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

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Intern
Joined: 18 Mar 2017
Posts: 38
Re: How many people are directors of both Company K and Company  [#permalink]

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25 May 2017, 14:32
Bunuel wrote:
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?

Thanks! Do you know some 500-600 level questions I can practice the formula on (and that are not solvable by using a matrix)?
Math Expert
Joined: 02 Sep 2009
Posts: 51215
Re: How many people are directors of both Company K and Company  [#permalink]

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25 May 2017, 14:36
guenthermat wrote:

Thanks! Do you know some 500-600 level questions I can practice the formula on (and that are not solvable by using a matrix)?

Check here: https://gmatclub.com/forum/search.php?view=search_tags

Mark Overlapping sets and 500-600 level questions and go through them.
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Intern
Joined: 18 Mar 2017
Posts: 38
Re: How many people are directors of both Company K and Company  [#permalink]

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25 May 2017, 14:42
Bunuel wrote:

Check here: https://gmatclub.com/forum/search.php?view=search_tags

Mark Overlapping sets and 500-600 level questions and go through them.

Merci!

But Bunuel, I do have one last question:

If (2) Company K has 12 and Company R has 8 directors, so 20 directors in total, how can only 17 directors be present at a joint meeting of Company K and Company R when no director is absent? There are 20 directors overall but only 17 at joint meeting and no director is missing?
Math Expert
Joined: 02 Sep 2009
Posts: 51215
Re: How many people are directors of both Company K and Company  [#permalink]

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25 May 2017, 14:49
1
guenthermat wrote:
Bunuel wrote:

Check here: https://gmatclub.com/forum/search.php?view=search_tags

Mark Overlapping sets and 500-600 level questions and go through them.

Merci!

But Bunuel, I do have one last question:

If (2) Company K has 12 and Company R has 8 directors, so 20 directors in total, how can only 17 directors be present at a joint meeting of Company K and Company R when no director is absent? There are 20 directors overall but only 17 at joint meeting and no director is missing?

The total number of directors is 17, not 20.

12 in K
8 in R
3 in common

12 + 8 - 3 = 17.

You should go through the solutions provided and read them carefully. All your questions are addressed there multiple times.

Also, you should brush up fundamentals before attempting questions:

Hope it helps.
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Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: How many people are directors of both Company K and Company  [#permalink]

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31 May 2017, 18:04
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.

We must determine how many individuals are directors for both Company K and Company R. To solve this "overlapping sets" problem, we can employ the following equation:

Total Directors = Directors in Company K + Directors in Company R – Directors in both Companies K and R

Statement One Alone:

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

From statement one we know that there are 17 total directors. This is not enough information to determine how many individuals are directors of both Company K and Company R. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

Company K has 12 directors and Company R has 8 directors.

Although we know that Company K has 12 directors and Company R has 8 directors, we still do not have enough information to determine how many individuals are directors of both Company K and Company R. Statement two is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

From statements one and two, we know that there are 17 total directors and that Company K has 12 directors and Company R has 8 directors. We can use this information in the our equation to determine the number of individuals who are directors of both Company K and Company R.

Total Directors = Directors in Company K + Directors in Company R – Directors of both Companies K and R

17 = 12 + 8 – Both

17 = 20 – Both

Both = 3

There are 3 individuals who are directors of both Company R and Company K.

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Jeffery Miller

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

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30 Jun 2018, 01:30
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Re: How many people are directors of both Company K and Company &nbs [#permalink] 30 Jun 2018, 01:30

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