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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

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]

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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]

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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]

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07 May 2015, 12:11

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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

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]

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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 Ekland on 11 Jan 2016, 22:05, edited 1 time in total.

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.

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 5891 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.
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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 !

Can someone please help me with what I am missing?

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.

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

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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

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?

Appreciate your thoughts! Thanks!

Your notations are not precise.

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

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

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

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25 May 2017, 08:54

Bunuel wrote:

Your notations are not precise.

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?

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.
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