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

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Jun 24, 2018 5:21 am

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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

Brent Hanneson - Creator of GMATPrepNow.com

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Source: Beat The GMAT — Problem Solving | Sun Jun 24, 2018 5:21 am

swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

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 (wâ‰ 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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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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:

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...

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...

Now focus your attention on the two boxes in the RIGHT-HAND COLUMN.
When we add those boxes, we get: y + z - w...

Brent Hanneson - Creator of GMATPrepNow.com

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

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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