320.

I dont get why 435 = Almonds + 10x + y + x? as it is 3 sets overlap formula. So i think we need to know 2 more variables: bags that contain raisin & almonds and bags that contain almonds & peanuts?

Thank you

LOOK AT THE DIAGRAM: Total = 435 = {Almonds} + 10x + y + x;
_________________

Re: Each of 435 bags contains at least one of the following [#permalink]

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26 Nov 2017, 08:14

Hi Bunuel,

I dont get why 435 = Almonds + 10x + y + x? as it is 3 sets overlap formula. So i think we need to know 2 more variables: bags that contain raisin & almonds and bags that contain almonds & peanuts?

Thank you[/quote]

LOOK AT THE DIAGRAM: Total = 435 = {Almonds} + 10x + y + x;[/quote]

Yes but I understand here is that Y is the numbers of bags that contain raisin and peanuts and we need to know the number of bags that contain raisin & almonds and bags that contain almonds & peanuts, even bags that contain three of them to form the formula of 3 sets overlap. Where am I wrong?

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. 350

Fill the diagram step by step:

Also given that there are total of 435 bags and 210 bags contain almonds.

From the diagram 20y=5x; y = x/4.

Now, Total = 435 = {Almonds} + 10x + y + x; 435 = 210 + 10x + x/4 + x; x = 20.

The number of bags that contain only one kind of item is the sum of yellow segments: 10x + x + 5x = 16x = 320.

Answer: D.

Yes but I understand here is that Y is the numbers of bags that contain raisin and peanuts and we need to know the number of bags that contain raisin & almonds and bags that contain almonds & peanuts, even bags that contain three of them to form the formula of 3 sets overlap. Where am I wrong?

Thank you

You did not read the question ans solutions carefully.

We need to find the number of bags in YELLOW regions: How many bags contain ONLY one kind of item?

Region with y, is the number of bags that contain ONLY raisins and peanuts, but NOT almonds.
_________________