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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]

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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, 04:20, edited 1 time in total.
Renamed the topic and edited the question.

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Re: Overlapping Sets - Freshman at a College [#permalink]

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New post 10 Jan 2013, 21:53
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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 6789 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]

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New post 12 Jan 2013, 16:36
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]

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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]

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New post 13 Jan 2013, 23:15
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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]

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New post 21 Nov 2013, 19:04
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]

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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]

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Re: There are 100 freshmen at a particular college, all of whom [#permalink]

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New post 30 Jun 2016, 08:21
Very good Question..

Another Approach:-

3k(k- freshmen who did not opt for Arts at all) + 20(arts+one other) +5 (freshmen who took all) => 3k+25....

Only 61 among all other options is in the form of 3k+25....

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Re: There are 100 freshmen at a particular college, all of whom [#permalink]

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New post 20 May 2017, 04:51
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



Can someone please provide a more easier approach with detailed explanation?
Thank you!

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Re: There are 100 freshmen at a particular college, all of whom [#permalink]

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New post 20 May 2017, 04:56
SergeyOrshanskiy wrote:
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.)



Hi Sergey!
How did you derive this one "Dividing 48 in proportion 3:1, we conclude that 48*3/4=36 students take only Art."

Please clarify.

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Re: There are 100 freshmen at a particular college, all of whom [#permalink]

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New post 20 May 2017, 05:20
Michaelkalend13 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



Can someone please provide a more easier approach with detailed explanation?
Thank you!


My friend, you can find detailed solutions HERE and HERE. You can also find link to the theory HERE. If the question is still unclear please ask more specific question on it.

In addition please check the links below:


Hope it helps.
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Re: There are 100 freshmen at a particular college, all of whom [#permalink]

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New post 20 May 2017, 06:10
Bunuel wrote:
Michaelkalend13 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



Hi, my friend Bunuel!

Thank you very much for the links. I will study them very carefully.
I've sent you PM, kindly respond at your earliest convenience.

Thanks!

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Re: There are 100 freshmen at a particular college, all of whom [#permalink]

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Re: There are 100 freshmen at a particular college, all of whom   [#permalink] 20 May 2017, 06:13
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