Suppose 18% of the students at a college receive some academic scholarship, 43% receive some need-based financial aid, and 52% receive academic scholarship or need-based financial aid (or both). What is the percentage receives both?

38%

Step-by-step explanation:

Percentage of the students at a who receive academic scholarship (A) = 18

Percentage of the students at a who receive need-based financial aid (B) = 43

Percentage of the students at a who receive academic scholarship or need-based financial aid (or both). = 52

Now from Set Theory,

n (A∪B) = n (A) + n (B) - n (A ∩ B)

Written in Words

n (A OR B) = n (A) + n (B) - n (A AND B)

Total Percentage=100

100 = 18+44-n (A AND B)

100=62-n (A AND B)

n (A AND B) = 100-62=38

This means percentage who receive BOTH=38%