Mr. Anderson has more than 25 students in his class. He has more than 2 but fewer than 10 boys and more than 14 but fewer than 23 girls in his class. How many different class sizes would satisfy these conditions?
(A) 5
(B) 6
(C) 7
(D) 3
(E) 4
Mr. Anderson has more than 25 students in his class. He has more than 2 but fewer than 10 boys and more than 14 but fewer than 23 girls in his class. How many different class sizes would satisfy these conditions?
(A) 5
(B) 6
(C) 7
(D) 3
(E) 4

## Solution

Let $b$ represent the number of boys and $g$ represent the number of girls in Mr. Anderson's class. We know that $b+g>25$. We also know $2<b<10$ and $14<g<23$.

The following pairs $(b, g)$ satisfy all three conditions: $(4,22),(5,21),(5,22),(6,20),(6,21),(6,22),(7,19)$, $(7,20),(7,21),(7,22),(8,18),(8,19),(8,20),(8,21),(8,22),(9,17),(9,18),(9,19),(9,20),(9,21),(9,22)$.

All of the different pairs $(b, g)$ lead to the following different class sizes: 26, 27, 28, 29, 30, 31 .

Thus, only 6 different class sizes are possible.

ANSWER: (B)