Sets again

[Fokin]

If all the 20 student living in a dormitory are taking physics or math or both, how many of the student are both physics and math
1) Of the 20 students 10 are taking only physics
2)Of the 20 students, 12 are taking math and 16 are taking physics

[liferocks]

This will have same approach as https://www.beatthegmat.com/how-to-resol ... 56750.html

from 1 we cannot conclude anything
from 2 12 are taking math hence 20-12=8 are taking only physics as all students are taking at least one subject
hence 16-8=8 are taking both physics and math

Ans B

[tpr-becky]

So the formula is

(physics only +both) +(Math only +both) -Both=20

Statement 1 says 10 are taking physics only - so we know that at most 10 students can be taking both but we don't know how many.

Insufficient - BCE

Statement 2 says 12 are taking math and 20 are taking physics - because it doesn't say only we know that physics only +both=16 and math+both=12 - this is enough to solve the above equation for the number of students taking both.

B