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There are 100 freshmen at a particular college, all of whom [#permalink]
10 Jan 2013, 16:44
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Question Stats:
40% (04:20) correct
60% (03:46) wrong based on 284 sessions
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?
Re: Overlapping Sets - Freshman at a College [#permalink]
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 [ 18.68 KiB | Viewed 4506 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 _________________
Re: Overlapping Sets - Freshman at a College [#permalink]
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?
Re: Overlapping Sets - Freshman at a College [#permalink]
13 Jan 2013, 22:15
1
This post received KUDOS
Expert's post
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.
Re: There are 100 freshmen at a particular college, all of whom [#permalink]
27 Jun 2015, 02:42
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