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

Redeem

OG13:If 75 percent of the employees of a certain company....

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 12
Joined: Thu Nov 14, 2013 12:20 pm

OG13:If 75 percent of the employees of a certain company....

by nataras » Fri Jul 04, 2014 11:16 am
If 75 percent of the employees of a certain company take a winter vacation, 40 percent take a winter and a summer vacation, and 20 percent take neither a winter nor a summer vacation, what percent of the employees take a summer vacation but not a winter vacation?

A) 5%
B) 15%
C) 25%
D) 35%
E) 45%

OA: A
I was able to back into this answer by doing the following (assuming 100 employees): 100-75 (winter)-20 (neither) = 5 (summer only). However is there a more technical way to solve this? Why does the Winter + Summer + Neither - Both formula not work for this question?[/img]
Top
Source: — Problem Solving |

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 » Fri Jul 04, 2014 11:28 am
HINT: This question can be solved using the Double Matrix Method. This 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 employees, and the two characteristics are:
- take a winter vacation or don't take a winter vacation
- take a summer vacation or don't take a summer vacation

Watch our free video on the Double Matrix Method, and I'm certain that you'll be able to quickly solve the question: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you've mastered the technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/the-aam-aadm ... 72242.html
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.beatthegmat.com/probability- ... 73360.html
- 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/ds-french-ja ... 22297.html

Difficult Problem Solving questions
- 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.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://www.beatthegmat.com/double-set-m ... 71423.html
- 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
User avatar
Legendary Member
Posts: 1100
Joined: Sat May 10, 2014 11:34 pm
Location: New Delhi, India
Thanked: 205 times
Followed by:24 members

by GMATinsight » Fri Jul 04, 2014 10:40 pm
Hi Nataras,

Please Check the explanation


Image


CORRECT ANSWER OPTION A
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 116
Joined: Wed Mar 14, 2012 1:02 pm
Thanked: 20 times
Followed by:11 members
GMAT Score:760

by mcdesty » Sat Jul 05, 2014 6:41 am
This question type is extremely common on the GMAT. I absolutely recommend that you complete all the exercises provided by Brent above: Your score will thank you for it.

See image for a solution to the problem above.
Attachments
Gmat_06.jpg
Last edited by mcdesty on Sun Jul 13, 2014 2:33 pm, edited 1 time in total.
Top
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Thu Sep 12, 2013 1:29 am

by nnasr » Sat Jul 05, 2014 12:32 pm
Thanks Brent for your post.

Nataras, I believe the formula result you have referred to, which gives the result of 45 - is the 'total Summer' . If you draw the matrix, the row of 'Total Summer' = 45 and comprises of 40 ( those who spend summer + winter) + 5 ( those who spend summer but not winter) - this yields 45.

The Formula is A + B - Both + Neither = 45
75 + x - 40 + 20 = 45

I think you were trying to match the answer with an incorrect component of the formula.
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sat Jul 05, 2014 1:40 pm
nataras wrote:If 75 percent of the employees of a certain company take a winter vacation, 40 percent take a winter and a summer vacation, and 20 percent take neither a winter nor a summer vacation, what percent of the employees take a summer vacation but not a winter vacation?

A) 5%
B) 15%
C) 25%
D) 35%
E) 45%

OA: A
I was able to back into this answer by doing the following (assuming 100 employees): 100-75 (winter)-20 (neither) = 5 (summer only). However is there a more technical way to solve this? Why does the Winter + Summer + Neither - Both formula not work for this question?[/img]
I would use a double-matrix here.
That said, we could also use the following formula:

Total = Winter + Summer - Both + Neither.

The big idea behind the formula above is to SUBTRACT THE OVERLAP.
When we count everyone who takes a winter vacation and everyone who takes a summer vacation, the overlap -- the percentage who take BOTH types of vacation -- is counted TWICE.
Thus, we must SUBTRACT the percentage who take BOTH types of vacation so that they are not double-counted.

Let the total = 100.
Plugging into the formula the given values for winter (75%), both (40%) and neither (20%), we get:
100 = 75 + Summer - 40 + 20
100 = 55 + Summer
Summer = 45.

Since a total of 45% take a summer vacation, while 40% take BOTH types of vacation, the percentage who take ONLY a summer vacation = 45-40 = 5.

The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
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 » Mon Jul 14, 2014 8:00 pm
nataras wrote:If 75 percent of the employees of a certain company take a winter vacation, 40 percent take a winter and a summer vacation, and 20 percent take neither a winter nor a summer vacation, what percent of the employees take a summer vacation but not a winter vacation?

A) 5%
B) 15%
C) 25%
D) 35%
E) 45%
mcdesty's Double Matrix solution is perfect.
For those who are less familiar with the technique, I thought I'd take a step-by-step approach.

We have a population of employees, and the two characteristics are:
- take a winter vacation or don't take a winter vacation
- take a summer vacation or don't take a summer vacation

So, we'll set up our matrix as follows:
Image
NOTE: Since we're need to find a PERCENT (rather than the actual number of people), we'll say that there are 100 employees altogether. This will make our calculations easier.

75 percent of the employees of a certain company take a winter vacation
If 75% TAKE a winter vacation, the remaining 25% DON'T take a winter vacation.
Since we've let 100 = the total number of employees, we can see that 75 take a winter vacation and 25 don't. We'll add this to our diagram:
Image

40 percent take a winter and a summer vacation
So, 40 employees take a winter AND a summer vacation, which we can add to our diagram.
Image


20 percent take neither a winter nor a summer vacation
Add that here:
Image

what percent of the employees take a summer vacation but not a winter vacation
We'll place a heart in the box that represents the value we're trying to solve for.
Image

IMPORTANT: Since the bottom 2 boxes must add to 25, we can see that the bottom left box must equal 5.
Image

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Senior | Next Rank: 100 Posts
Posts: 66
Joined: Fri Jun 06, 2014 11:48 pm
Followed by:1 members

by phanikpk » Mon Jul 14, 2014 8:40 pm
Total number of members= n(A)+ n(B)+ n(C)+ n(A^B^C)- (n(A^B)+n(B^C)+ n(A^C)+ neither
Since only two groups are there

P.S. ^ intersection
Total-neither= n(A)+ n(B)-n(A^B)
Which gives

100-20= 75+x-40
80= x+35
x=45

Finally, only summer vacation includes n(B)-n(A^B)
45-40=5%
Top
Post new topic Post Reply
• Page 1 of 1