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There are 100 freshmen at a particular college, all of whom

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There are 100 freshmen at a particular college, all of whom [#permalink] New post 10 Jan 2013, 16:44
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There are 100 freshmen at a particular college, all of whom must take at least one of the three core classes: Art, Biology, and Calculus. Of these freshmen, 17 take only Biology, 10 take only Calculus, 5 take all three classes, and 20 take Art and exactly one of the other two core classes. If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art, how many freshmen take Art?

(A) 25
(B) 32
(C) 36
(D) 48
(E) 61
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Jan 2013, 03:20, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Overlapping Sets - Freshman at a College [#permalink] New post 10 Jan 2013, 20:53
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skiingforthewknds wrote:
There are 100 freshmen at a particular college, all of whom must take at least one of the three core classes: Art, Biology, and Calculus. Of these freshmen, 17 take only Biology, 10 take only Calculus, 5 take all three classes, and 20 take Art and exactly one of the other two core classes. If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art, how many freshmen take Art?



(A) 25

(B) 32

(C) 36

(D) 48

(E) 61


Make a venn diagram to get a clear picture. Look at the diagram:
Each letter represents only one color. b represents the people who take only Art. d represents people who take only Art and Bio etc.

Attachment:
Ques3.jpg
Ques3.jpg [ 18.68 KiB | Viewed 2665 times ]


d + f = 20 (People who take Art and one other class)
b = 3e (people who take only Art is 3 times the people who take Bio and Calculus)
17 + 10 + 5 + b + d + e + f = 100 (Total people)
b + b/3 = 48
b = 36

Number of freshmen who take Art = 36 + 20 + 5 = 61
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Re: Overlapping Sets - Freshman at a College [#permalink] New post 12 Jan 2013, 15:36
VeritasPrepKarishma wrote:
skiingforthewknds wrote:
There are 100 freshmen at a particular college, all of whom must take at least one of the three core classes: Art, Biology, and Calculus. Of these freshmen, 17 take only Biology, 10 take only Calculus, 5 take all three classes, and 20 take Art and exactly one of the other two core classes. If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art, how many freshmen take Art?



(A) 25

(B) 32

(C) 36

(D) 48

(E) 61


Make a venn diagram to get a clear picture. Look at the diagram:
Each letter represents only one color. b represents the people who take only Art. d represents people who take only Art and Bio etc.

Attachment:
Ques3.jpg


d + f = 20 (People who take Art and one other class)
b = 3e (people who take only Art is 3 times the people who take Bio and Calculus)
17 + 10 + 5 + b + d + e + f = 100 (Total people)
b + b/3 = 48
b = 36

Number of freshmen who take Art = 36 + 20 + 5 = 61


Hello Karishma, very nice job with this question.
I solved by using the formula below and got the same answer.

Total = (# in A + # in B + # in C) - (# enrolled in 2 courses) - 2(# enrolled in 3 courses) + (# in 0 courses)

Because of all the variables, solving the problem using the formula took me too much time. Your approach is far better! Could you describe a situation when you would be required to use the formula above or will the method you used always be appropriate?

Thanks
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Re: There are 100 freshmen at a particular college, all of whom [#permalink] New post 12 Jan 2013, 21:57
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During an actual exam I would not even introduce any letters.

100 - 17 - 10 - 5 - 20 = 48 students take either only Art or only Biology and Calculus.

Dividing 48 in proportion 3:1, we conclude that 48*3/4=36 students take only Art.

Thus, we get 36 + 20 + 5 = 61.
(Only Art, Art and one course, Art and two courses, respectively.)
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Re: Overlapping Sets - Freshman at a College [#permalink] New post 13 Jan 2013, 22:15
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holidayhero wrote:

Hello Karishma, very nice job with this question.
I solved by using the formula below and got the same answer.

Total = (# in A + # in B + # in C) - (# enrolled in 2 courses) - 2(# enrolled in 3 courses) + (# in 0 courses)

Because of all the variables, solving the problem using the formula took me too much time. Your approach is far better! Could you describe a situation when you would be required to use the formula above or will the method you used always be appropriate?

Thanks


I use venn diagrams for most sets questions. It's very easy to see the relation between what is given and what is asked when you see it in a venn diagram. The process becomes completely mechanical and quick. There are various ways to represent the formulas in sets and that can get a little messy hence I avoid them.

Check out a post I wrote sometime back on overlapping sets:
http://www.veritasprep.com/blog/2012/09 ... ping-sets/
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Re: There are 100 freshmen at a particular college, all of whom [#permalink] New post 21 Nov 2013, 17:55
Where are u Bunnel? ...please suggest any easy way....
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Re: There are 100 freshmen at a particular college, all of whom [#permalink] New post 21 Nov 2013, 18:04
Hey Karishma ,

Could you please explain ,where from b/3 is derive?
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Re: There are 100 freshmen at a particular college, all of whom [#permalink] New post 21 Nov 2013, 20:06
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taleesh wrote:
Hey Karishma ,

Could you please explain ,where from b/3 is derive?


The question says:
"If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art"

Freshmen who take every class except art are the freshmen who take Bio and Calculus only.
So b = 3e
or e = b/3

Now, Total = 100 = 17 + 10 + 5 + b + d + e + f
100 - 32 = b + (d + f) + e
68 = b + 20 + b/3

(Note that d + f = 20 and e = b/3)

You get b = 36
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Re: There are 100 freshmen at a particular college, all of whom [#permalink] New post 23 Nov 2013, 11:46
Thanks a lot Karishma .......kudos to this explanation !!!!!!
Re: There are 100 freshmen at a particular college, all of whom   [#permalink] 23 Nov 2013, 11:46
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