2020 AMC 12B Problems/Problem 4

Problem

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 $b$ ?

$\textbf{(A) }2\qquad\textbf{(B) }3\qquad\textbf{(C) }5\qquad\textbf{(D) }7\qquad\textbf{(E) }11$

Solution

$a+b+90=180$ , so $a+b=90$ . The largest primes less than $90$ are $89, 83, 79, ...$ If $a=89$ , then $b=1$ , which is not prime. However, if $a=83$ , then $b=7$ , which is prime. Hence the answer is $\boxed{\mathrm{(D)}}$

2020 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
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All AMC 12 Problems and Solutions

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2020 AMC 12B Problems/Problem 4

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