Venn Diagrams

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sparkle6: Senior | Next Rank: 100 Posts; Posts: 54; Joined: Tue Sep 20, 2011 7:58 amFollowed by: 1 member; Thanked: 1 times

by sparkle6 » Thu Sep 22, 2011 10:59 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 they buy product P but not product Q

2) 1/2 of the people surveyed said that they buy Product Q.

[spoiler]OA: C. Please explain how to solve[/spoiler]

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Source: Beat The GMAT — Data Sufficiency | Thu Sep 22, 2011 10:59 pm

shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Thu Sep 22, 2011 11:48 pm

You could do it using Venn diagrams, here since the answer choices are straight forward let us choose numbers;

Assume total of 6 people are there;

Statement 1: 1/3rd (or) 2 people buy product P alone(No info about Q and others) Insufficient
Statement 2: 1/2 (or) 3 people buy Q (include people who buy both, but not sure of others)

Together you know 2 buy P alone and 3 buy Q (also includes those who buy both)

Hence people who do not buy either is 6-(2+3) = 1.

Hence C

sparkle6 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 they buy product P but not product Q

2) 1/2 of the people surveyed said that they buy Product Q.

[spoiler]OA: C. Please explain how to solve[/spoiler]

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Fri Sep 23, 2011 12:19 am

sparkle6 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 they buy product P but not product Q

2) 1/2 of the people surveyed said that they buy Product Q.

[spoiler]OA: C. Please explain how to solve[/spoiler]

We can take the total no. of people surveyed = 6
We have to find (Neither P nor Q)/6

(1) 1/3 of the people surveyed said they buy product P but not product Q implies (1/3) *(6) = 2; NOT sufficient.

(2) 1/2 of the people surveyed said that they buy Product Q implies (1/2) * 6 = 3; NOT sufficient.

Combining (1) and (2), 6 = 2 + 3 + (Neither P nor Q) implies Neither P nor Q = 1
So, the required ratio = 1/6; SUFFICIENT.

The correct answer is C.

Anurag Mairal, Ph.D., MBA
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Gurome, Inc.
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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Sep 23, 2011 6:08 am

This question is a perfect candidate for solving using the Double Matrix Method.

If you're unfamiliar with the Double Matrix Method, his BTG article (and related videos) will get you started: https://www.beatthegmat.com/mba/2011/05/ ... question-1

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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tpr-becky: GMAT Instructor; Posts: 509; Joined: Wed Apr 21, 2010 1:08 pmFollowed by: 85 members; Location: Irvine, CA; Thanked: 199 times; GMAT Score:750

by tpr-becky » Fri Sep 23, 2011 9:09 am

This problem can be solved using the two group formula

G1 + G2 - B + N = Total

G1 = only P + both
G2 = Only Q + both

So P + B + Q +B - B + N = total

Statement 1 - only info about P - no Q (insufficient)

Statement 2 - only info about B and B - no Q (insufficient)

1/2 + B + 1/3 - B + N = 1

the B's cancel out to get 5/6 + N = 1

N = 1/6

Because this is DS you don't have to solve, just get the formula to the point at which you can.

Take a free practice exam https://www.princetonreview.com/testfest.aspx

Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA

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