In a group of 68 students, each student is registered for at : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 20 Jan 2017, 20:34

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Status: Current MBA Student
Joined: 19 Nov 2009
Posts: 127
Concentration: Finance, General Management
GMAT 1: 720 Q49 V40
Followers: 13

Kudos [?]: 350 [3] , given: 210

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

### Show Tags

18 Dec 2010, 10:55
3
KUDOS
19
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

68% (01:59) correct 32% (01:16) wrong based on 793 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?

A. 13
B. 10
C. 9
D. 8
E. 7
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 36583
Followers: 7087

Kudos [?]: 93287 [9] , given: 10555

Re: MGMAT CAT 3 Overlapping Sets [#permalink]

### Show Tags

18 Dec 2010, 11:20
9
KUDOS
Expert's post
8
This post was
BOOKMARKED
tonebeeze wrote:
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}:

68 = 25 + 25 + 34 - {people in exactly 2 groups} - 2*3 + 0 --> {people in exactly 2 groups}=10

Look at the diagram:
Attachment:

untitled.PNG [ 5.66 KiB | Viewed 19700 times ]
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}.

For more on this check: formulae-for-3-overlapping-sets-69014.html#p729340

As for your question: yes, questions on 3 overlapping sets are quite common for the GMAT.

Hope it helps.
_________________
Kaplan GMAT Instructor
Joined: 21 Jun 2010
Posts: 148
Location: Toronto
Followers: 44

Kudos [?]: 186 [1] , given: 0

Re: MGMAT CAT 3 Overlapping Sets [#permalink]

### Show Tags

18 Dec 2010, 11:27
1
KUDOS
Hi!

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.
Manager
Joined: 13 Jul 2010
Posts: 169
Followers: 1

Kudos [?]: 73 [0], given: 7

Re: MGMAT CAT 3 Overlapping Sets [#permalink]

### Show Tags

18 Dec 2010, 12:15
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.
VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1420
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Followers: 175

Kudos [?]: 1335 [0], given: 62

Re: MGMAT CAT 3 Overlapping Sets [#permalink]

### Show Tags

07 Sep 2012, 06:42
Can this question be done with the help if matrix?
If yes, then please let me know the procedure.
_________________
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 100

Kudos [?]: 891 [0], given: 43

Re: MGMAT CAT 3 Overlapping Sets [#permalink]

### Show Tags

07 Sep 2012, 11:05
siddharthasingh wrote:
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.

VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1420
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Followers: 175

Kudos [?]: 1335 [0], given: 62

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

### Show Tags

07 Sep 2012, 11:27
Why can't a 3x3 matrix be used here?
_________________
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 100

Kudos [?]: 891 [0], given: 43

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.

VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1420
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Followers: 175

Kudos [?]: 1335 [0], given: 62

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

### Show Tags

07 Sep 2012, 12:48
Thanks. That has helped.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 36583
Followers: 7087

Kudos [?]: 93287 [0], given: 10555

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

### Show Tags

11 Jun 2013, 07:24
Expert's post
1
This post was
BOOKMARKED
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Overlapping Sets:
how-to-draw-a-venn-diagram-for-problems-98036.html

All DS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=45
All PS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=65

_________________
Senior Manager
Joined: 07 Apr 2012
Posts: 464
Followers: 2

Kudos [?]: 53 [1] , given: 58

Re: MGMAT CAT 3 Overlapping Sets [#permalink]

### Show Tags

21 Nov 2013, 03:05
1
KUDOS
Bunuel wrote:
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....
Math Expert
Joined: 02 Sep 2009
Posts: 36583
Followers: 7087

Kudos [?]: 93287 [0], given: 10555

Re: MGMAT CAT 3 Overlapping Sets [#permalink]

### Show Tags

21 Nov 2013, 03:08
ronr34 wrote:
Bunuel wrote:
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....

Yes, typo edited. Thank you.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13468
Followers: 575

Kudos [?]: 163 [0], given: 0

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.
_________________
SVP
Joined: 17 Jul 2014
Posts: 2206
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '19 (S)
GMAT 1: 560 Q42 V26
GMAT 2: 550 Q39 V27
GMAT 3: 560 Q43 V24
GMAT 4: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Followers: 20

Kudos [?]: 270 [0], given: 140

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

### Show Tags

30 Jan 2016, 16:57
Suppose A=all 3
B=History and english
C=history and math
D=math and english
E=english only
F=history only
G=math only

we know that:
A+B+C+D+E+F+G=68
A+B+C+F=25
A+C+D+G=25
A+B+D+E=34
A=3

OK, so we have
B+C+F=22
C+D+G=22
B+D+E=34

2B+2C+2D+E+F+G=75
we then have:
B+C+D+E+F+G=65

substract from first one the second one:
B+C+D=10
B,C,D - 2 objects only.
Intern
Joined: 12 Dec 2015
Posts: 20
Followers: 0

Kudos [?]: 1 [0], given: 27

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

Thanks!
Senior Manager
Joined: 17 Jun 2015
Posts: 270
GMAT 1: 540 Q39 V26
GMAT 2: 680 Q46 V37
GMAT 3: Q V
Followers: 3

Kudos [?]: 20 [0], given: 165

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
_________________

Fais de ta vie un rêve et d'un rêve une réalité

Intern
Status: preparing
Joined: 30 Dec 2013
Posts: 15
Location: United Arab Emirates
Concentration: Technology, Entrepreneurship
GMAT 1: 640 Q49 V28
GMAT 2: 640 Q49 V28
GMAT 3: 640 Q49 V28
GMAT 4: 640 Q49 V28
GMAT 5: 640 Q49 V28
GPA: 2.84
WE: General Management (Consumer Products)
Followers: 0

Kudos [?]: 6 [0], given: 24

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
Re: In a group of 68 students, each student is registered for at   [#permalink] 30 Nov 2016, 01:04
Similar topics Replies Last post
Similar
Topics:
6 Walking across campus, a student interviewed a group of students. 2 16 Dec 2014, 08:51
A group of students was interviewed for that if it was asked 2 23 Aug 2014, 06:21
9 A class is divided into four groups of four students each. 4 02 Feb 2012, 11:07
6 In a group of 68 students, each student is registered for at least one 7 05 Dec 2009, 06:14
19 In a survey of students, each student selected from a list 15 16 Jun 2008, 20:23
Display posts from previous: Sort by

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

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.