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A certain college has a total of 400 seniors, each majoring in exactly [#permalink]

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08 Nov 2004, 21:30

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A

B

C

D

E

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35% (medium)

Question Stats:

70% (02:25) correct
30% (02:13) wrong based on 201 sessions

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A certain college has a total of 400 seniors, each majoring in exactly one of six subjects. A minimum of 20 seniors major in each of the six subjects. If three-quarters 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?

Re: A certain college has a total of 400 seniors, each majoring in exactly [#permalink]

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08 Nov 2004, 21:36

There's a lot of verbiage here. I believe it's B) 80
There is 100 remaining for other 2 topics. 20 min to 1 of them. The max the other can have is 80. _________________

Re: A certain college has a total of 400 seniors, each majoring in exactly [#permalink]

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08 Nov 2004, 21:41

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Let's say you have 6 subjects {A,B,C,D,E,F}
First four subjects, you have 3/4 of 400. So 300 people goes to those first four subjects. For remaining E and F, you have 100 left. Since you need a minimum per subject, if E is 20, F can have a max value of 80 and vice versa _________________

Re: A certain college has a total of 400 seniors, each majoring in exactly [#permalink]

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12 Jul 2015, 22:47

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Re: A certain college has a total of 400 seniors, each majoring in exactly [#permalink]

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02 Sep 2015, 09:15

The wording makes no sense. By "If three-quarters of the seniors major in one of four subjects," I understood that 300 major in one of the four, therefore leaving 100 left for the other 5 (20 in each).

This question is poorly worded, but here is the "intent":

If 300 seniors major in 4 of the subjects, what is the MAXIMUM number of seniors that COULD be majoring in either of the other 2 subjects?

From here, we have to consider that a minimum of 20 seniors major in each subject. With the 300 seniors accounted for, the other 100 have to be placed in the remaining 2 subjects. To maximize one of the subjects, we'd have to minimize the other; we'd have 80 in one and 20 in the other.

I understand your point, the question would be quite easy if it was writen correctly.

On the question sten we have "three-quarters of the seniors major in one of four subjects". This says that 300 major in ONE of the four subjects, not that 300 major in four of the subjects. Considering this and the fact that "A minimum of 20 seniors major in each of the six subjects.", we would be left with 20 as the maximun for each of the remaining five subjects.

As you have also determined, the original prompt is poorly worded. With your interpretation of the prompt, the answer would be 20... but that answer is NOT among the answer choices, which means that your interpretation cannot be correct. You can actually use this type of logic on the Official GMAT to get 'unstuck' from certain questions. If you end up with an answer that is not among the 5 choices, then there is some logical flaw in the handful of 'steps' that you went through - likely a mis-interpration of information that you've been given (or potentially a calculation error in your work).

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