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

 It is currently 22 Oct 2019, 11:58

### 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

# 70 students are enrolled in maths, english and german.

Author Message
TAGS:

### Hide Tags

Manager
Joined: 25 Dec 2011
Posts: 51
GMAT Date: 05-31-2012
70 students are enrolled in maths, english and german.  [#permalink]

### Show Tags

30 Dec 2011, 08:16
00:00

Difficulty:

(N/A)

Question Stats:

100% (00:41) correct 0% (00:00) wrong based on 17 sessions

### HideShow timer Statistics

70 students are enrolled in maths, english and german.
40 are in maths
35 are in english
30 are in german
15 students are involved in all three of the courses
How many are enrolled in exactly 2 of the 3 courses - maths, english and german.

Let N stand for the number enrolled in exactly 2 courses
70=40+35+30-N-2(15)
N = 5

I don't understand why they do 2 times 15 :- 2(15)

Best
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4472
Re: 70 students are enrolled in maths, english and german.  [#permalink]

### Show Tags

30 Dec 2011, 11:21
Hi, there! I'm happy to help with this question.

The Barron's answer is correct, but they shot through some complicated stuff awfully quickly.

Fact #1 = There are 70 students total.

Fact #2 = There are 40 in maths, 35 in English, 30 in German, for a total of 105.

This 105 is, of course, more than the total number of students ---- this is because the folks taking exactly two courses (the "doublers") have been counted twice, and the folks taking three courses (the "triplers") have been counted three times.

Fact #3 = 15 students are taking all three, i.e. there are 15 triplers.

So, if we want to make the 105 number jive with the actual total of 70, we have do two things
a) subtract the doublers once -- they are counted twice, and we only want them counted once
b) subtract the triplers twice --- they are counted three times, and we only want them counted once, so we have to subtract twice that total. That's where the mysterious factor of 2 arises ------ it's what you have to subtract from how many times they've been counted (3x) so that you are left with only counting them once. (If we subtracted the number of triplers times 3, the result would be that they wouldn't be counted at all!)

If we call the number of doublers N, this logic leads us to the Barron's equation

70 = 105 - N - 2*15

Does that make sense? Please let me know if you have any further question.

Mike
_________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Manager
Joined: 13 May 2011
Posts: 190
WE 1: IT 1 Yr
WE 2: Supply Chain 5 Yrs
Re: 70 students are enrolled in maths, english and german.  [#permalink]

### Show Tags

30 Dec 2011, 11:30
Bunuel did excellent discussion on the topic covering whole concept on the following link:

formulae-for-3-overlapping-sets-69014.html
Manager
Joined: 25 Dec 2011
Posts: 51
GMAT Date: 05-31-2012
Re: 70 students are enrolled in maths, english and german.  [#permalink]

### Show Tags

30 Dec 2011, 12:42
1
1
Hi Mike
Thank you very much.

I worked through this as follows and took quiet some time. I am not very good at understanding and applying formulas...

Fact 1 :- 70 students are taking either 3 or 2 or 1 subject
Fact 2 :- 15 are definitely taking all 3

so now 70-15= 55 remaining are taking 2 or 1 subject

When you draw a Venn diagram ..it is seen..
Students taking Maths remaining are 40 - 15 = 25
Students taking English are 35-15=20
Students taking German are 30 - 15 = 15

So sum of these are total students taking only 1 subject = 60

Therefore 60-55=5 are students who take only 2 subjects.

Cheers
Non-Human User
Joined: 09 Sep 2013
Posts: 13410
Re: 70 students are enrolled in maths, english and german.  [#permalink]

### Show Tags

31 Jan 2019, 03:58
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: 70 students are enrolled in maths, english and german.   [#permalink] 31 Jan 2019, 03:58
Display posts from previous: Sort by