Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

A school has 3 classes, math class has 14 students [#permalink]

Show Tags

01 Apr 2013, 11:43

2

This post received KUDOS

3

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

50% (04:25) correct
50% (02:18) wrong based on 183 sessions

HideShow timer Statistics

A school has 3 classes, math class has 14 students. English class has 10 students, PE class has 11 students. There are 20 students taking only one class, 3 students are taking all three classes. How many students are taking two classes?

A) 3 B) 6 C) 9 D) 18 E)20

could any one show me the solution using 3 overlapping groups formula .

T = A + B + C - (AB + AC + BC) - 2(ABC) ... I am getting a wrong answer

Here I would use those: 2. To determine the No of persons in exactly one set : P(A) + P(B) + P(C) – 2P(A n B) – 2P(A n C) – 2P(B n C) + 3P(A n B n C) \(x\)=number in 2 classes or P(A n B) + P(A n C) + P(B n C) \(20=14+10+11-2x+9*3\) \(x=12\) 3. To determine the No of persons in exactly two of the sets : P(A n B) + P(A n C) + P(B n C) – 3P(A n B n C) That's the answer: Answer \(=x-3*3\) \(12-9=3\) _________________

It is beyond a doubt that all our knowledge that begins with experience.

Re: A school has 3 classes, math class has 14 students [#permalink]

Show Tags

01 Apr 2013, 21:54

1

This post received KUDOS

guerrero25 wrote:

A school has 3 classes, math class has 14 students. English class has 10 students, PE class has 11 students. There are 20 students taking only one class, 3 students are taking all three classes. How many students are taking two classes?

A) 3 B) 6 C) 9 D) 18 E)20

could any one show me the solution using 3 overlapping groups formula .

T = A + B + C - (AB + AC + BC) - 2(ABC) ... I am getting a wrong answer

thanks !

T = 14 + 10 + 11 - 2[P(A U B) + P(A U C) + P(C U B)] + 3P(A U B U C) Let the sum of students attending 2 classes be Y

Re: A school has 3 classes, math class has 14 students [#permalink]

Show Tags

02 Apr 2013, 08:02

1

This post received KUDOS

guerrero25 wrote:

A school has 3 classes, math class has 14 students. English class has 10 students, PE class has 11 students. There are 20 students taking only one class, 3 students are taking all three classes. How many students are taking two classes?

A) 3 B) 6 C) 9 D) 18 E)20

could any one show me the solution using 3 overlapping groups formula .

T = A + B + C - (AB + AC + BC) - 2(ABC) ... I am getting a wrong answer

thanks !

Hi guerrero25,

There are 2 forumulaes T = A+B+C - (Sum of 2 groups) + ( Sum of all three groups) + Neither

and T = A+B+C - (Sum of exactly 2 groups) - 2( sum of all three groups) + Neither

In this Q, Neither = 0

T = 14+10+11

35= 14+10+11 - x + 3 +0 x =3

Note the 2nd Forumlae will be applied when we are asked about exactly 2 classes where as 1st formulae will be applied for group attending 2 classes. _________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Re: A school has 3 classes, math class has 14 students [#permalink]

Show Tags

02 Apr 2013, 10:11

1

This post received KUDOS

If we put up a Venn diagram of the situation, we get something like this :

Attachment:

venn.jpg [ 55.63 KiB | Viewed 2429 times ]

With :

A : the number of students only attending math class ; B : the number of students only attending english class ; C : the number of students only attending PE class ; x : the number of students attending both math and english ; y : the number of students attending both math and PE ; z : the number of students attending both english and PE.

If we use the data we're given, we get the following system :

14 students attend math classes => \(x + y + 3 + A = 14\) (1) 10 students attend english classes => \(x + z + 3 + B = 10\) (2) 11 students attend PE classes =>\(y + z + 3 + C = 11\) (3)

We also know that there are only 20 students attending only one class, which means that : \(A + B + C = 20\) (4)

If we add equations (1), (2) and (3) and take into account equation (4) we get : \(2*(x + y + z) + 9 + 20 =35\)

The quantity \((x + y + z)\) represents the total number of students attending 2 classes, which is what we're looking for. So completing the computation, we get : \(2*(x + y + z) + 9 + 20 =35\) => \(2*(x + y + z) = 6\) => \((x + y + z) = 3\) which is answer choice A.

Re: A school has 3 classes, math class has 14 students [#permalink]

Show Tags

02 Apr 2013, 15:10

mridulparashar1 wrote:

guerrero25 wrote:

A school has 3 classes, math class has 14 students. English class has 10 students, PE class has 11 students. There are 20 students taking only one class, 3 students are taking all three classes. How many students are taking two classes?

A) 3 B) 6 C) 9 D) 18 E)20

could any one show me the solution using 3 overlapping groups formula .

T = A + B + C - (AB + AC + BC) - 2(ABC) ... I am getting a wrong answer

thanks !

Hi guerrero25,

There are 2 forumulaes T = A+B+C - (Sum of 2 groups) + ( Sum of all three groups) + Neither

and T = A+B+C - (Sum of exactly 2 groups) - 2( sum of all three groups) + Neither

In this Q, Neither = 0

T = 14+10+11

35= 14+10+11 - x + 3 +0 x =3

Note the 2nd Forumlae will be applied when we are asked about exactly 2 classes where as 1st formulae will be applied for group attending 2 classes.

Hello Mridul ,Thanks for the explanation . Could you elaborate more when you say "Note the 2nd Forumlae will be applied when we are asked about exactly 2 classes where as 1st formulae will be applied for group attending 2 classes"..I could not understand the difference .

Re: A school has 3 classes, math class has 14 students [#permalink]

Show Tags

02 Apr 2013, 21:26

3

This post received KUDOS

Expert's post

guerrero25 wrote:

mridulparashar1 wrote:

Hi guerrero25,

There are 2 forumulaes T = A+B+C - (Sum of 2 groups) + ( Sum of all three groups) + Neither

and T = A+B+C - (Sum of exactly 2 groups) - 2( sum of all three groups) + Neither

In this Q, Neither = 0

T = 14+10+11

35= 14+10+11 - x + 3 +0 x =3

Note the 2nd Forumlae will be applied when we are asked about exactly 2 classes where as 1st formulae will be applied for group attending 2 classes.

Hello Mridul ,Thanks for the explanation . Could you elaborate more when you say "Note the 2nd Forumlae will be applied when we are asked about exactly 2 classes where as 1st formulae will be applied for group attending 2 classes"..I could not understand the difference .

thanks again !

To understand the two different formulas, look at the diagram given here:

Attachment:

SetsThree_1_23Sept.jpg [ 20.19 KiB | Viewed 2381 times ]

A - No of people in set A = a + d + e + g B - No of people in set B = b + d + g + f C - No of people in set C = c + e + g + f

Notice that Total = a + b+ c + d + e + f + g But depending on the given data, we often don't have values for a, b, c etc separately. When the question says, Math class has 14 students, it means a + d + e + g = 14. Similarly, if English class has 10 students, it means b + d + g + f = 10 and so on... So we need to subtract the things we have counted twice/thrice. Note that if we write 14 + 10, we have already counted d and g twice here.

When we add A + B, we have counted (d +g) twice so we need to subtract it out once. When we add C to it as well, we have counted (e + g) and (f + g) twice too so we need to subtract them out as well. But when we do this, we have subtracted the g region 3 times and hence, it's not accounted for now. So we add it back. This is how you get T = A+B+C - (Sum of 2 groups) + ( Sum of all three groups) + Neither

On the other hand, If after adding A + B + C, you subtract the region which is common to ONLY two sets i.e. d, e and f, then you still need to subtract the g region twice since it is present in A, B and C. That is how you get the formula: T = A+B+C - (Sum of ONLY 2 groups) - 2*( Sum of all three groups) + Neither

The formula to use depends on what data is given in the question.

Re: A school has 3 classes, math class has 14 students [#permalink]

Show Tags

16 Apr 2013, 09:34

Isn't the question ambiguous?

A is answer is the question is only two classes

B is the answer if it is at least two classes

Correct me if i am wrong... _________________

You've been walking the ocean's edge, holding up your robes to keep them dry. You must dive naked under, and deeper under, a thousand times deeper! - Rumi

Re: A school has 3 classes, math class has 14 students [#permalink]

Show Tags

16 Apr 2013, 09:53

Expert's post

Transcendentalist wrote:

Isn't the question ambiguous?

A is answer is the question is only two classes

B is the answer if it is at least two classes

Correct me if i am wrong...

I don't think there is any ambiguity. If they were asking for "atleast two classes", the question would have mentioned that specifically.Also, the fact that they have given the number of students who take all three classes, doesn't really add anything new to the scenario of "atleast two classes". _________________

Re: A school has 3 classes, math class has 14 students [#permalink]

Show Tags

16 Apr 2013, 09:57

Maybe i am confusing my verbal with quant

But the right answer to the question "How many students are taking two classes? " is 6 as there are 6 students taking two classes _________________

You've been walking the ocean's edge, holding up your robes to keep them dry. You must dive naked under, and deeper under, a thousand times deeper! - Rumi

Re: A school has 3 classes, math class has 14 students [#permalink]

Show Tags

16 Apr 2013, 10:23

Expert's post

Transcendentalist wrote:

Maybe i am confusing my verbal with quant

But the right answer to the question "How many students are taking two classes? " is 6 as there are 6 students taking two classes

You can think of it as this : number of students taking two classes : M and E OR E and PE OR M and PE. Question asks how many take either M and E OR E and PE OR M and PE? The students who take all three will not fall under this category as they take all three. Again, the answer will be 6 , only for number of students taking atleast two classes,i.e. two or more. I think the word "only" is inherent for the given question. _________________

Re: A school has 3 classes, math class has 14 students [#permalink]

Show Tags

16 Apr 2013, 22:40

Expert's post

Transcendentalist wrote:

Isn't the question ambiguous?

A is answer is the question is only two classes

B is the answer if it is at least two classes

Correct me if i am wrong...

Yes, I would think twice too. The official questions will say either 'how many take EXACTLY two classes' or 'How many take AT LEAST two classes'. GMAC digs potholes for you but it is not unfair. You will never wonder what they want to know - you may ignore what they want to know or you may wonder how to get it. _________________

Re: A school has 3 classes, math class has 14 students [#permalink]

Show Tags

25 Jan 2014, 03:41

Yup I agree with Transcendentalist. The question asks how many students take 2 classes. Those 3 people who take 3 classes ALSO take two classes. Hence 6 seems correct choice. _________________

Re: A school has 3 classes, math class has 14 students [#permalink]

Show Tags

15 Mar 2015, 21:14

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: A school has 3 classes, math class has 14 students [#permalink]

Show Tags

11 Oct 2015, 09:25

guerrero25 wrote:

A school has 3 classes, math class has 14 students. English class has 10 students, PE class has 11 students. There are 20 students taking only one class, 3 students are taking all three classes. How many students are taking two classes?

A) 3 B) 6 C) 9 D) 18 E)20

could any one show me the solution using 3 overlapping groups formula .

T = A + B + C - (AB + AC + BC) - 2(ABC) ... I am getting a wrong answer

thanks !

Here we have to find (AB + AC + BC), and given (A + B + C) = 20, (ABC) =3

so we use formula Sum of individual Total of A , B and C = (A + B + C) +2(AB + AC + BC) +3(ABC)

=> 14 + 10 + 11 = 20 + 2(AB + AC + BC) +3(3)

=> (AB + AC + BC) = 3 Answer

If explanation is of help, give kudos to motivate me.

gmatclubot

Re: A school has 3 classes, math class has 14 students
[#permalink]
11 Oct 2015, 09:25

Part 2 of the GMAT: How I tackled the GMAT and improved a disappointing score Apologies for the month gap. I went on vacation and had to finish up a...

I’m a little delirious because I’m a little sleep deprived. But whatever. I have to write this post because... I’M IN! Funnily enough, I actually missed the acceptance phone...

So the last couple of weeks have seen a flurry of discussion in our MBA class Whatsapp group around Brexit, the referendum and currency exchange. Most of us believed...

This highly influential bestseller was first published over 25 years ago. I had wanted to read this book for a long time and I finally got around to it...