GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Oct 2019, 17:49 GMAT Club Daily Prep

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

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.  A school has 3 classes, math class has 14 students

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Senior Manager  Joined: 10 Apr 2012
Posts: 262
Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)
A school has 3 classes, math class has 14 students  [#permalink]

Show Tags

2
5 00:00

Difficulty:   75% (hard)

Question Stats: 60% (02:10) correct 40% (02:39) wrong based on 237 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 thanks !
Manager  Joined: 24 Jan 2013
Posts: 65
Re: A school has 3 classes, math class has 14 students  [#permalink]

Show Tags

6
1
This could be solved easier:

(1) There are 14+10+11 = 35 seats to fill (some students occupy only 1 seat, others 2, others 3).

(2) 20 students occupy only 1 seat: 35-20 = 15... now we have 15 seats to fill

(3) 3 students occupy 3 seats: 15-9 = 6 seats left

(4) We have 6 seats for students that occupy 2 seats ---> solution is 3 students!!

General Discussion
VP  Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1019
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: A school has 3 classes, math class has 14 students  [#permalink]

Show Tags

1
1
The right formula is:

P(A u B u C) : P(A) + P(B) + P(C) – P(A n B) – P(A n C) – P(B n C) + P(A n B n C)
formulae-for-3-overlapping-sets-69014.html

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)
Answer $$=x-3*3$$
$$12-9=3$$
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]
Manager  Status: Trying.... & desperate for success.
Joined: 17 May 2012
Posts: 55
Location: India
Schools: NUS '15
GPA: 2.92
WE: Analyst (Computer Software)
Re: A school has 3 classes, math class has 14 students  [#permalink]

Show Tags

2
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

T = 35 - 2Y + 9 = 44 - 2Y ------- I

Also,
T = 20 + Y + 3
T = 23 + Y --------- II

Comparing I & II we get Y = 3
Director  Joined: 25 Apr 2012
Posts: 660
Location: India
GPA: 3.21
WE: Business Development (Other)
Re: A school has 3 classes, math class has 14 students  [#permalink]

Show Tags

1
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.”
Intern  Status: Currently Preparing the GMAT
Joined: 15 Feb 2013
Posts: 29
Location: United States
GMAT 1: 550 Q47 V23 GPA: 3.7
WE: Analyst (Consulting)
Re: A school has 3 classes, math class has 14 students  [#permalink]

Show Tags

3
If we put up a Venn diagram of the situation, we get something like this :
Attachment: venn.jpg [ 55.63 KiB | Viewed 4567 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.

Hope that helped Senior Manager  Joined: 10 Apr 2012
Posts: 262
Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)
Re: A school has 3 classes, math class has 14 students  [#permalink]

Show Tags

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 .

thanks again !
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India
Re: A school has 3 classes, math class has 14 students  [#permalink]

Show Tags

3
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 4463 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.

To avoid confusion, it is a good idea to use venn diagrams instead.
Check out my post: http://www.veritasprep.com/blog/2012/09 ... ping-sets/
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Manager  Joined: 24 Nov 2012
Posts: 143
Concentration: Sustainability, Entrepreneurship
GMAT 1: 770 Q50 V44 WE: Business Development (Internet and New Media)
Re: A school has 3 classes, math class has 14 students  [#permalink]

Show Tags

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

http://www.manhattangmat.com/blog/index.php/author/cbermanmanhattanprep-com/ - This is worth its weight in gold

Economist GMAT Test - 730, Q50, V41 Aug 9th, 2013
Manhattan GMAT Test - 670, Q45, V36 Aug 11th, 2013
Manhattan GMAT Test - 680, Q47, V36 Aug 17th, 2013
GmatPrep CAT 1 - 770, Q50, V44 Aug 24th, 2013
Manhattan GMAT Test - 690, Q45, V39 Aug 30th, 2013
Manhattan GMAT Test - 710, Q48, V39 Sep 13th, 2013
GmatPrep CAT 2 - 740, Q49, V41 Oct 6th, 2013

GMAT - 770, Q50, V44, Oct 7th, 2013
My Debrief - http://gmatclub.com/forum/from-the-ashes-thou-shall-rise-770-q-50-v-44-awa-5-ir-162299.html#p1284542
Verbal Forum Moderator B
Joined: 10 Oct 2012
Posts: 590
Re: A school has 3 classes, math class has 14 students  [#permalink]

Show Tags

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".
_________________
Manager  Joined: 24 Nov 2012
Posts: 143
Concentration: Sustainability, Entrepreneurship
GMAT 1: 770 Q50 V44 WE: Business Development (Internet and New Media)
Re: A school has 3 classes, math class has 14 students  [#permalink]

Show Tags

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

http://www.manhattangmat.com/blog/index.php/author/cbermanmanhattanprep-com/ - This is worth its weight in gold

Economist GMAT Test - 730, Q50, V41 Aug 9th, 2013
Manhattan GMAT Test - 670, Q45, V36 Aug 11th, 2013
Manhattan GMAT Test - 680, Q47, V36 Aug 17th, 2013
GmatPrep CAT 1 - 770, Q50, V44 Aug 24th, 2013
Manhattan GMAT Test - 690, Q45, V39 Aug 30th, 2013
Manhattan GMAT Test - 710, Q48, V39 Sep 13th, 2013
GmatPrep CAT 2 - 740, Q49, V41 Oct 6th, 2013

GMAT - 770, Q50, V44, Oct 7th, 2013
My Debrief - http://gmatclub.com/forum/from-the-ashes-thou-shall-rise-770-q-50-v-44-awa-5-ir-162299.html#p1284542
Verbal Forum Moderator B
Joined: 10 Oct 2012
Posts: 590
Re: A school has 3 classes, math class has 14 students  [#permalink]

Show Tags

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.
_________________
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India
Re: A school has 3 classes, math class has 14 students  [#permalink]

Show Tags

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.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Manager  Joined: 25 Oct 2013
Posts: 142
Re: A school has 3 classes, math class has 14 students  [#permalink]

Show Tags

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.
_________________
Click on Kudos if you liked the post!

Practice makes Perfect.
Manager  P
Joined: 01 Mar 2015
Posts: 69
Re: A school has 3 classes, math class has 14 students  [#permalink]

Show Tags

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.
Non-Human User Joined: 09 Sep 2013
Posts: 13412
Re: A school has 3 classes, math class has 14 students  [#permalink]

Show Tags

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] 10 Aug 2018, 03:03
Display posts from previous: Sort by

A school has 3 classes, math class has 14 students

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  