2024 AMC 10A Problems/Problem 4: Difference between revisions
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== Problem == | |||
The number <math>2024</math> is written as the sum of not necessarily distinct two-digit numbers. What is the least number of two-digit numbers needed to write this sum? | |||
<math>\textbf{(A) }20\qquad\textbf{(B) }21\qquad\textbf{(C) }22\qquad\textbf{(D) }23\qquad\textbf{(E) }24</math> | |||
== Solution == | |||
Since we want the least number of two-digit numbers, we maximize the two-digit numbers by choosing as many <math>99</math>s as possible. Since <math>2024=99\cdot20+44\cdot1,</math> we choose twenty <math>99</math>s and one <math>44,</math> for a total of <math>\boxed{\textbf{(B) }21}</math> two-digit numbers. | |||
~MRENTHUSIASM | |||
Revision as of 15:38, 8 November 2024
Problem
The number 
is written as the sum of not necessarily distinct two-digit numbers. What is the least number of two-digit numbers needed to write this sum?
Solution
Since we want the least number of two-digit numbers, we maximize the two-digit numbers by choosing as many 
s as possible. Since 
we choose twenty s and one 
for a total of 
two-digit numbers.
~MRENTHUSIASM
