OG11 - 239

[maolivie]

OF the 200 students at College T majoring in one or more of th esciences, 130 are majoing 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

I understand why 130 is a number, but I don't understand why you subtract 170 from 280. I know where the numbers come from, but don't understand why it happens. Can someone please clarify?

Thanks

[jayhawk2001]

OF the 200 students at College T majoring in one or more of th esciences, 130 are majoing 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

I understand why 130 is a number, but I don't understand why you subtract 170 from 280. I know where the numbers come from, but don't understand why it happens. Can someone please clarify?

Thanks

Using set theory, total number of students = num chemistry +
num biology - num chemistry & biology + num no-chem-no-bio

C + B - CB + not-C-not-B = 200

130 + 150 - CB + 30 = 200

CB = 110

This is the least number if max of 30 students don't take both. If this
number goes higher, CB goes higher as well.

Since number of students who take chemistry is 130, there can only
be max of 130 students who can qualify in CB category.

So range is 110 - 130

[maolivie]

hah thanks. Why do you explain things better than the official book does? They never mentioned set theory once.

Thanks man

[Cybermusings]

OF the 200 students at College T majoring in one or more of th esciences, 130 are majoing 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

30 student majoring in neither chemistry or biology...thus 200-30 = 170 student either study biology,chemistry or both...

Let students who studied both = x
130-x = Students who study Chemistry
150-x = Students who study Biology
(130-x+150-x)+x = 170
280-x = 170
x = 110

So x can be anything from 110 to 130 (it can't be 150 since total number of students majoring in chemistry is 130)