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Re: In a group of x students, w students [#permalink]
GreenlightTestPrep wrote:
GreenlightTestPrep 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


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: To learn more about the Double Matrix Method, watch this video:


Crystal clear explanation, thank you so much!!
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Re: In a group of x students, w students [#permalink]
1
Expert Reply
GreenlightTestPrep 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

*I'll post a solution in 2 days

A simpler way will be to take number s...
Let total =x=100
w be 20, and y=10....
let people not taking french be 80, so people taking both chemistry and french is x-z-y=100-80-10=10..
People taking chemistry is w+10=20+10=30..
check for choice that gives 30 as the answer.
A) x - y - z - w = 100-10-80-20=-10..NO
B) x - y + z + w = 100-10+80+20=190..NO
C) x - y - z + w = 100-10-80+20=30..YES
D) x + y - z - w = 100+10-80-20=10..NO
E) x - y + z - w = 100-10+80-20=150..NO

Hence C
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Re: In a group of x students, w students [#permalink]
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