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A manufacturer conducted a survey

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shuba
 Post subject: A manufacturer conducted a survey
 Post Posted: Sun Mar 25, 2012 12:57 pm 
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Students


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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 product Q
(2) 1/2 of the people surveyed said that they buy product Q

OA is C. Could someone explain? Thanks.

Added snapshot as requested.
http://postimage.org/image/fgq5frdb3


Last edited by shuba on Tue Mar 27, 2012 3:19 am, edited 6 times in total.

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RonPurewal
 Post subject: Re: A manufacturer conducted a survey
 Post Posted: Mon Mar 26, 2012 7:51 am 
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ManhattanGMAT Staff


Posts: 8179
hi,
if you have our strategy guides, note that (if we assume every respondent actually says whether he/she purchases each product, i.e., no non-responses) this problem is a perfectly straightforward application of the “double set matrix” device given in the word translations strategy guide. check it out.

_________________
Being well-dressed gives a feeling of inward tranquillity [that] religion is powerless to bestow.
C.F. Forbes
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matthew.sanchez.ca
 Post subject: Re: * A manufacturer conducted a survey
 Post Posted: Sun Apr 28, 2013 4:55 pm 
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I also got this question from the official GMAT Prep software in my practice exam... I too had incorrectly answered E. The OA is C.

when trying to come to the OA, this is my line of reasoning:

I drew a Venn Diagram so I had a circle for

P + overlap+ Q, and a separate circle for Neither P nor Q.

(1) says 1/3 buy P but not Q.

since it does not tell me about the fraction of Q or neither P nor Q-insufficient.

(2) says 1/2 buy Q.
since it does not tell me about the fraction for P or neither P nor Q-insufficient.

Combined: 2/6 are in P circle, 3/6 are either in Q circle or the P&Q overlap => 1/6 are Neither P nor Q. so the answer is C.

is my reasoning correct?
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RonPurewal
 Post subject: Re: * A manufacturer conducted a survey
 Post Posted: Mon Apr 29, 2013 10:20 am 
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ManhattanGMAT Staff


Posts: 8179
matthew.sanchez.ca wrote:
I also got this question from the official GMAT Prep software in my practice exam... I too had incorrectly answered E. The OA is C.

when trying to come to the OA, this is my line of reasoning:

I drew a Venn Diagram so I had a circle for

P + overlap+ Q, and a separate circle for Neither P nor Q.

(1) says 1/3 buy P but not Q.

since it does not tell me about the fraction of Q or neither P nor Q-insufficient.

(2) says 1/2 buy Q.
since it does not tell me about the fraction for P or neither P nor Q-insufficient.

Combined: 2/6 are in P circle, 3/6 are either in Q circle or the P&Q overlap => 1/6 are Neither P nor Q. so the answer is C.

is my reasoning correct?


If you use a venn diagram, then statement #1 is the crescent-moon-shaped part that's IN the "p" circle but NOT in the "q" circle. Statement #2 is the ENTIRE "q" circle. So, together, they make up the whole part inside the circles, with no overlap—that's 1/2 + 1/3 = 5/6 of the respondents.
If that's true, then the "neither" people, i.e., the people who are outside both circles, must be the other 1/6 of the population.

Try setting up a double-set matrix—it will basically always be easier than using a Venn diagram.

_________________
Being well-dressed gives a feeling of inward tranquillity [that] religion is powerless to bestow.
C.F. Forbes
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