|
|
| (2 intermediate revisions by 2 users not shown) |
| Line 1: |
Line 1: |
| − | ==Problem==
| + | #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{\mathrm{(D)}}</math>
| |
| − | ==See Also==
| |
| − | | |
| − | {{AMC12 box|year=2020|ab=B|num-b=3|num-a=5}}
| |
| − | {{MAA Notice}}
| |
