2020 AMC 12B Problem 4

Problem 4 of 25EasierGeometry Number Theory

The acute angles of a right triangle are

a^\circ

and

b^\circ,

where

a \gt b

and both

a

and

b

are prime numbers. What is the least possible value of

b?

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Solution

Since the angles are complementary,

a + b = 90.

To minimize

b,

try small primes and require

90 - b

to be prime as well. For

b = 2, 3, 5,

the value

90 - b = 88, 87, 85

is not prime. For

b = 7,

we get

90 - 7 = 83,

which is prime. So the least possible value is

b = 7.

Thus, the correct answer is D.