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

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10 Jan 2013, 17:44

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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?

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 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
_________________

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

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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?

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]

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27 Jun 2015, 03:42

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

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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!

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.

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

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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.