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

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Manager
Joined: 16 Mar 2010
Posts: 142
A certain collage has total of 400 seniors each majoring in exactly on  [#permalink]

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03 Sep 2010, 03:31
7
00:00

Difficulty:

45% (medium)

Question Stats:

67% (02:07) correct 33% (02:29) wrong based on 87 sessions

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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
Manager
Joined: 29 Aug 2010
Posts: 153
Schools: Wharton/Lauder - Class of 2013
WE 1: Project Management, Telecommunications
Re: A certain collage has total of 400 seniors each majoring in exactly on  [#permalink]

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03 Sep 2010, 03:44
2

Six majors are as follows: a + b + c + d + e + f
Each has at least 20 seniors: 20 + 20 + 20 + 20 + 20 + 20

4 of the majors have 300 seniors: a + b + c +d = 300
There are a total of 400 seniors.

So e + f = 100. One of the subjects has to be 20 for the other to be maximized. If e = 20, then f = 80.
Manager
Joined: 07 Aug 2010
Posts: 62
Re: A certain collage has total of 400 seniors each majoring in exactly on  [#permalink]

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10 Oct 2010, 23:56
B

400 = 300 + 20 + x => x = 80
= 3/4 * 400 in 4 subjects + 20 min for 5th subject + x = 400
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Re: A certain collage has total of 400 seniors each majoring in exactly on  [#permalink]

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17 Mar 2018, 04:57
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Re: A certain collage has total of 400 seniors each majoring in exactly on &nbs [#permalink] 17 Mar 2018, 04:57
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