2020 AMC 10 B

Complete problem set with solutions and individual problem pages

Problem 4 Easy

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 ?(2020 AMC 10B, Question #4)

  • A.

    2

  • B.

    3

  • C.

    5

  • D.

    7

  • E.

    11

Answer:D

Solution 1:

Since the three angles of a triangle add up to 180^{\circ} and one of the angles is 90^{\circ} because it's a right triangle, a^{\circ}+b^{\circ}=90^{\circ}. The greatest prime number less than 90 is 89 . If a=89^{\circ}, then b=90^{\circ}-89^{\circ}=1^{\circ}, which is not prime. The next greatest prime number less than 90 is 83 . If a=83^{\circ}, then b=7^{\circ}, which IS prime, so we have our answer (D) 7

Solution 2:

Looking at the answer choices, only 7 and 11 are coprime to 90 . Testing 7 , the smaller angle, makes the other angle 83 which is prime, therefore our answer (\text{D}) 7

Related Problems
Problem 2 2020 AMC 10 B
Problem 3 2020 AMC 10 B
Problem 5 2020 AMC 10 B
Problem 6 2020 AMC 10 B
Think Academy Powered by ChatGPT