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

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20 Sep 2009, 08:32
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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
[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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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 --> $$\frac{neither}{total}=\frac{30}{100}=\frac{3}{10}$$.

Hope it helps.
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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 --> $$\frac{neither}{total}=\frac{30}{100}=\frac{3}{10}$$.

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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petrifiedbutstanding

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02 Jul 2012, 00:47
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 --> $$\frac{neither}{total}=\frac{30}{100}=\frac{3}{10}$$.

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]

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02 Jul 2012, 01:16
Do we need to consider "neither" case in all such set theoory questions?
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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 --> $$\frac{neither}{total}=\frac{30}{100}=\frac{3}{10}$$.

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]

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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 [ 10 KiB | Viewed 4284 times ]

Thus, probability = 30/100 = 3/10

Regards,
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Re: A certain manufacturer of cake, muffin, and bread mixes has [#permalink]

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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]

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11 Jul 2013, 05:47
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.
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Re: A certain manufacturer of cake, muffin, and bread mixes has [#permalink]

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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 [ 6.56 KiB | Viewed 2939 times ]

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Re: A certain manufacturer of cake, muffin, and bread mixes has [#permalink]

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14 Dec 2014, 14:23
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Re: A certain manufacturer of cake, muffin, and bread mixes has [#permalink]

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22 Dec 2016, 00:39
Bunuel wrote:
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.

Yes, this makes sense. I was looking for an answer to the same question. Your point helps here, Bunuel
Re: A certain manufacturer of cake, muffin, and bread mixes has   [#permalink] 22 Dec 2016, 00:39
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