Difference between revisions of "2024 AMC 10A Problems/Problem 3"

Revision as of 15:26, 8 November 2024

What is the sum of the digits of the smallest prime that can be written as a sum of $5$ distinct primes?

$\textbf{(A) }5\qquad\textbf{(B) }7\qquad\textbf{(C) }9\qquad\textbf{(D) }10\qquad\textbf{(E) }13$

Recall that $2$ is the only even prime.

Let the requested sum be $S.$ Clearly, $S$ is odd. It follows that the five distinct primes are all odd.

2024 AMC 10A (Problems • Answer Key • Resources)
Preceded by 2	Followed by Problem 4
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 10 Problems and Solutions

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 == Solution ==
+Recall that <math>2</math> is the only even prime.
+Let the requested sum be <math>S.</math> Clearly, <math>S</math> is odd. It follows that the five distinct primes are all odd.
 ==See also==
 {{AMC10 box|year=2024|ab=A|before=2|num-a=4}}
 {{MAA Notice}}