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Difference between revisions of "2020 AMC 12B Problems/Problem 4"

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==Solution==
 
==Solution==
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<math>a+b+90=180</math>, so <math>a+b=90</math>. The largest primes less than <math>90</math> are <math>89, 83, 79, ...</math> If <math>a=89</math>, then <math>b=1</math>, which is not prime. However, if <math>a=83</math>, then <math>b=7</math>, which is prime. Hence the answer is <math>\boxed{\mathrm{(D)}}</math>
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<math>a+b+90=180</math>, so <math>a+b=90</math>. The largest primes less than <math>90</math> are <math>89, 83, 79, ...</math> If <math>a=89</math>, then <math>b=1</math>, which is not prime. However, if <math>a=83</math>, then <math>b=7</math>, which is prime. Hence the answer is <math>\boxed{\textbf{(D) }7}</math>
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==See Also==
 
==See Also==
  
 
{{AMC12 box|year=2020|ab=B|num-b=3|num-a=5}}
 
{{AMC12 box|year=2020|ab=B|num-b=3|num-a=5}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 21:41, 7 February 2020

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 $\boxed{\textbf{(D) }7}$

See Also

2020 AMC 12B (Problems • Answer Key • Resources)
Preceded by
Problem 3 		Followed by
Problem 5
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 12 Problems and Solutions

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