Difference between revisions of "2020 AMC 12B Problems/Problem 4"
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==Problem== | ==Problem== | ||
| − | 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>? | + | 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== | ==Solution== | ||
Revision as of 21:41, 7 February 2020
Problem
The acute angles of a right triangle are 
and 
, where 
and both 
and 
are prime numbers. What is the least possible value of ?
Solution
, so 
. The largest primes less than 
are 
If 
, then 
, which is not prime. However, if 
, then 
, which is prime. Hence the answer is 
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 | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
