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A manufacturer

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

Post 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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vinay1983 Legendary Member
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Post Sat Oct 05, 2013 5:18 pm
took the LCM of 2 and 3, say 6
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Post 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:
- buy product Q or not buy product Q
- buy product P or not buy product P
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:
ttp://postimg.org/image/ddcujbfxz/" target="_blank">
Aside: To learn more about this technique, watch our free video: http://www.gmatprepnow.com/module/gmat-word-problems?id=919

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).
ttp://postimg.org/image/594qektiv/" target="_blank">

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.
ttp://postimg.org/image/7ez192wzb/" target="_blank">
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
ttp://postimg.org/image/3la6do513/" target="_blank">
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:
ttp://postimg.org/image/efam6j8i9/" target="_blank">
Does this provide enough information to find the number of people in the bottom right box (where the happy face is)?
YES.
ttp://postimg.org/image/ifyrruelz/" target="_blank">
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

Answer = C

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

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vinay1983 Legendary Member
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Post Sat Oct 05, 2013 5:18 pm
took the LCM of 2 and 3, say 6
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Post 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:
- buy product Q or not buy product Q
- buy product P or not buy product P
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:
ttp://postimg.org/image/ddcujbfxz/" target="_blank">
Aside: To learn more about this technique, watch our free video: http://www.gmatprepnow.com/module/gmat-word-problems?id=919

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).
ttp://postimg.org/image/594qektiv/" target="_blank">

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.
ttp://postimg.org/image/7ez192wzb/" target="_blank">
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
ttp://postimg.org/image/3la6do513/" target="_blank">
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:
ttp://postimg.org/image/efam6j8i9/" target="_blank">
Does this provide enough information to find the number of people in the bottom right box (where the happy face is)?
YES.
ttp://postimg.org/image/ifyrruelz/" target="_blank">
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

Answer = C

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

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

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Post Sat Oct 05, 2013 5:42 pm

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

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rakeshd347 Master | Next Rank: 500 Posts Default Avatar
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Post 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
answer should be C

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.
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vinay1983 Legendary Member
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Post 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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