Problem Solving

Within a group of students, x students are taking English, y students are taking Math, and z students are taking both English and Math. Which of the following represents the number of students who are taking English or Math but not both?
A) x + y - z
B) x + y + z
C) 2x + 2y - z
D) x + y - 2z
E) x + y + 2z

Answer: D
Difficulty level: 600 - 650
Source: www.gmatprepnow.com

*full solution posted in 2 days

Brent@GMATPrepNow wrote:Within a group of students, x students are taking English, y students are taking Math, and z students are taking both English and Math. Which of the following represents the number of students who are taking English or Math but not both?
A) x + y - z
B) x + y + z
C) 2x + 2y - z
D) x + y - 2z
E) x + y + 2z

Answer: D
Difficulty level: 600 - 650
Source: www.gmatprepnow.com

*full solution posted in 2 days

We can solve this by using 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 students, and the two characteristics are:
- taking English or not taking English
- taking Math or not taking Math

We want to find: (number of students taking English but not Math) + (number of students taking Math but not English)
So, we can set up our matrix as follows:

We need to find the number of students in the 2 boxes with stars in them.

GIVEN: x students are taking English, and y students are taking Math
So, we can add this information to our diagram as follows:


GIVEN: z students are taking both English and Math
So, we can add this information to our diagram as follows:


Let's first examine the top ROW.
If a total of x students are taking English, and z of them are also taking Math, then x-z of them are NOT taking Math.


Now examine the left-hand COLUMN.
If a total of y students are taking Math, and z of them are also taking English, then y-z of them are NOT taking English.


So, the number of students who are taking English or Math but not both = (x - z) + (y - z)
= x + y - 2z

Answer: D

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-maj ... 67425.html

Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- https://www.beatthegmat.com/posted-spee ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appl ... 70255.html
- https://www.beatthegmat.com/opening-nig ... 64869.html
- https://www.beatthegmat.com/at-least-10 ... 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-pe ... 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-peo ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume- ... 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- ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05 ... question-3

Cheers,
Brent