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college T

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college T

Post Wed Jun 22, 2016 10:11 am
Of the 200 students at college T majoring in one or more of the science, 130 are majoring in chemistry and 150 are majoring in biology. If at least 30 of the students are not majoring in either chemistry or biology, then the number of students majoring in both chemistry and biology could be any number from

A) 20 to 50

B) 40 to 70

C) 50 to 130

D) 110 to 130

E) 110 to 150

OAD

Please explain why not E?

Why 130 is the maximum?

Thanks in advance.

Kavin

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Post Thu Jun 23, 2016 3:54 pm
Needgmat wrote:
Please explain why not E?

Why 130 is the maximum?

Thanks in advance.
This is a great question! If you had 150 students in both, the overlap (150) would be MORE than the number of students in biology at all (130). But the overlap (dual major) is a SUBSET of the number of students in biology at all, so 130 ≥ Overlap.

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Post Thu Jun 23, 2016 3:53 pm
You'd have the maximum overlap if everyone in the less populated major is also in the more populated major: if every chem major is a bio major.

You'd have the minimum overlap if you have the fewest possible people in neither major: if you have exactly 30 who aren't majoring in chem or bio.

In the first case we have 130 in both, 20 only in bio, and 50 in neither.

In the second case, we have 30 in neither, leaving (130 + 150 - Overlap) = 170, or Overlap = 110.

That gives us our range: 110 to 130.

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Post Thu Jun 23, 2016 3:54 pm
Needgmat wrote:
Please explain why not E?

Why 130 is the maximum?

Thanks in advance.
This is a great question! If you had 150 students in both, the overlap (150) would be MORE than the number of students in biology at all (130). But the overlap (dual major) is a SUBSET of the number of students in biology at all, so 130 ≥ Overlap.

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Post Thu Jun 23, 2016 3:53 pm
You'd have the maximum overlap if everyone in the less populated major is also in the more populated major: if every chem major is a bio major.

You'd have the minimum overlap if you have the fewest possible people in neither major: if you have exactly 30 who aren't majoring in chem or bio.

In the first case we have 130 in both, 20 only in bio, and 50 in neither.

In the second case, we have 30 in neither, leaving (130 + 150 - Overlap) = 170, or Overlap = 110.

That gives us our range: 110 to 130.

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