In a group of x students, w students are taking

Given: P(Only Chemistry) = w | P(Only French) = y | P(Only Chemistry) + P(Neither) = z | P(Total) = x

Formula used: P(Total) = P(Only French) + P(Only Chemistry) + P(Both) + P(Neither)

P(Neither) = z - P(Only Chemistry) = z - x

Substituting values in the formula, we get x = w + y + z - w + P(Both) -> P(Both) = x - y - z

Therefore, the number of students taking Chemistry = P(Only Chemistry) + P(Both) = w + x - y - z (Option C)

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...

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:

I completely second your opinion, question language is a bit odd and not GMAT like

Can this problem be solved using Venn? If so, can anyone put up the solution?
thanks

I respectfully disagree.
Can you elaborate on your position?

Cheers,
Brent

As per given information
w = n(C) - n(C⋂F) --- (1)
y = n(F) - n(C⋂F) --- (2)
x - z = n(F) --- (3)

From (2) and (3)
y = x - z - n(C⋂F)
=> n(C⋂F) = x - z - y

Therefore, from (1)
n(C) = w + n(C⋂F)
= w + x - z - y
= x - y - z + w

Variables in the question that are repeated in the answers means I'm going to see if I can use Plugging In.

Let's say X=100, W=20, and Y=25. Plug those into a Venn diagram like the one attached. There are still two regions left for us to assign numbers. Let's go ahead and make the overlap 10. Okay, now the question says Z students aren't taking French, and we know that 35 ARE taking French. That leaves 65 who are not taking French, so that's Z, and we have 45 taking neither. Throw that on the outside.

X=100
Y=25
Z=65
W=20

We are asked for the number taking Chemistry. That's 20+10=30.

Let's check the answer choices:
A) x - y - z - w = 100-25-65-20 Wrong.
B) x - y + z + w = 100-25+65+20 Wrong.
C) x - y - z + w = 100-25-65+20 Keep it.
D) x + y - z - w = 100+25-65-20 Wrong.
E) x - y + z - w = 100-25+65-20 Wrong.

Answer choice C.


ThatDudeKnowsPluggingIn

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