Help requred for Sets problem : Quant Question Archive [LOCKED]
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 19 Jan 2017, 08:10

### 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

# Help requred for Sets problem

Author Message
Senior Manager
Joined: 06 Apr 2005
Posts: 352
Location: USA
Followers: 2

Kudos [?]: 97 [0], given: 1

Help requred for Sets problem [#permalink]

### Show Tags

08 Apr 2005, 02:24
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Can anyone help me solve this sets problem. Sets is my weakest link in PS.

70 students are enrolled in Math, english or German. 40 students are in Math, 35 are in English, and 30 are in German. 15 students are enrolled in all three courses. How many of the students are enrolled in exactly two of the courses: Math, English and German?

Thanks,

Darth
Senior Manager
Joined: 19 Feb 2005
Posts: 486
Location: Milan Italy
Followers: 1

Kudos [?]: 22 [0], given: 0

### Show Tags

08 Apr 2005, 02:31
Total students in all 3 classes= 40+35+30=105
Students in only one class= 70
students in 3 classes= 15
students in 2 classes= 105-15-70=20
Senior Manager
Joined: 15 Mar 2005
Posts: 419
Location: Phoenix
Followers: 2

Kudos [?]: 26 [0], given: 0

Re: Help requred for Sets problem [#permalink]

### Show Tags

08 Apr 2005, 02:52
Can anyone help me solve this sets problem. Sets is my weakest link in PS.

70 students are enrolled in Math, english or German. 40 students are in Math, 35 are in English, and 30 are in German. 15 students are enrolled in all three courses. How many of the students are enrolled in exactly two of the courses: Math, English and German?

Thanks,

Darth

If R1 - R7 represent regions,

R1 + R2 + R3 + R4 + R5 + R6 + R7 = 70.

When you just add Maths + English + German, you get
(R1+R2+R7+R6) + (R4+R5+R6+R7) + (R2+R3+R4+R7) = 40 + 35 + 30

70 + R2 + R4 + R6 + R7 + R7 = 105
=> R2 + R4 + R6 + 2xR7 = 35.
Since R7 = 15,
R2 + R4 + R6 = 5.

Hope that helps.
Attachments

File comment: Illustration of regions discussed in the solution.

sets.JPG [ 7.44 KiB | Viewed 768 times ]

_________________

Who says elephants can't dance?

Senior Manager
Joined: 19 Feb 2005
Posts: 486
Location: Milan Italy
Followers: 1

Kudos [?]: 22 [0], given: 0

### Show Tags

08 Apr 2005, 03:51
Godd explanation and drawing, kapslock.
Could you explain why
70=R(1->7)
and not
70=R1+R3+R5
Senior Manager
Joined: 15 Mar 2005
Posts: 419
Location: Phoenix
Followers: 2

Kudos [?]: 26 [0], given: 0

### Show Tags

08 Apr 2005, 04:17
Good question theReach !!

Actually this has to do with the conventional way of stating the set questions.
When they say 70 people are enrolled in Maths, English or German, they just mean to imply that 70 makes up the Universal Set.

Of course the real statement should have been "70 people are enrolled in Maths, English and German, not counting the people pursuing two or more courses two or more times".

Taking this assumption, you'd agree with me that R(1-7) does specify the universal set.

Hope this helps.
_________________

Who says elephants can't dance?

Senior Manager
Joined: 06 Apr 2005
Posts: 352
Location: USA
Followers: 2

Kudos [?]: 97 [0], given: 1

### Show Tags

11 Apr 2005, 04:08
Thank you so much Kapslock. Your answer is correct. It is 5. I got the question from Barrons, but the explanation wasn't clear. Your venn diagram was very useful, and so were your explanations.

I also thank Thearch for helping me answer the question.
Intern
Joined: 28 Dec 2004
Posts: 35
Followers: 0

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

### Show Tags

11 Apr 2005, 17:57
Here is the way I think about any set problem

Total = # in set 1 + # in set 2 + # in set 3 - # in two sets - 2*(number in 3 sets) - 3 * (number in 4 sets)

So for this example:

70 = (40 + 35 + 30) - x - (2*15)
70 = 105 - 30 - x
70 = 75 - x
so x == 5
Manager
Joined: 04 Mar 2005
Posts: 106
Location: NYC
Followers: 2

Kudos [?]: 4 [0], given: 0

### Show Tags

14 Apr 2005, 18:50
I get 5 as well.. Same methodology as Kapslock - but slightly different way. I used x, y & z for the 2 subject intersections

70 = 25 -(x+y) + 20 -(y+z) + 15 -(x+z) + x+y+z +15
=> x+y+z = 75 -70 =5
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5062
Location: Singapore
Followers: 30

Kudos [?]: 357 [0], given: 0

Re: Help requred for Sets problem [#permalink]

### Show Tags

14 Apr 2005, 22:24
Can anyone help me solve this sets problem. Sets is my weakest link in PS.

70 students are enrolled in Math, english or German. 40 students are in Math, 35 are in English, and 30 are in German. 15 students are enrolled in all three courses. How many of the students are enrolled in exactly two of the courses: Math, English and German?

Thanks,

Darth

I have a document on "working with sets" here. Hope it's helpful

http://www.gmatclub.com/phpbb/viewtopic.php?t=14576&start=20
Re: Help requred for Sets problem   [#permalink] 14 Apr 2005, 22:24
Display posts from previous: Sort by