• e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep

Double Set Matrix question

This topic has 1 expert reply and 1 member reply
gmattesttaker2 Legendary Member Default Avatar
Joined
14 Feb 2012
Posted:
641 messages
Followed by:
8 members
Upvotes:
11

Double Set Matrix question

Post Sun Nov 03, 2013 8:57 pm
Hello,

Can you please let me know how to solve Statement 2 using Double Set Matrix method? I am able to solve Statement 1.

Last year in a group of 30 businesses, 21 reported a net profit and 15 had investments in foreign markets. How many of the businesses did not report a net profit nor invest in foreign markets last year?

(1) last year 12 of the 30 businesses reported a net profit and had investments
in foreign markets.

(2) last year 24 of the 30 businesses reported a net profit or invested in
foreign markets, or both.


OA: D
Attachments

This post contains an attachment. You must be logged in to download/view this file. Please login or register as a user.

  • +1 Upvote Post
  • Quote
  • Flag
gmattesttaker2 Legendary Member Default Avatar
Joined
14 Feb 2012
Posted:
641 messages
Followed by:
8 members
Upvotes:
11
Post Sun Nov 03, 2013 11:34 pm
Brent@GMATPrepNow wrote:
gmattesttaker2 wrote:
Hello,

Can you please let me know how to solve Statement 2 using Double Set Matrix method? I am able to solve Statement 1.

Last year in a group of 30 businesses, 21 reported a net profit and 15 had investments in foreign markets. How many of the businesses did not report a net profit nor invest in foreign markets last year?

(1) last year 12 of the 30 businesses reported a net profit and had investments
in foreign markets.

(2) last year 24 of the 30 businesses reported a net profit or invested in
foreign markets, or both.
The Double Matrix Method can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of businesses, and the two characteristics are:
- had a net profit or didn't have a net profit
- invested in foreign markets or didn't invest in foreign markets

So, we can set up our diagram as follows:
ttp://postimg.org/image/yno617x9t/" target="_blank">

Now, if there are 30 businesses and 21 reported a net profit, then 9 did NOT report a net profit.
Similarly, if there are 30 businesses and 15 had investments in foreign markets, then 15 did NOT have investments in foreign markets. So, we can add that information to the diagram.
ttp://postimg.org/image/gneywu52p/" target="_blank">
Note: I placed a star in the bottom right box to remind me that this is the value we are trying to determine.

Statement 1: Last year 12 of the 30 businesses reported a net profit and had investments in foreign markets.
When we add this information to our diagram, we get the following:
ttp://postimg.org/image/t0rt3qur5/" target="_blank">

Since we know the sums of the rows and columns, we can determine the values in every box to get the following:
ttp://postimg.org/image/dhyykdbu9/" target="_blank">
Notice that we can determine the value for the bottom right box, which means we can answer the target question with certainty.
So, statement 1 is SUFFICIENT

Statement 2: last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both.
The three shaded boxes below represent the businesses that reported a net profit or invested in foreign markets, or both.
ttp://postimg.org/image/t4q7xqpm9/" target="_blank">

Since all 4 boxes must add to 30, we can see last remaining box must contain the 6 remaining businesses.
ttp://postimg.org/image/6hayrla29/" target="_blank">
So, we can determine the value for the bottom right box, which means statement 2 is SUFFICIENT

Answer: D

To learn more about this technique, watch our free video: http://www.gmatprepnow.com/module/gmat-word-problems?id=919

Then try these additional practice questions that can be solved using the Double Matrix Method:
- http://www.beatthegmat.com/mba/2011/05/05/random-double-matrix-question-1
- http://www.beatthegmat.com/mba/2011/05/09/random-double-matrix-question-2
- http://www.beatthegmat.com/mba/2011/05/16/random-double-matrix-question-3
- http://www.beatthegmat.com/ds-quest-t187706.html
- http://www.beatthegmat.com/overlapping-sets-questions-t183320.html
- http://www.beatthegmat.com/finance-majors-non-finance-majors-overlapping-set-question-t167425.html
- http://www.beatthegmat.com/ds-french-japanese-t222297.html
- http://www.beatthegmat.com/sets-t269449.html#692540
- http://www.beatthegmat.com/in-costume-for-halloween-t269355.html#692116

Cheers,
Brent
Hello Brent,

Thanks a lot for your detailed and excellent (as always!) explanation. Thanks also for sharing the free tutorial videos.

Best Regards,
Sri

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Sun Nov 03, 2013 10:45 pm
gmattesttaker2 wrote:
Hello,

Can you please let me know how to solve Statement 2 using Double Set Matrix method? I am able to solve Statement 1.

Last year in a group of 30 businesses, 21 reported a net profit and 15 had investments in foreign markets. How many of the businesses did not report a net profit nor invest in foreign markets last year?

(1) last year 12 of the 30 businesses reported a net profit and had investments
in foreign markets.

(2) last year 24 of the 30 businesses reported a net profit or invested in
foreign markets, or both.
The Double Matrix Method can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of businesses, and the two characteristics are:
- had a net profit or didn't have a net profit
- invested in foreign markets or didn't invest in foreign markets

So, we can set up our diagram as follows:
ttp://postimg.org/image/yno617x9t/" target="_blank">

Now, if there are 30 businesses and 21 reported a net profit, then 9 did NOT report a net profit.
Similarly, if there are 30 businesses and 15 had investments in foreign markets, then 15 did NOT have investments in foreign markets. So, we can add that information to the diagram.
ttp://postimg.org/image/gneywu52p/" target="_blank">
Note: I placed a star in the bottom right box to remind me that this is the value we are trying to determine.

Statement 1: Last year 12 of the 30 businesses reported a net profit and had investments in foreign markets.
When we add this information to our diagram, we get the following:
ttp://postimg.org/image/t0rt3qur5/" target="_blank">

Since we know the sums of the rows and columns, we can determine the values in every box to get the following:
ttp://postimg.org/image/dhyykdbu9/" target="_blank">
Notice that we can determine the value for the bottom right box, which means we can answer the target question with certainty.
So, statement 1 is SUFFICIENT

Statement 2: last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both.
The three shaded boxes below represent the businesses that reported a net profit or invested in foreign markets, or both.
ttp://postimg.org/image/t4q7xqpm9/" target="_blank">

Since all 4 boxes must add to 30, we can see last remaining box must contain the 6 remaining businesses.
ttp://postimg.org/image/6hayrla29/" target="_blank">
So, we can determine the value for the bottom right box, which means statement 2 is SUFFICIENT

Answer: D

To learn more about this technique, watch our free video: http://www.gmatprepnow.com/module/gmat-word-problems?id=919

Then try these additional practice questions that can be solved using the Double Matrix Method:
- http://www.beatthegmat.com/mba/2011/05/05/random-double-matrix-question-1
- http://www.beatthegmat.com/mba/2011/05/09/random-double-matrix-question-2
- http://www.beatthegmat.com/mba/2011/05/16/random-double-matrix-question-3
- http://www.beatthegmat.com/ds-quest-t187706.html
- http://www.beatthegmat.com/overlapping-sets-questions-t183320.html
- http://www.beatthegmat.com/finance-majors-non-finance-majors-overlapping-set-question-t167425.html
- http://www.beatthegmat.com/ds-french-japanese-t222297.html
- http://www.beatthegmat.com/sets-t269449.html#692540
- http://www.beatthegmat.com/in-costume-for-halloween-t269355.html#692116

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

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

Best Conversation Starters

1 Roland2rule 125 topics
2 lheiannie07 110 topics
3 ardz24 60 topics
4 LUANDATO 55 topics
5 swerve 51 topics
See More Top Beat The GMAT Members...

Most Active Experts

1 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

151 posts
2 image description GMATGuruNY

The Princeton Review Teacher

135 posts
3 image description Scott@TargetTestPrep

Target Test Prep

129 posts
4 image description Rich.C@EMPOWERgma...

EMPOWERgmat

111 posts
5 image description DavidG@VeritasPrep

Veritas Prep

83 posts
See More Top Beat The GMAT Experts