In a group of x students, w students are taking

Question

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

*kudos for all correct solutions

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

*kudos for all correct  solutions

niks18 · Answer

We know  w  students have taken Chemistry. Now out of 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  probables for Chemistry. Also given that z have not taken French and assuming that  w≠z , remove these z students to get the final left over students as  x-y-z

So total students who can take chemistry  = x-y-z+w

Option  C

Hi  GMATPrepNow

I am not totally comfortable with the language of the question. We are not given that there are only 2 subjects to chose from. What if there could be a third subject which could correspond to z?, then in that case Option B would have been more feasible. Also the question step IMO should read as "Which of the following COULD represents the number of students who are taking Chemistry?"

kindly share your thoughts on this.

kindly share your thoughts on this.

BrentGMATPrepNow · Answer

Good question, niks18.

It's quite likely that the given students are taking tons of courses other than French and Chemistry. However, this doesn't change the question, because each student is either taking French or not taking French . Likewise, each student is either taking Chemistry or not taking Chemistry.

If you aren't convinced, see if you can insert values in the diagram that contradict the correct answer.

Cheers,
Brent

pushpitkc · Answer

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)

BrentGMATPrepNow · Answer

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: 
 https://i.imgur.com/IhfD6iM.png

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...
 https://i.imgur.com/IeADyuA.png

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... 
 https://i.imgur.com/MuaPZXT.png

Now focus your attention on the two boxes in the RIGHT-HAND COLUMN. 
When we add those boxes, we get: y +  z - w ...
 https://i.imgur.com/dJ5E5lj.png 
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.youtube.com/watch?v=jK-tiBrrf04

swagatamoitra · Answer

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

Mansoor50 · Answer

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

BrentGMATPrepNow · Answer

I respectfully disagree. 
Can you elaborate on your position?

Cheers,
Brent

VishakhaBharti · Answer

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

ThatDudeKnows · Answer

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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In a group of x students, w students are taking

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