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Each of 435 bags contains at least one of the following

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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?

A. 256
B. 260
C. 316
D. 320
E. 350
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Each of 435 bags contains at least one of the following [#permalink]

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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


Fill the diagram step by step:

Image

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.

[Reveal] Spoiler:
Attachment:
Raisins, almonds, and peanuts.PNG
Raisins, almonds, and peanuts.PNG [ 6.49 KiB | Viewed 17915 times ]

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

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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
ratio application.png [ 36.31 KiB | Viewed 14907 times ]


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

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New post 14 Aug 2013, 10:57
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?

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

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New post 14 Aug 2013, 11:36
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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?


Please tell me what exactly didn't you understand. Thank you.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 14 Aug 2013, 11:42
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.

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

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New post 14 Aug 2013, 12:00
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Diipz wrote:
Diipz wrote:
Bunuel 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.


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.

{only almonds}=5x=20y --> y=x/4.

Total=435={Almonds}+10x+y+x --> 435=210+10x+x/4+x

What else?
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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New post 23 Oct 2013, 17:08
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?//
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Re: Each of 435 bags contains at least one of the following [#permalink]

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New post 17 Nov 2013, 20:49
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)

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

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alphabeta1234 wrote:
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)


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

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New post 29 Oct 2014, 00:52
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...

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

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New post 25 Aug 2016, 15:12
Is this a real GMAT question? Isn't it a bit more complex and lengthy. How are we supposed to get this done in 2 minutes.

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

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New post 28 Oct 2016, 07:19
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.

Whereas that is not the case with option A.

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Re: Each of 435 bags contains at least one of the following   [#permalink] 28 Oct 2016, 07:19
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