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A certain collage has total of 400 seniors each majoring in exactly on

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A certain collage has total of 400 seniors each majoring in exactly on  [#permalink]

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New post 21 Jun 2019, 00:03
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Question Stats:

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A certain collage has total of 400 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?

A. 100
B. 80
C. 75
D. 60
E. 50

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Re: A certain collage has total of 400 seniors each majoring in exactly on  [#permalink]

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New post 21 Jun 2019, 00:14
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Bunuel wrote:
A certain collage has total of 400 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?

A. 100
B. 80
C. 75
D. 60
E. 50


Total 400; 3/4 majoring in one of 4 subjects = 300;

So 2 subjects put together is 100,

Minimum 20 in each so one can have a Max of 80 seniors Option (B)
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Re: A certain collage has total of 400 seniors each majoring in exactly on  [#permalink]

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New post 21 Jun 2019, 05:19
Bunuel wrote:
A certain collage has total of 400 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?

A. 100
B. 80
C. 75
D. 60
E. 50


Total Seniors = 400
three quarter of the seniors major in one of four subjects
--> 3/4*400 = 300 seniors are in one of the 4 subjects

Let the remaining subjects be x and y {x - Max, y -Min}
--> x + y = 100
A minimum of 20 seniors major in each six subjects
--> y = 20
--> x = 80

IMO Option B

Pls Hit Kudos if you like the solution
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Re: A certain collage has total of 400 seniors each majoring in exactly on  [#permalink]

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New post 21 Jun 2019, 10:26
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Bunuel wrote:
A certain collage has total of 400 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?

A. 100
B. 80
C. 75
D. 60
E. 50


total 400
for 4 subjects ; 3/4 * 400 ; 300
left with 100 for 2 subjects so max 100-20 ; 80
IMO B
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Re: A certain collage has total of 400 seniors each majoring in exactly on   [#permalink] 21 Jun 2019, 10:26
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