Challenge question: In a group of x students, w students are

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In a group of x students, w students are taking Chemistry but not French, y students are taking French but not Chemistry, and z students are NOT taking French. Which of the following represents the number of students who are taking Chemistry?

A) x - y - z - w
B) x - y + z + w
C) x - y - z + w
D) x + y - z - w
E) x - y + z - w

Answer: C
Difficulty level: 650 - 700
Source: www.gmatprepnow.com

*I'll post a solution in 2 days
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by swerve » Sun Jun 24, 2018 8:19 am
We know w students have taken Chemistry. Now out of the total x, students we need to find that how many of the remaining students can take Chemistry.

Since y have taken French, so they are out and we are left with (x - y) probable for Chemistry. Also given that z have not taken French and assuming that (w≠z), removed this z students to get the final leftover students as (x - y - z).

So, the total students who can take Chemistry = x-y-z+w.

Hence, C is the correct answer. Regards!

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by Brent@GMATPrepNow » Tue Jun 26, 2018 6:05 am
Brent@GMATPrepNow wrote:In a group of x students, w students are taking Chemistry but not French, y students are taking French but not Chemistry, and z students are NOT taking French. Which of the following represents the number of students who are taking Chemistry?

A) x - y - z - w
B) x - y + z + w
C) x - y - z + w
D) x + y - z - w
E) x - y + z - w

Answer: C
Difficulty level: 650 - 700
Source: www.gmatprepnow.com

*I'll post a solution in 2 days
Let's apply the Double Matrix Method, a technique that 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 French or not taking French
- taking Chemistry or not taking Chemistry

In a group of x students, w students are taking Chemistry but not French, y students are taking French but not Chemistry, and z students are NOT taking French.
We can set up our matrix as follows:
Image

Which of the following represents the number of students who are taking Chemistry?
In other words, we want to determine the SUM of the boxes in the left-hand column.
So, let's note this on our diagram to remind us that this is our goal...
Image

Now focus your attention on the two boxes in the LOWER ROW.
We know that the SUM of those two boxes is z
So, if one box contains w students, then the other box must contain z-w students, which we'll add to our diagram...
Image

Now focus your attention on the two boxes in the RIGHT-HAND COLUMN.
When we add those boxes, we get: y + z - w...
Image
This means that, out of a total of x students, (y + z - w) are taking NOT taking Chemistry

So, the number of students TAKING Chemistry = x - (y + z - w)
= x - y - z + w

Answer: C

ASIDE: 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:

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- https://www.beatthegmat.com/finance-majo ... 67425.html

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Medium Data Sufficiency questions
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Difficult Data Sufficiency questions
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- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Jeff@TargetTestPrep » Thu Jun 28, 2018 6:30 am
Brent@GMATPrepNow wrote:In a group of x students, w students are taking Chemistry but not French, y students are taking French but not Chemistry, and z students are NOT taking French. Which of the following represents the number of students who are taking Chemistry?

A) x - y - z - w
B) x - y + z + w
C) x - y - z + w
D) x + y - z - w
E) x - y + z - w
We can use the formulas:

1) Total = Chemistry only + French only + both + neither

x = w + y + both + neither

2) Not taking French = Chemistry only + neither

z = w + neither

z - w = neither

So we have:

x = w + y + both + (z - w)

x = y + z + both

x - y - z = both

Finally, we can use the formula:

Chemistry = Chemistry only + both

Chemistry = w + (x - y - z)

Chemistry = x - y - z + w

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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