In a certain group of 50 people, how many are doctors

[jjjinapinch]

In a certain group of 50 people, how many are doctors who have a law degree?
(1) In the group, 36 people are doctors.
(2) In the group, 18 people have a law degree.

Official Guide question
Answer: E

[Brent@GMATPrepNow]

In a certain group of 50 people, how many are doctors who have a law degree?
(1) In the group, 36 people are doctors.
(2) In the group, 18 people have a law degree.

Official Guide question
Answer: E

Target question: How many are doctors who have a law degree?

Given: There are 50 people

When I scan the two statements, I see that we have the ingredients for applying 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 (aka overlapping sets questions).
Here, we have a population of 50 people, and the two characteristics are:
- Doctor or NOT a doctor
- Has law degree or doesn't have law degree

So, we can set up our double matrix as follows:

NOTE: I have placed a star in the box that represents doctors who have a law degree, since this is what the target question is asking us about

Statement 1: In the group, 36 people are doctors.
If the group has 50 people, and 36 are doctors, we can conclude that there are 14 non-doctors in the group.
Let's add this information to our matrix:


As you can see, there's no way to determine the value that must go in the starred box.
As such, statement 1 is NOT SUFFICIENT

Statement 2: In the group, 18 people have a law degree
If 18 of the 50 people have a law degree, than the remaining 32 people do NOT have a law degree.
Let's add this information to our matrix:


As you can see, there's no way to determine the value that must go in the starred box.
As such, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
When we combine the two statements, we get the following:


There are several ways to complete this matrix. Here are two cases:

case a:

In this case, there are 10 doctors with law degrees.

case a:

In this case, there are 5 doctors with law degrees.
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

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

Once you're familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- 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/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- 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.gmatprepnow.com/module/gmat- ... /video/943
- 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://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent

[Jay@ManhattanReview]

In a certain group of 50 people, how many are doctors who have a law degree?

(1) In the group, 36 people are doctors.
(2) In the group, 18 people have a law degree.

Official Guide question
Answer: E

Given that there are 50 people. We have to find out how many are doctors who have a law degree.

Statement 1: In the group, 36 people are doctors.

No information about the number of people with the law degree. Insufficient.

Statement 2: In the group, 18 people have a law degree.

No information about the number of doctors. Insufficient.

Statement 1 & 2 combined:

Case 1: There are 50 - 36 = 14 non-doctors, and all have law degree, thus doctors with law degree = 18 - 14 = 4.

Case 2: There are 50 - 36 = 14 non-doctors, and none have law degree, thus doctors with law degree = 18.

No unique answer. Insufficient.

The correct answer: E

Hope this helps!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
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[Jeff@TargetTestPrep]

In a certain group of 50 people, how many are doctors who have a law degree?
(1) In the group, 36 people are doctors.
(2) In the group, 18 people have a law degree.

Official Guide question
Answer: E

We have a group of 50 people and need to determine how many of those people are doctors with a law degree.

We can use the following formula:

total = # of doctors + # of lawyers - # both + # neither

50 = # of doctors + # of lawyers - # both + # neither

Statement One Alone:

In the group, 36 people are doctors.

So, we have:

50 = 36 + # of lawyers - # both + # neither

24 = # of lawyers - # both + # neither

We cannot determine the number of people who are both. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

In the group, 18 people have a law degree.

So, we have:

50 = # of doctors + 18 - # both + # neither

32 = # of doctors - # both + # neither

We cannot determine the number of people who are both. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using statements one and two, we have:

50 = 36 + 18 - # both + # neither

-4 = - # both + # neither

# both = 4 + # neither

We still cannot determine the number of "both" since we don't know the number of "neither."

Answer: E

[[email protected]]

Hi All,

We're told that we have a group of 50 people. We're asked for the number of people in that group who are Doctors WITH a Law Degree. This question is a variation of an Overlapping Sets question and it can be approached in a number of different ways. With Overlapping Sets questions, you often need a LOT of really specific information to answer the question that is asked - so if you're given only a little information, then you just have to consider a couple of possibilities to avoid doing lots of work.

1) In the group, 36 people are Doctors.

With the information in Fact 1, we know that that the number of Doctors WITH a Law Degree can be any number from 0 to 36, inclusive - but we don't know exactly how many.
Fact 1 is INSUFFICIENT

2) In the group, 18 people have a Law Degree.

With the information in Fact 2, we know that that the number of Doctors WITH a Law Degree can be any number from 0 to 18, inclusive - but we don't know exactly how many.
Fact 2 is INSUFFICIENT

Combined, we know the two possible 'ranges' of Doctors who COULD have a Law Degree (0 to 36 and 0 to 18). With the added information that there are only 50 total people, there WILL end up being at least a few Doctors WITH a Law Degree (it ends up being at least 4, but you don't have to calculate that to know that there are still lots of possibilities). Combined, INSUFFICIENT

Final Answer: E

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