It is currently 26 Jun 2017, 14:35

### GMAT Club Daily Prep

#### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# How many people are directors of both Company K and Company

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 39702
How many people are directors of both Company K and Company [#permalink]

### Show Tags

24 Sep 2012, 05:21
Expert's post
11
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

78% (01:52) correct 22% (00:55) wrong based on 1071 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
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 39702
Re: How many people are directors of both Company K and Company [#permalink]

### Show Tags

24 Sep 2012, 05:22
4
KUDOS
Expert's post
2
This post was
BOOKMARKED
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.

_________________
Moderator
Joined: 01 Sep 2010
Posts: 3213
Re: How many people are directors of both Company K and Company [#permalink]

### Show Tags

28 Sep 2012, 07:25
1
KUDOS
The question ask us to find a person (s) that is (are) both director of 2 companies

1) 17 total people is not enough to establish how many of them are both director

2) he we know only the member of the 2 companies but not both

1) + 2) if we have 17 persons from 1 and 20 from 2----> 3 people MUST be both companies X and Y

_________________
Intern
Joined: 05 Aug 2012
Posts: 4
Re: How many people are directors of both Company K and Company [#permalink]

### Show Tags

17 Aug 2013, 00:24
1
KUDOS
On applying the 2X2 matrix method, I guess we should assume or mark neither K nor M column as 0 to get C?
Math Expert
Joined: 02 Sep 2009
Posts: 39702
Re: How many people are directors of both Company K and Company [#permalink]

### Show Tags

17 Aug 2013, 03:13
1
KUDOS
Expert's post
rakshaki wrote:
On applying the 2X2 matrix method, I guess we should assume or mark neither K nor M column as 0 to get C?

We don't need to assume that, it follows from the statements.
_________________
Intern
Joined: 09 Sep 2013
Posts: 19
Re: How many people are directors of both Company K and Company [#permalink]

### Show Tags

14 Oct 2013, 21:15
Would someone mind constructing a double matrix with this problem?

Thanks,
C
Manager
Joined: 18 May 2014
Posts: 63
Location: United States
Concentration: General Management, Other
GMAT Date: 07-31-2014
GPA: 3.99
WE: Analyst (Consulting)
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.
Current Student
Joined: 21 Oct 2013
Posts: 193
Location: Germany
GMAT 1: 660 Q45 V36
GPA: 3.51
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.
Manager
Joined: 26 Feb 2015
Posts: 127
Re: How many people are directors of both Company K and Company [#permalink]

### Show Tags

07 May 2015, 12:11
8
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

Hope this helps!
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 9271
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: How many people are directors of both Company K and Company [#permalink]

### Show Tags

08 May 2015, 11:46
2
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

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

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Senior Manager Joined: 15 Oct 2015 Posts: 376 Concentration: Finance, Strategy GPA: 3.93 WE: Account Management (Education) 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. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 9271 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 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. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 3460
GPA: 3.82
Re: How many people are directors of both Company K and Company [#permalink]

### Show Tags

12 Jan 2016, 00:47
Expert's post
1
This post was
BOOKMARKED
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 4126 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.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Intern
Joined: 15 Feb 2016
Posts: 15
Re: How many people are directors of both Company K and Company [#permalink]

### Show Tags

15 Aug 2016, 20:05
Hi , I have one issue with this answer.

The question does not state 'what is the minimum possible number of directors who belong to both Company K and Company R.

If I were to not use any formula and just plot this out I see multiple possible solutions.

Only Company K + Both + Only Company R = 17

9 + 3 + 5 = 17 Or
9 + 4 + 4 = 17
9 + 5 + 3 = 17
9 + 6 + 2 = 17
9 + 7 + 1 = 17
9 + 8 + 0 = 17

Since there is no specified number of employees who are only part of Company R, the number 8 can be split up in multiple ways and the answer can range from 3,4,5,6,7,8 !

Sheetal - 7 days to go!!!!
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 9271
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: How many people are directors of both Company K and Company [#permalink]

### Show Tags

16 Aug 2016, 19:51
Hi sheetaldodani,

There's an error in your logic - while you've accounted for the fact that the total number of people in BOTH and "Only R" would total 8, you have NOT accounted for the fact that the total number of people in "Only K" and BOTH would total 12. That piece of information would eliminate 5 of your 6 options - leaving you with just the one possibility.

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

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

# Special Offer: Save \$75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Intern
Joined: 15 Feb 2016
Posts: 15
Re: How many people are directors of both Company K and Company [#permalink]

### Show Tags

17 Aug 2016, 05:50
Oops ... feel very stupid once you pointed it out :p ... thank you for making me see it
Intern
Joined: 18 Mar 2017
Posts: 44
Re: How many people are directors of both Company K and Company [#permalink]

### Show Tags

25 May 2017, 06:15
Bunuel wrote:
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.

Hi all - despite all your lovely explanations, I am still confused:

(1) There are 17 directors present at the joint meeting of Company K and Company R. Some only work for K, some for R and some for both (B). So, the equation should be K + R + B = 17
(2) Now I know: K = 12, R = 8 --> K + R = 20

(1) & (2) Substitute K + R = 20 into the equation from (1) leads to: 20 + B = 17 --> B = -3

But a number of people cannot be negative?

Thanks!
Math Expert
Joined: 02 Sep 2009
Posts: 39702
Re: How many people are directors of both Company K and Company [#permalink]

### Show Tags

25 May 2017, 07:11
guenthermat wrote:
Bunuel wrote:
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.

Hi all - despite all your lovely explanations, I am still confused:

(1) There are 17 directors present at the joint meeting of Company K and Company R. Some only work for K, some for R and some for both (B). So, the equation should be K + R + B = 17
(2) Now I know: K = 12, R = 8 --> K + R = 20

(1) & (2) Substitute K + R = 20 into the equation from (1) leads to: 20 + B = 17 --> B = -3

But a number of people cannot be negative?

Thanks!

The formula is:
{group 1} + {group 2} - {both} + {neither} = {total}

OR
{ONLY group 1} + {ONLY group 2} + {both} + {neither} = {total}

Which one are you using?
_________________
Intern
Joined: 18 Mar 2017
Posts: 44
Re: How many people are directors of both Company K and Company [#permalink]

### Show Tags

25 May 2017, 08:54
Bunuel wrote:

The formula is:
{group 1} + {group 2} - {both} + {neither} = {total}

OR
{ONLY group 1} + {ONLY group 2} + {both} + {neither} = {total}

Which one are you using?

Usually, I solve overlapping sets with a matrix but was stuck on this issue so I just tried to translate the given values into an equation. I didn't work with a formula at all.

I do understand the formulas above but I don't get why {neither} is 0?

According to the first formula:
Statement (2) tells me that Company K has 12 directors and Company R has 8 directors --> {total} = 20
Statement (1) tells me that there were 17 director present at a joint meeting of Company K and Company R and no directors were absent --> {group 1} + {group 2} = 17

But why leads no directors were absent to 0 for {neither}?
As 17 directors are present at a joint meeting of Company K and Company R, how do I know that 0 directors work neither for K nor for R?

Thank you!
Math Expert
Joined: 02 Sep 2009
Posts: 39702
Re: How many people are directors of both Company K and Company [#permalink]

### Show Tags

25 May 2017, 10:29
1
KUDOS
Expert's post
guenthermat wrote:
Bunuel wrote:

The formula is:
{group 1} + {group 2} - {both} + {neither} = {total}

OR
{ONLY group 1} + {ONLY group 2} + {both} + {neither} = {total}

Which one are you using?

Usually, I solve overlapping sets with a matrix but was stuck on this issue so I just tried to translate the given values into an equation. I didn't work with a formula at all.

I do understand the formulas above but I don't get why {neither} is 0?

According to the first formula:
Statement (2) tells me that Company K has 12 directors and Company R has 8 directors --> {total} = 20
Statement (1) tells me that there were 17 director present at a joint meeting of Company K and Company R and no directors were absent --> {group 1} + {group 2} = 17

But why leads no directors were absent to 0 for {neither}?
As 17 directors are present at a joint meeting of Company K and Company R, how do I know that 0 directors work neither for K nor for R?

Thank you!

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

This means that 17 directors on the meeting were either from K or R.
_________________
Re: How many people are directors of both Company K and Company   [#permalink] 25 May 2017, 10:29

Go to page    1   2    Next  [ 25 posts ]

Similar topics Replies Last post
Similar
Topics:
A certain company currently has how many employees? 3 08 Jan 2017, 06:50
1 There are 50 people in Company X. If 12 of the people quit, how many 3 22 Feb 2016, 21:16
A certain company currently has how many employees? 4 25 Sep 2013, 02:47
2 How many people are directors of both Company K and Company 6 13 Nov 2012, 07:08
12 How many people are directors of both Company K and Company 11 06 Feb 2016, 21:40
Display posts from previous: Sort by