OG13 - Quant Review - DS - 49

[vittovangind]

Hello,

"49. How many directors of both Company K and Company R?

(1) Thee were 17 directors present at 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."

Please could someone rephrase the solution taking (1) and (2) together. Specificall, I don't understand why the 3 peoples missing at the joint meeting must be joint directors.

Many Thanks,

Vitto[/list]

[[email protected]]

Hi Vitto,

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

[Patrick_GMATFix]

The solution below is taken from the GMATFix App.



-Patrick

[Brent@GMATPrepNow]

Hello,

How many directors of both Company K and Company R?

(1) Thee were 17 directors present at 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."

Another approach is to use 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 directors, and the two characteristics are:
- director at company K or not a director at company K
- director at company R or not a director at company R

To learn more about the Double Matrix Method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with the Double Matrix Method, you can attempt the original question above, as well as 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

[abhigupta85]

Brent

Can you please draw double matrix for this question.

Thanks
Abhishek

[abhigupta85]

[Brent@GMATPrepNow]

Perfect! The tricky part is recognizing that there are zero attendees in the bottom-right box.

Cheers,
Brent

[Jeff@TargetTestPrep]

How many directors of both Company K and Company R?

(1) Thee were 17 directors present at 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. We can use 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 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.

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.

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 original 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

Answer: C