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A certain manufacturer of cake, muffin, and bread mixes has

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A certain manufacturer of cake, muffin, and bread mixes has [#permalink] New post 20 Sep 2009, 08:32
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Question Stats:

76% (01:56) correct 23% (01:02) wrong based on 126 sessions
A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchase cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?

A. 1/10
B. 3/10
C. 1/2
D. 7/10
E. 9/10
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Feb 2012, 07:11, edited 2 times in total.
Edited the question and added the OA
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Re: cake muffin bread probability problem [#permalink] New post 17 Feb 2012, 07:10
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A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchase cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?
A. 1/10
B. 3/10
C. 1/2
D. 7/10
E. 9/10

Total = {cake} + {muffin} - {both} + {neither}

100 = 50 + 40 - 20 + {neither} --> {neither} = 30 --> \frac{neither}{total}=\frac{30}{100}=\frac{3}{10}.

Answer: B.

Hope it helps.
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Re: cake muffin bread probability problem [#permalink] New post 01 Jul 2012, 23:01
Bunuel wrote:
A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchase cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?
A. 1/10
B. 3/10
C. 1/2
D. 7/10
E. 9/10

Total = {cake} + {muffin} - {both} + {neither}

100 = 50 + 40 - 20 + {neither} --> {neither} = 30 --> \frac{neither}{total}=\frac{30}{100}=\frac{3}{10}.

Answer: B.

Hope it helps.


Bunuel,

I have a question. I got this right, but I still think I'm missing something. If you considered this in a Venn-diagram format, it would be clear that there can be buyer who purchase cake mix and bread mix or muffin mix and bread mix. This would alter the equation somewhat. And I noticed that you didn't consider this. Can you please explain why?
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Re: cake muffin bread probability problem [#permalink] New post 02 Jul 2012, 00:47
Expert's post
petrifiedbutstanding wrote:
Bunuel wrote:
A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchase cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?
A. 1/10
B. 3/10
C. 1/2
D. 7/10
E. 9/10

Total = {cake} + {muffin} - {both} + {neither}

100 = 50 + 40 - 20 + {neither} --> {neither} = 30 --> \frac{neither}{total}=\frac{30}{100}=\frac{3}{10}.

Answer: B.

Hope it helps.


Bunuel,

I have a question. I got this right, but I still think I'm missing something. If you considered this in a Venn-diagram format, it would be clear that there can be buyer who purchase cake mix and bread mix or muffin mix and bread mix. This would alter the equation somewhat. And I noticed that you didn't consider this. Can you please explain why?


I'm not sure that I understand what you mean.

We are told that "A certain manufacturer has 100 buyers, of whom 50 purchase cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix."

So, Total = {cake} + {muffin} - {both} + {neither} --> 100 = 50 + 40 - 20 + {neither} --> {neither} = 30.

What should be altered above and why?
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Re: A certain manufacturer of cake, muffin, and bread mixes has [#permalink] New post 02 Jul 2012, 01:16
Do we need to consider "neither" case in all such set theoory questions?
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Re: cake muffin bread probability problem [#permalink] New post 03 Jul 2012, 08:53
Bunuel wrote:
petrifiedbutstanding wrote:
Bunuel wrote:
A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchase cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?
A. 1/10
B. 3/10
C. 1/2
D. 7/10
E. 9/10

Total = {cake} + {muffin} - {both} + {neither}

100 = 50 + 40 - 20 + {neither} --> {neither} = 30 --> \frac{neither}{total}=\frac{30}{100}=\frac{3}{10}.

Answer: B.

Hope it helps.


Bunuel,

I have a question. I got this right, but I still think I'm missing something. If you considered this in a Venn-diagram format, it would be clear that there can be buyer who purchase cake mix and bread mix or muffin mix and bread mix. This would alter the equation somewhat. And I noticed that you didn't consider this. Can you please explain why?


I'm not sure that I understand what you mean.

We are told that "A certain manufacturer has 100 buyers, of whom 50 purchase cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix."

So, Total = {cake} + {muffin} - {both} + {neither} --> 100 = 50 + 40 - 20 + {neither} --> {neither} = 30.

What should be altered above and why?


You're right actually. I considered buyers of the bread mix as well, which is clearly not necessary in the problem.
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Re: A certain manufacturer of cake, muffin, and bread mixes has [#permalink] New post 03 Jul 2012, 23:16
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Hi,

Referring to the following venn diagram, the area marked in grey represents the buyers who purchases neither cake mix nor muffin mix.
=100-70
=30
Attachment:
venn3.jpg
venn3.jpg [ 10 KiB | Viewed 1836 times ]


Thus, probability = 30/100 = 3/10

Answer (B)

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Re: A certain manufacturer of cake, muffin, and bread mixes has [#permalink] New post 11 Jul 2013, 05:42
Why does the question mention bread mixes? What's the purpose of that if it isn't used to solve the problem?
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Re: A certain manufacturer of cake, muffin, and bread mixes has [#permalink] New post 11 Jul 2013, 05:47
Expert's post
fozzzy wrote:
Why does the question mention bread mixes? What's the purpose of that if it isn't used to solve the problem?


In order {neither} to make sense. We are told there are 100 buyers. Neither cake mix nor muffin mix byers must be buyers of something else.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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: A certain manufacturer of cake, muffin, and bread mixes has [#permalink] New post 23 Oct 2013, 06:02
fozzzy wrote:
Why does the question mention bread mixes? What's the purpose of that if it isn't used to solve the problem?

I got confused too, the "bread mix" is not necessary to be mentioned (could be cookies, or pasty, you name it), it's just confuses.
What it really is, is a 2x2 matrix as shown in the picture.
Attachments

gmat.png
gmat.png [ 6.56 KiB | Viewed 510 times ]

Re: A certain manufacturer of cake, muffin, and bread mixes has   [#permalink] 23 Oct 2013, 06:02
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