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# 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]

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10 Dec 2010, 11:32
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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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A manufacturer conducted a survey to determine how many peop [#permalink]

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10 Dec 2010, 12:01
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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.

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;

Not sufficient to get the ratio we need.

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

{buy neither P nor Q} = 1;
{buy neither P nor Q}/{Total} = 1/6. Sufficient.

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Re: Product P and Q [#permalink]

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10 Dec 2010, 12:29
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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]

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10 Dec 2010, 13:09
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]

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10 Dec 2010, 14:22
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144144 wrote:
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.

Venn diagram makes this question MUCH easier:
Attachment:

untitled.PNG [ 7.28 KiB | Viewed 13146 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.

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

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10 Dec 2010, 14:25
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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]

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10 Dec 2010, 16:42
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]

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10 Dec 2010, 22:16
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]

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28 Feb 2013, 03:38
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]

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05 Mar 2013, 09:26
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]

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06 Mar 2013, 01:53
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]

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06 Mar 2013, 05:53
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?

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.

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]

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06 Mar 2013, 07:55
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?

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.

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+

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]

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

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22 Jul 2015, 04:06
Bunuel wrote:
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.

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.

i could solve the que with help of ven dia. but i am unable to understand the highlighted portion of explanation. pls help.
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Re: A manufacturer conducted a survey to determine how many peop [#permalink]

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22 Jul 2015, 04:45
riyazgilani wrote:
Bunuel wrote:
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.

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.

i could solve the que with help of ven dia. but i am unable to understand the highlighted portion of explanation. pls help.

From (1): {buy P} - {buy both P and Q} = 1/3*6 = 2, so {buy both P and Q} = {buy P} - 2.

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

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05 Sep 2015, 08:59
vyassaptarashi wrote:
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"

I find this solution WAY more intuitive, big thanks
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A manufacturer conducted a survey to determine how many peop [#permalink]

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05 Sep 2015, 21:52
Forget conventional ways of solving math questions. In DS, Variable approach is

the easiest and quickest way to find the answer without actually solving the

problem. Remember equal number of variables and equations ensures a solution.

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.

==> this is a common 2by2 question in GMAT tests that we use variable approach method to solve.

as we can see from above, the original condition is asking for d and since we have 4 variables (a,b,c,d), we need 4 equations to match the number of variables and equations. Since we have 1 each in 1) and 2), E is likely the answer. Using both 1) and 2) together, c=1/3 and a+b=1/2 thus we have c+d=1/2. substituting c=1/3 gives us d=1/6, therefore the answer is C. Here we were able to find the answer, but normally for 90% of these questions with 4 variables the the answer is E. This case was a special case.
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Re: A manufacturer conducted a survey to determine how many peop [#permalink]

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08 Dec 2015, 01:12
Bunuel wrote:
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.

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;

Not sufficient to get the ratio we need.

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

{buy neither P nor Q} = 1;
{buy neither P nor Q}/{Total} = 1/6. Sufficient.

Hi Bunuel,

I have a query on st1.

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

can we infer from above statement 2/3 of people surveyed said they buy product P and product Q.

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

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20 Dec 2015, 00:44
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I believe, this is the quickest possible solution.

Cheers!
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