BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

In a group of students, 5 participate in no after school...

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 2599
Joined: Sun Oct 29, 2017 2:08 pm
Followed by:2 members

In a group of students, 5 participate in no after school...

by AAPL » Wed Nov 01, 2017 8:12 am
In a group of students, 5 participate in no after school activities and 16 participate in basketball. If 15 participate in field hockey and the group contains 26 students, how many students participate in both field hockey and basketball?

A. 4
B. 5
C. 6
D. 10
E. 21

The OA is D.

I don't understand why that is the correct answer. Please, can any expert explain this PS question for me?
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 555
Joined: Wed Oct 04, 2017 4:18 pm
Thanked: 180 times
Followed by:12 members

Answer

by EconomistGMATTutor » Wed Nov 01, 2017 9:15 am
Hello AAPL.

Let's see your question.

We have that the total of students in the group is 26.

Also, we have that 5 students participate in NO after school activities.

So, we have that 21 students PARTICIPATE in after school activities.

From this 21 students, 16 participate in basketball and 15 participate in field hockey.

So, 5 students participate in field hockey but not in basketball (21-16=5).

Finally, we can conclude that 10 students participate in both, field hockey and basketball (15-5=10).

So, the correct answer is D.

I really hope this can help you.

Feel free to ask me again if you have ny doubt.

Regards.
Last edited by EconomistGMATTutor on Wed Nov 01, 2017 9:17 am, edited 1 time in total.
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

Image
Top

GMAT/MBA Expert

User avatar
Legendary Member
Posts: 503
Joined: Thu Jul 20, 2017 9:03 am
Thanked: 86 times
Followed by:15 members
GMAT Score:770

by ErikaPrepScholar » Wed Nov 01, 2017 9:15 am
This is an overlapping sets problem, where we have two overlapping sets (Basketball vs. No Basketball and Hockey vs. No Hockey). When we have two overlapping sets, your best bet is to make a double matrix.

Image

Then, we fill in what we know:

Image

To answer the question, we need to find how many students play both basketball and hockey, which is the top left white cell.

In a double matrix, the top two cells in each column should add up to the total in the bottom cell in the column, and the leftmost two cells in each row should add up to the total in the rightmost cell in the row. This means that if we have two cells in one row or two cells in one columns, we can use that information in the table to fill in the third cell. Let's see what else we can determine in our table:

Image

then

Image

then finally

Image

So 10 students play both basketball and hockey.
Image

Erika John - Content Manager/Lead Instructor
https://gmat.prepscholar.com/gmat/s/

Get tutoring from me or another PrepScholar GMAT expert: https://gmat.prepscholar.com/gmat/s/tutoring/

Learn about our exclusive savings for BTG members (up to 25% off) and our 5 day free trial

Check out our PrepScholar GMAT YouTube channel, and read our expert guides on the PrepScholar GMAT blog
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Wed Nov 01, 2017 11:39 am
I thought I'd point out that Erika's Double Matrix technique 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 students, and the two characteristics are:
- plays field hockey or does NOT play field hockey
- plays basketball or does NOT play basketball

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8086
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Fri Nov 01, 2019 7:02 pm
AAPL wrote:In a group of students, 5 participate in no after school activities and 16 participate in basketball. If 15 participate in field hockey and the group contains 26 students, how many students participate in both field hockey and basketball?

A. 4
B. 5
C. 6
D. 10
E. 21

The OA is D.

I don't understand why that is the correct answer. Please, can any expert explain this PS question for me?
We can use the formula:

Total = Basketball + Field Hockey - Both + Neither

26 = 16 + 15 - B + 5

26 = 36 - B

B = 10

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1