Difference between revisions of "2020 AMC 12B Problems/Problem 4"
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==Solution== | ==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== | ==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 20:08, 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. 
