Gmat_mission wrote: ↑

Fri Jan 08, 2021 1:51 am

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.

Answer: E

Source: Official Guide

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