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:

In a group of 68 students, each student is registered for at [#permalink]

Show Tags

18 Dec 2010, 10:55

3

This post received KUDOS

19

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

68% (01:59) correct
32% (01:16) wrong based on 792 sessions

HideShow timer Statistics

In a group of 68 students, each student is registered for at least one of three classes – History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?

What is the quickest method to solve 3-Set, Overlapping Set problems? Are they common on the GMAT (if you are scoring 46+ on Quant)?

In a group of 68 students, each student is registered for at least one of three classes – History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?

a. 13 b. 10 c. 9 d. 8 e. 7

"Each student is registered for at least one of three classes" means that there are no students who are registered for none of the classes.

Total = {people in group A} + {people in group B} + {people in group C} - {people in exactly 2 groups} - 2*{people in exactly 3 groups} + {people in none of the groups}:

We need to find {people in exactly 2 groups}, so yellow section. Now, when we sum {people in group A} + {people in group B} + {people in group C} we count students who are in exactly 2 groups (yellow section) twice, so to get rid of double counting we are subtracting {people in exactly 2 groups} once.

Similarly when we sum {people in group A} + {people in group B} + {people in group C} we count students who are in exactly 3 groups (blue section) thrice (as it is the portion of all three groups), so to count this group only once we are subtracting 2*{people in exactly 3 groups}.

There are two approaches you can take for 3 overlapping set questions. Which one works best for you is really a matter of preference.

Many people find Venn diagrams to be the best approach - draw 3 circles that have both double and triple overlapping sections. Venn diagrams are an excellent tool, especially for visual learners.

On the other hand, if you're an equation kind of guy (or gal), there are two different equations that come in handy:

True # of objects = (total # in group 1) + (total # in group 2) + (total # in group 3) - (# in exactly 2 groups) - 2(# in all 3 groups);

and:

True # of objects = (total in exactly 1 group) + (total in exactly 2 groups) + (total in exactly 3 groups).

There are a few other variations of those equations as well. In theory, you should add "+ total in none of the groups" to each equation, but I don't think I've ever seen a 3-set question on the GMAT in which everyone wasn't a member of at least one group.

Even at high levels of the exam, 3 set questions aren't particularly common - most test takers see 0 or 1 of them, rarely 2.

tonebeeze Bunuel's explanation at the link he provides was very helpful for me. I recommend sticking to the equations as the venn diagrams tend to throw me off.

Can this question be done with the help if matrix? If yes, then please let me know the procedure.

The matrix method of 2 X 2 works well for two overlapping sets. For three overlapping sets we would need a 3D matrix of 2 X 2 X 2, which is hard (if not impossible) to visualize on a 2D paper or computer screen.

So, stick with the Venn diagrams or the formulas.
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: In a group of 68 students, each student is registered for at [#permalink]

Show Tags

07 Sep 2012, 12:16

siddharthasingh wrote:

Why can't a 3x3 matrix be used here?

We have 3 types of classes, call them A, B, C. Each student can be or not in A - 2 possibilities, can be or not in B, also 2 possibilities, can be or not in C, another two possibilities. So there is a total of 2 x 2 x 2 = 8 different subsets and not 3 x 3 = 9.

If for two overlapping sets A and B you would use a 2 x 2 matrix (A nonA, B nonB), you don't have where to put the information regarding the third set C. Imagine a cube of 2 X 2 X 2, such that you add the third characteristic related to C on the vertical axis, above the base of 2 x 2 for A and B. The 3D cube of dimensions 2 X 2 x 2 for three overlapping sets is the parallel of the 2D matrix of dimensions 2 X 2 for two overlapping sets.
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Similarly when we sum {people in group A} + {people in group B} + {people in group C} we count students who are in exactly 3 groups (blue section) thrice (as it is the portion of all three groups), so to count this group only once we are subtracting 2*{people in exactly 2 groups}.

Bunuel, did you mean that we subtract 2*{people in exactly 3 groups} right? not people in exactly 2 groups....

Similarly when we sum {people in group A} + {people in group B} + {people in group C} we count students who are in exactly 3 groups (blue section) thrice (as it is the portion of all three groups), so to count this group only once we are subtracting 2*{people in exactly 2 groups}.

Bunuel, did you mean that we subtract 2*{people in exactly 3 groups} right? not people in exactly 2 groups....

Re: In a group of 68 students, each student is registered for at [#permalink]

Show Tags

22 Nov 2014, 07:20

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: In a group of 68 students, each student is registered for at [#permalink]

Show Tags

19 Feb 2016, 17:40

Hi Brunel, I am also new to Venn Diagrams - can I calculate this problem as 68-3-(25-3)-(25-3)-(34-3)=-10? Even though the answer is negative, if I transform it to positive - seems to be correct

Re: In a group of 68 students, each student is registered for at [#permalink]

Show Tags

12 Sep 2016, 12:02

The master information collation on all things Overlapping Sets. Thanks to this(and the authors ) for making life simpler overlapping-sets-made-easy-205636.html _________________

Re: In a group of 68 students, each student is registered for at [#permalink]

Show Tags

30 Nov 2016, 01:04

tonebeeze wrote:

In a group of 68 students, each student is registered for at least one of three classes – History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?

A. 13 B. 10 C. 9 D. 8 E. 7

Solution: Let student who attended exactly 1 course= X, 2 courses =Y, 3 courses = Z (GIVEN Z=3)

Total = X+Y+Z 68= X+Y+3 X+Y=65 ---------(1)

SUM of all the courses :

h + m + e = X +2Y +3Z : Reason : every course considered common between 2 is repeated 2 times, while Z is repeated 3 times : each times whenever we take 2 courses together ( x is in anb , bnc, anc) 25+25+34 = X+2Y +3(3) 84-9 = X+2Y X+2Y = 75 X+Y=65 FROM EQUATION (1) solving this we get : Y=10

gmatclubot

Re: In a group of 68 students, each student is registered for at
[#permalink]
30 Nov 2016, 01:04

Happy New Year everyone! Before I get started on this post, and well, restarted on this blog in general, I wanted to mention something. For the past several months...

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Happy 2017! Here is another update, 7 months later. With this pace I might add only one more post before the end of the GSB! However, I promised that...

The words of John O’Donohue ring in my head every time I reflect on the transformative, euphoric, life-changing, demanding, emotional, and great year that 2016 was! The fourth to...