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## A manufacturer

tagged by: Brent@GMATPrepNow

This topic has 2 expert replies and 5 member replies
Java_85 Master | Next Rank: 500 Posts
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#### A manufacturer

Sat Oct 05, 2013 4:32 pm
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.

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Brent@GMATPrepNow GMAT Instructor
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Sat Oct 05, 2013 5:42 pm
Java_85 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?

(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 great candidate for a technique called the Double Matrix Method. It can be used for most questions featuring a population in which each member has two criteria associated with it.
Here, the criteria are:
When I scan the two statements I see that they mention 1/3 of the people surveyed and 1/2 of the people surveyed. I also see that the target question asks us to find a fraction of the people surveyed (not the actual number). So, let's pick a nice number that works well with 1/3 and 1/2.
Let's say there 12 people were surveyed.

So, we'll start by setting up our diagram like this:

We want to find the fraction of the people surveyed said that they neither buy product P nor product Q. So, to answer this question, we need to know the number of people in the bottom right box (where the happy face is).

We're now ready to check the statements.

Statement 1: 1/3 of the people surveyed said that they buy product P but not product Q.
1/3 of 12 = 4. So, 4 people buy product P but not product Q.

Does this provide enough information to find the number of people in the bottom right box (where the happy face is)?
No.
Statement 1 is NOT SUFFICIENT

Statement 2: 1/2 of the people surveyed said that they buy product Q.
So, 6 people buy product Q, which means 6 people do not buy product Q

Does this provide enough information to find the number of people in the bottom right box (where the happy face is)?
No.
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
We get:

Does this provide enough information to find the number of people in the bottom right box (where the happy face is)?
YES.

Since the two boxed in the right-hand column must add to 6, the bottom right box must have 2 people, which means 2/12 people said that they neither buy product P nor product Q.

Since we can now answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent

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Brent@GMATPrepNow GMAT Instructor
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Sat Oct 05, 2013 5:42 pm

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Brent Hanneson â€“ Founder of GMATPrepNow.com
Use our video course along with

Check out the online reviews of our course
Come see all of our free resources

GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months!
vinay1983 Legendary Member
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Sat Oct 05, 2013 4:39 pm
Java_85 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?

(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.
Is it C

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You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!

Java_85 Master | Next Rank: 500 Posts
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Sat Oct 05, 2013 4:43 pm
Yes, It is, I think to answer this question we need to know how many people are buying both products P and Q, but question didn't say anything about it.

vinay1983 wrote:
Java_85 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?

(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.
Is it C

vinay1983 Legendary Member
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Sat Oct 05, 2013 4:59 pm
This can be solved using the double matrix method. You have to quickly realize that Individually the statements are not enough. So combine and solve

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rakeshd347 Master | Next Rank: 500 Posts
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Sat Oct 05, 2013 5:01 pm
Java_85 wrote:
Yes, It is, I think to answer this question we need to know how many people are buying both products P and Q, but question didn't say anything about it.

vinay1983 wrote:
Java_85 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?

(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.
Is it C
Hi Mate

we are asked about the fraction so two statements together are sufficient. Have a look at my explanation through attachment. i have used double matrix method to solve it.
Attachments

vinay1983 Legendary Member
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Sat Oct 05, 2013 5:18 pm
took the LCM of 2 and 3, say 6
Attachments

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