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

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==Problem==
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#REDIRECT [[2020 AMC 10B Problems/Problem 4]]
The acute angles of a right triangle are <math>a^{\circ}</math> and <math>b^{\circ}</math>, where <math>a>b</math> and both <math>a</math> and <math>b</math> are prime numbers. What is the least possible value of <math>b</math>?
 
 
 
<math>\textbf{(A) }2\qquad\textbf{(B) }3\qquad\textbf{(C) }5\qquad\textbf{(D) }7\qquad\textbf{(E) }11</math>
 
 
 
==Solution==
 
<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>
 
 
 
==Video Solution==
 
https://youtu.be/WfTty8Fe5Fo
 
 
 
~IceMatrix
 
 
 
==See Also==
 
 
 
{{AMC12 box|year=2020|ab=B|num-b=3|num-a=5}}
 
{{MAA Notice}}
 

Latest revision as of 21:27, 12 February 2020

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