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# A manufacturer conducted a survey to determine how many

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A manufacturer conducted a survey to determine how many [#permalink]

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13 Aug 2006, 04:52
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A manufacturer conducted a survey to determine how many people buy products P and Q. What fraction of the people surveyed said that they buy neither product P nor product Q?

1) 1/3 of the people surveyed said that they buy product P but not Q
2)1/2 of the people surveyed said that they buy Product Q.

I thought E was a slamdunked answer, I guess I was wrong. What am I missing here?

Total number= People who buy product P+ People who buy product Q+ People who buy neither P nor Q - people who buy both P and Q. Don't know how the answer could be C. Please help
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13 Aug 2006, 05:00
I would have guessed (E) too.
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13 Aug 2006, 05:09
Yeah was shocked to find out the OA
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13 Aug 2006, 05:10

From 1) we get the no of people who buy Product P but not Q. 1/3

From 2) we get the no of people who buy Product Q : 1/2

A U B = A + B - AB
total = 1

People who bought neither P nor Q 1 - 1/2-1/3 = 1/6

So we can get to the answer using both.
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13 Aug 2006, 06:19
Hi Achiles,

Yup the equation you gave us is correct AUB= A+B-AB, however from 1 1/3 is not equal to A From 2, 1/2 is equal to B. So combined we neither have A nor AB. AUB does not necessarily equal 1.

Thanks
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13 Aug 2006, 06:38
Hi guys,

My mistake upon further inspection the sum of 1/2 and 1/3 does in fact represent PUQ. My bad.

Thanks
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13 Aug 2006, 09:14
C

This can be easily Solved using venn diagram.

Diagram consisits of 3 region:

Buy P only + Buy Pand Q both + Buy Q only = PUQ ( all people buy P&Q)

from (1) Buy P only P= 1/3
from (2) Buy Pand Q both + Buy Q only = 1/2

So PUQ = 1/3 + 1/2 = 5/6

people buy neither product P nor product Q = 1- (5/6) = 1/6
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13 Aug 2006, 18:31
I suggest drawing a matrix of all options and filling out ..
Option is C

1-(1/3+1/2)
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14 Aug 2006, 02:39
C

1) 1/3 use only P. No information on Q Hence Insuff

2) 1/2 use Q. No information on P Hence Insuff.

Together

The 1/2 people who use Q also include people who use Q and P
Total using P and Q = 1/3 + 1/2 = 5/6

Hence people using neither = 1-5/6 = 1/6
Suff
[#permalink] 14 Aug 2006, 02:39
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# A manufacturer conducted a survey to determine how many

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