In a tree 3/5 of the birds are robins while the rest are bluejays. If 1/4 of the robins are female and 3/4 of the bluejays are female, what fraction of the birds in the tree are male?

A. 7/15

B. 1/2

C. 11/20

D. 2/3

E. 7/10

(C) First we need to determine the fraction of the birds that are bluejays:

(fraction that are bluejays) = 1 (total birds) – 3/5 (fraction that are robins) = 5/5 (total birds) – 3/5 (fraction that are robins) = 2/5

Next, determine the fraction of all the birds that are female:

(fraction of all birds that are female) = (3/5) × (1/4) (female robins) + (2/5) × (3/4) (female bluejays) = 3/20 (female robins) + 6/20 (female bluejays) = 9/20 of all birds are female.

The fraction of male birds then is:

(fraction of all birds that are male) = 1 (total birds) – 9/20 (female birds) = 20/20 (total birds) – 9/20 (female birds) = 11/20 of all birds are male.

**The alternative way**:

Suppose there were 100 birds in the tree. Using the fractions in the question, you can fill up this table.

Therefore 55 out of 100 birds are male, implying a fraction of

55/100 = 11/20.