2020 AMC 10B Problem 4

Question

The acute angles of a right triangle are

a^{\circ}

and

b^{\circ},

where

a>b

and both

a

and

b

are prime numbers. What is the least possible value of

b?

2

3

5

7

11

The two acute angles in a right triangle add to

90^\circ

To make

b

small, try the largest possible prime value of

a

The acute angles satisfy

a+b=90.

Testing primes

b

from least to greatest,

b=2,3,5

would give

a=88,87,85,

none of which is prime. For

b=7,

however,

a=83

is prime and is greater than

b.

Therefore the least possible value of

b

is

7.

Thus, D is the correct answer.

Problem 4 in other years