Author 
Message 
TAGS:

Hide Tags

Manager
Status: Current MBA Student
Joined: 19 Nov 2009
Posts: 90
Concentration: Finance, General Management

In a group of 68 students, each student is registered for at
[#permalink]
Show Tags
18 Dec 2010, 11:55
Question Stats:
74% (01:46) correct 26% (02:07) wrong based on 835 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. Twentyfive students are registered for History, twentyfive students are registered for Math, and thirtyfour 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
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 59265

Re: MGMAT CAT 3 Overlapping Sets
[#permalink]
Show Tags
18 Dec 2010, 12:20
tonebeeze wrote: What is the quickest method to solve 3Set, 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. Twentyfive students are registered for History, twentyfive students are registered for Math, and thirtyfour 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}=10Answer: B. Look at the diagram: Attachment:
untitled.PNG [ 5.66 KiB  Viewed 46823 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: formulaefor3overlappingsets69014.html#p729340As 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: 142
Location: Toronto

Re: MGMAT CAT 3 Overlapping Sets
[#permalink]
Show Tags
18 Dec 2010, 12:27
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 3set 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: 103

Re: MGMAT CAT 3 Overlapping Sets
[#permalink]
Show Tags
18 Dec 2010, 13:15
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.



Director
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 990
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75

Re: MGMAT CAT 3 Overlapping Sets
[#permalink]
Show Tags
07 Sep 2012, 07:42
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: 584
WE: Science (Education)

Re: MGMAT CAT 3 Overlapping Sets
[#permalink]
Show Tags
07 Sep 2012, 12:05
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.



Director
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 990
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75

Re: In a group of 68 students, each student is registered for at
[#permalink]
Show Tags
07 Sep 2012, 12:27
Why can't a 3x3 matrix be used here?
_________________



Director
Joined: 22 Mar 2011
Posts: 584
WE: Science (Education)

Re: In a group of 68 students, each student is registered for at
[#permalink]
Show Tags
07 Sep 2012, 13:16
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.



Director
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 990
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75

Re: In a group of 68 students, each student is registered for at
[#permalink]
Show Tags
07 Sep 2012, 13:48
Thanks. That has helped.
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 59265

Re: In a group of 68 students, each student is registered for at
[#permalink]
Show Tags
11 Jun 2013, 08:24
Bumping for review and further discussion*. Get a kudos point for an alternative solution! *New project from GMAT Club!!! Check HERE
_________________



Board of Directors
Joined: 17 Jul 2014
Posts: 2494
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: In a group of 68 students, each student is registered for at
[#permalink]
Show Tags
30 Jan 2016, 17:57
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
add all these 3: 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.



Manager
Joined: 17 Jun 2015
Posts: 191
GMAT 1: 540 Q39 V26 GMAT 2: 680 Q46 V37

Re: In a group of 68 students, each student is registered for at
[#permalink]
Show Tags
12 Sep 2016, 13:02
The master information collation on all things Overlapping Sets. Thanks to this(and the authors ) for making life simpler overlappingsetsmadeeasy205636.html
_________________
Fais de ta vie un rêve et d'un rêve une réalité



Current Student
Status: preparing
Joined: 30 Dec 2013
Posts: 36
Location: United Arab Emirates
Concentration: Technology, Entrepreneurship
GMAT 1: 660 Q45 V35 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)

Re: In a group of 68 students, each student is registered for at
[#permalink]
Show Tags
30 Nov 2016, 02:04
tonebeeze wrote: In a group of 68 students, each student is registered for at least one of three classes – History, Math and English. Twentyfive students are registered for History, twentyfive students are registered for Math, and thirtyfour 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) 849 = X+2Y X+2Y = 75 X+Y=65 FROM EQUATION (1) solving this we get : Y=10



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15503
Location: United States (CA)

Re: In a group of 68 students, each student is registered for at
[#permalink]
Show Tags
09 Feb 2018, 11:53
Hi All, 3Group Overlapping Sets questions are relatively rare on the Official GMAT (you likely will NOT see this version of Overlapping Sets on Test Day). However, there is a formula that you can use to solve it. Total = (1st group) + (2nd group) + (3rd group)  (1st and 2nd)  (1st and 3rd)  (2nd and 3rd)  2(all 3 groups). In overlapping sets questions, any person who appears in more than one group has been counted more than once. When dealing with groups of people, you're not supposed to count any individual more than once, so the formula 'subtracts' all of the extra times that a person is counted. For example, someone who is in BOTH the 1st group and the 2nd group will be counted twice....that's why we SUBTRACT that person later on [in the (1st and 2nd) group]. In this prompt, we're given the Total, a number for each of the 3 individual groups and the number of people who appear in all 3 groups. The equation would look like this... 68 = 25 + 25 + 34  (1st and 2nd)  (1st and 3rd)  (2nd and 3rd) 2(3) 68 = 84  6  (1st and 2nd)  (1st and 3rd)  (2nd and 3rd) 68 = 78  (1st and 2nd)  (1st and 3rd)  (2nd and 3rd) (1st and 2nd) + (1st and 3rd) + (2nd and 3rd) = 10 Since the prompt asks for the total number of students that are in exactly 2 classes, we have our answer. Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Intern
Joined: 30 Jun 2018
Posts: 16

Re: In a group of 68 students, each student is registered for at
[#permalink]
Show Tags
08 Nov 2018, 10:41
Hi guys, I actually got the right answer for this problem, but wanted to confirm if my method of solving it is actually accurate or if I just "got lucky."
History 25 Math 25 English 34
Subtract 3 from each number is 3 people are in all three classes
History 253 = 22 Math 253 = 22 English 343 = 31
Additionally, subtract 3 from the original 68 number since you want to "get rid of them" while you count for the pool.
683 = 65
Add up 22+22+31 to get 75
7565 = 10
Appreciate your help!!



NonHuman User
Joined: 09 Sep 2013
Posts: 13634

Re: In a group of 68 students, each student is registered for at
[#permalink]
Show Tags
18 Nov 2019, 04:54
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]
18 Nov 2019, 04:54






