Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

How many people are directors of both Company K and Company [#permalink]

Show Tags

24 Sep 2012, 05:21

Expert's post

7

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

5% (low)

Question Stats:

76% (01:52) correct
24% (00:58) wrong based on 667 sessions

HideShow timer Statistics

How many people are directors of both Company K and Company R ?

(1) There were 17 directors present at a joint meeting of the directors of Company K and Company R, and no directors were absent. (2) Company K has 12 directors and Company R has 8 directors.

Practice Questions Question: 49 Page: 279 Difficulty: 600

Re: How many people are directors of both Company K and Company [#permalink]

Show Tags

24 Sep 2012, 05:22

1

This post received KUDOS

Expert's post

SOLUTION

How many people are directors of both Company K and Company R ?

(1) There were 17 directors present at a joint meeting of the directors of Company K and Company R, and no directors were absent. Together Company K and Company R have 17 directors (total #). Not sufficient to say how many people out of those 17 are directors of both.

(2) Company K has 12 directors and Company R has 8 directors. We know how many directors has each company, but it's still not sufficient to to say how many are directors of both.

(1)+(2) Company K has 12 directors and Company R has 8 directors, which adds up to 12+8=20, since we know that there are total of 17 directors then 20-17=3 people must be directors of both Company K and Company R. Sufficient.

Re: How many people are directors of both Company K and Company [#permalink]

Show Tags

18 May 2014, 10:58

Obviously stmt 1 and 2 alone are not sufficient. Let's try 1+2 : Let x be the number of directors of both K and R. If K has 12 directors and R has 8 directors. Then the number of directors who are present at the meeting will be: 12+8-X=17, X=3. Hence C.

Re: How many people are directors of both Company K and Company [#permalink]

Show Tags

21 Jul 2014, 05:09

Total = A + B - Both+None

(1) Total = 17. IS. (2) A = 12, B = 8. IS.

(1) + (2): From 1 we get there there are 17 directors. Since the number of directors of both companies exceeds this total number, we now know that there are no people that are "none". Hence its 12+8-both=17, both =3. SUFF.

Re: How many people are directors of both Company K and Company [#permalink]

Show Tags

07 May 2015, 12:11

6

This post received KUDOS

1

This post was BOOKMARKED

runningguy wrote:

Would someone mind constructing a double matrix with this problem?

Thanks, C

2 years later, but here you go

I think the biggest takeaway for this question is to realize the meaning of "no directors were absent". Without this information we can't actually solve the question

Re: How many people are directors of both Company K and Company [#permalink]

Show Tags

08 May 2015, 11:46

1

This post received KUDOS

Expert's post

Hi All,

It looks like everyone in this thread has answered the question correctly, so I won't rehash any of those steps here. This DS question is based on a variation of the "overlapping sets" concept that you'll likely see on the GMAT once or twice. There are several different ways to solve this problem, but since this is a simple variation, I'll show you the simple math.

The idea is this: If a person is a member of BOTH groups, then that person has been "counted" twice (once for the first group and once for the second). When calculating the total number of people, you're NOT supposed to count people twice, so you have to mathematically remove that "second count."

Here's a simple example: 3 people total 1 person in group A 1 person in group B 1 person in BOTH group A and B

Total in group A = 2 Total in group B = 2 But that DOES NOT mean that there are 4 people; there are only 3.

In this type of question, the "math" formula is Total = Group A + Group B - BOTH = 2 + 2 - 1 = 3 people total

The same logic applies in this question. Total = 17 Company K = 12 Company R = 8 Both = ?

Total = CompK + CompR - BOTH 17 = 12 + 8 - BOTH 17 = 20 - BOTH 3 = BOTH

How many people are directors of both Company K and Company [#permalink]

Show Tags

11 Jan 2016, 06:29

EMPOWERgmatRichC wrote:

Hi All,

It looks like everyone in this thread has answered the question correctly, so I won't rehash any of those steps here. This DS question is based on a variation of the "overlapping sets" concept that you'll likely see on the GMAT once or twice. There are several different ways to solve this problem, but since this is a simple variation, I'll show you the simple math.

The idea is this: If a person is a member of BOTH groups, then that person has been "counted" twice (once for the first group and once for the second). When calculating the total number of people, you're NOT supposed to count people twice, so you have to mathematically remove that "second count."

Here's a simple example: 3 people total 1 person in group A 1 person in group B 1 person in BOTH group A and B

Total in group A = 2 Total in group B = 2 But that DOES NOT mean that there are 4 people; there are only 3.

In this type of question, the "math" formula is Total = Group A + Group B - BOTH = 2 + 2 - 1 = 3 people total

The same logic applies in this question. Total = 17 Company K = 12 Company R = 8 Both = ?

Total = CompK + CompR - BOTH 17 = 12 + 8 - BOTH 17 = 20 - BOTH 3 = BOTH

GMAT assassins aren't born, they're made, Rich

Rich Cohen and his miracles. How did it not occur to me that this was a simple 2 set thing. Total = A + B + Neither - Both!. 17 = 12 + 8 + 0 - Both. -Both = 17 - 12 - 8 - B = - 3 B = 3 There should a "hail!" button in @EmpowerGmatRichC's profile.

Last edited by Nezdem on 11 Jan 2016, 22:05, edited 1 time in total.

Re: How many people are directors of both Company K and Company [#permalink]

Show Tags

11 Jan 2016, 14:37

1

This post received KUDOS

Expert's post

Hi Nez,

With the proper practice/training, you'll come to realize that everything you'll see on Test Day will remind you of some prompt that you've already faced. As the GMAT adapts to you, it will test you on the same general concepts, but in ways that you might not be used to thinking about those concepts. In that way, the test really is about measuring your critical thinking skills. This question serves as a reasonable example of that. This is all meant to say that when you face a question that seems 'weird', you should think about the parts of it that seem familiar - chances are pretty good that you already have the necessary knowledge to solve it.

And as an aside, you should double-check your last calculation; B does NOT equal 2.

Re: How many people are directors of both Company K and Company [#permalink]

Show Tags

12 Jan 2016, 00:47

Expert's post

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

How many people are directors of both Company K and Company R ?

(1) There were 17 directors present at a joint meeting of the directors of Company K and Company R, and no directors were absent. (2) Company K has 12 directors and Company R has 8 directors.

This question is frequently given in the Gmat Math test, which is “2 by 2” question like the table below.

Attachment:

B.jpg [ 16.32 KiB | Viewed 1160 times ]

In the table, there are 4 variables(a,b,c,d), which should match with the number of equations. So you need 4 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer as 2 more equations are needed. When 1) & 2), in 1), there are 2 equations(a+b+c=17, d=0) and in 2), 2 equations(a+c=12, a+b=8), which is sufficient. Therefore, the answer is C.

For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D. _________________

Part 2 of the GMAT: How I tackled the GMAT and improved a disappointing score Apologies for the month gap. I went on vacation and had to finish up a...

So the last couple of weeks have seen a flurry of discussion in our MBA class Whatsapp group around Brexit, the referendum and currency exchange. Most of us believed...

This highly influential bestseller was first published over 25 years ago. I had wanted to read this book for a long time and I finally got around to it...