A manufacturer conducted a survey to determine how many peop

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

10 Dec 2010, 12:32

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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.

[Reveal] Spoiler: OA

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Re: Product P and Q [#permalink]

10 Dec 2010, 13:01

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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?

You can solve this question with Venn diagram, matrix or as shown below.

{Total} = {buy P} + {buy Q} - {buy both P and Q} + {buy neither P nor Q}.
Question: {buy neither P nor Q} / {Total} = ?

Take total to be equal to 6 (as it's a multiple of both 2 and 3)

(1) 1/3 of the people surveyed said that they buy product P but not product Q --> {buy P} - {buy both P and Q}=1/3*6=2 --> 6 = {buy P} + {buy Q} - ({buy P} - 2) + {buy neither P nor Q} --> 4={buy Q} + {buy neither P nor Q}. Not sufficient to get the ratio we need.

(2) 1/2 of the people surveyed said that they buy product Q --> {buy Q}=1/2*6=3. Not sufficient.

(1)+(2) 4={buy Q} + {buy neither P nor Q} and {buy Q}=3 --> {buy neither P nor Q}=1 --> {buy neither P nor Q}/{Total}=1/6. Sufficient.

Answer: C.
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Re: Product P and Q [#permalink]

10 Dec 2010, 13:29

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This problem should be solved following way

There are 2 products "P" and "Q", and we have to answer what fraction of people do not select both the products.

Option 1- 1/3 of people select only P and not Q
So, suppose we have 90 people responded to survey then 1/3 of 90 = 30 people select only product P
But, this option does not tells us anything about Q, so not sufficient to answer the question.

Option 2- 1/2 people select product Q ....this includes people who selected inly product Q and people who selected
both product P and Q i.e. P intersection Q
Therefore if 90 people responded to survey 45 people selected product Q, but it does not tells us how
many people select only product p

Now, it we combine the options it gives us value of A U B i.e if we have 90 people on the survey 30 selected product P and 45 selected product Q along with P intersection Q

Therefore P U Q = 30 + 45 = 75
Therefore (P U Q)' = 90 - 75 = 15
Hence fraction of people did not select any product = 15/90

Hence we get the answer by taking both the options together... hence answer "C"
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Re: Product P and Q [#permalink]

10 Dec 2010, 14:09

i still dont understand.

lets take ur choices:

1. the total is 6. (1) means we have 2 ppl buy product P no Q.
(2) means 3 ppl buy Q (mayb together with P also).
i still cannot understand how u can figure out from that the area covered by both P+Q and by
none. Im not sure what im missing, but as i see it, we can have ppl that buy both P+Q
between none to 4 and it still wont make any logic problem with both sentences.

I guess im having hard time to understand why u chose to put the - {buy both P and Q}
in minus and not plus. the total should be a sum of all groups together isnt it?

thanks a lot for all the time and help for both of u guys.
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Re: Product P and Q [#permalink]

10 Dec 2010, 15:22

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144144 wrote:

Venn diagram makes this question MUCH easier:

Attachment:

untitled.PNG [ 7.28 KiB | Viewed 1878 times ]

First about the formula: {Total} = {buy P} + {buy Q} - {buy both P and Q} + {buy neither P nor Q}. Note that P={Only P}+{Both P&Q} and Q={Only Q}+{Both P&Q}. In {Total}={P}+{Q}-{Both P&Q}+{Neither P nor Q} we subtract {Both P&Q} as P and Q both contain this segment and thus in P+Q it's counted twice, so we should subtract it to count it only once.

Back to the question:

Again let's take total to be equal to 6: so 6=Green+Yellow+Blue+Grey. We need to get Grey/Total=Grey/6=?.

(1) 1/3 of the people surveyed said that they buy product P but not product Q --> Green=1/3*6=2. Not sufficient to get the ratio we need.

(2) 1/2 of the people surveyed said that they buy product Q --> Yellow+Blue=1/2*6=3. Not sufficient.

(1)+(2) 6=Green+Yellow+Blue+Grey=2+3+Grey --> Grey=1 --> Grey/Total=1/6. Sufficient.

Answer: C.

Hope it's clear.
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Re: Product P and Q [#permalink]

10 Dec 2010, 15:25

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144144 wrote:

I guess im having hard time to understand why u chose to put the - {buy both P and Q} in minus and not plus. the total should be a sum of all groups together isnt it?

thanks a lot for all the time and help for both of u guys.

Here's the equation:

True # of objects = (everyone in group 1) + (everyone in group 2) - (everyone in both groups) + people in neither group

You ask why we subtract everyone in both groups; it's because we've already counted those people twice!

If we break down the first two components

everyone in group 1 = (people only in group 1) + (people in both groups)
everyone in group 2 = (people only in group 2) + (people in both groups)

you can see that we've counted "people in both groups" twice. Subbing into the original equation:

True # of objects = ((people only in group 1) + (people in both groups)) + ((people only in group 2) + (people in both groups)) - (everyone in both groups) + people in neither group

which is why we need to subtract "everyone in both groups" to end up only counting them once.
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Re: Product P and Q [#permalink]

10 Dec 2010, 17:42

I got the right answer, but it took me awhile.

Thanks for the explanation on how to get it quickly!
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Re: Product P and Q [#permalink]

10 Dec 2010, 23:16

Thanks for the explanations guys.

Bunuel - thanks a lot for the time u put in the drawings and all.

appreciated very much.

+1 for both. thanks.
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A manufacturer conducted a survey to determine how many people b [#permalink]

28 Feb 2013, 04:38

Since we the objective is to obtain the value of 1 - PUQ there is a simple solution to this problem using the following formula:

PUQ = P + Q - PiQ

Statement 1 provides the following information:
P = 1/3 + PiQ

Statement 2 provides the following information:
Q = 1/2

Then we can conclude that
PUQ = 1/3 + PiQ + 1/2 - PiQ
PUQ = 5/6

Thus non-buyers are 1 - PUQ = 1 - 5/6 = 1/6

BOTH STATEMENTS TOGETHER ARE SUFFICIENT

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

05 Mar 2013, 10:26

Hey Bunuel this isn't clear to me because you write
(1)+(2) 6=Green+Yellow+Blue+Grey.

Isn't it suppose to be 6=Green-Yellow+Blue+Grey?
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Re: A manufacturer conducted a survey to determine how many peop [#permalink]

06 Mar 2013, 02:53

manimgoindowndown wrote:

Hey Bunuel this isn't clear to me because you write
(1)+(2) 6=Green+Yellow+Blue+Grey.

Isn't it suppose to be 6=Green-Yellow+Blue+Grey?

To get the entire space (total) we should add Green, Yellow, Blue, and Grey areas.

About the difference check here: a-polling-company-found-that-of-300-households-surveyed-148727.html?hilit=diagram#p1191678

Hope it helps.
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Re: A manufacturer conducted a survey to determine how many peop [#permalink]

06 Mar 2013, 06:53

Bunuel wrote:

manimgoindowndown wrote:

Hey Bunuel this isn't clear to me because you write
(1)+(2) 6=Green+Yellow+Blue+Grey.

Isn't it suppose to be 6=Green-Yellow+Blue+Grey?

With the Venn Diagram it makes sense but writing it out algabreically I wouldn't be able to do it I would get as far as this and wouldn't know how to figure out both the only Q and both values. I think I am missing a simple implication of the 2nd statement and what affect it has.

Total= P + Q -both +neither
6= 2+
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Re: A manufacturer conducted a survey to determine how many peop [#permalink]

06 Mar 2013, 08:55

manimgoindowndown wrote:

Bunuel wrote:

manimgoindowndown wrote:

Hey Bunuel this isn't clear to me because you write
(1)+(2) 6=Green+Yellow+Blue+Grey.

Isn't it suppose to be 6=Green-Yellow+Blue+Grey?

Can you please tell me what didn't you understand in the explanation of the second statement here: a-manufacturer-conducted-a-survey-to-determine-how-many-peop-106092.html#p831244 or here:http://gmatclub.com/forum/a-manufacturer-conducted-a-survey-to-determine-how-many-peop-106092.html#p831338 ?
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Re: A manufacturer conducted a survey to determine how many peop [#permalink] 06 Mar 2013, 08:55

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