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# In a group of x students, w students are taking

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CEO
Joined: 12 Sep 2015
Posts: 2710
In a group of x students, w students are taking  [#permalink]

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24 Jun 2018, 06:29
Top Contributor
8
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Difficulty:

45% (medium)

Question Stats:

67% (02:14) correct 33% (01:44) wrong based on 116 sessions

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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

*kudos for all correct solutions

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Brent Hanneson – Founder of gmatprepnow.com

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Re: In a group of x students, w students are taking  [#permalink]

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24 Jun 2018, 07:10
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

*kudos for all correct solutions

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.
CEO
Joined: 12 Sep 2015
Posts: 2710
In a group of x students, w students are taking  [#permalink]

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24 Jun 2018, 07:23
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niks18 wrote:
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.

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
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Re: In a group of x students, w students are taking  [#permalink]

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24 Jun 2018, 21:48
1
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

*kudos for all correct solutions

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)
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CEO
Joined: 12 Sep 2015
Posts: 2710
Re: In a group of x students, w students are taking  [#permalink]

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26 Jun 2018, 07:15
Top Contributor
2
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

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

ASIDE: This question type is VERY COMMON on the GMAT, so be sure to master the technique.

_________________

Brent Hanneson – Founder of gmatprepnow.com

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Joined: 05 Sep 2016
Posts: 26
Location: India
Concentration: General Management, Operations
WE: Engineering (Energy and Utilities)
Re: In a group of x students, w students are taking  [#permalink]

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14 Jul 2018, 22:45
1
niks18 wrote:
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

*kudos for all correct solutions

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.

I completely second your opinion, question language is a bit odd and not GMAT like
Intern
Joined: 29 May 2017
Posts: 35
Re: In a group of x students, w students are taking  [#permalink]

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25 Jul 2018, 02:12
Can this problem be solved using Venn? If so, can anyone put up the solution?
thanks
CEO
Joined: 12 Sep 2015
Posts: 2710
Re: In a group of x students, w students are taking  [#permalink]

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25 Jul 2018, 07:30
Top Contributor
swagatamoitra wrote:
I completely second your opinion, question language is a bit odd and not GMAT like

I respectfully disagree.
Can you elaborate on your position?

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Re: In a group of x students, w students are taking &nbs [#permalink] 25 Jul 2018, 07:30
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