Difference between revisions of "2021 AMC 12B Problems/Problem 7"

(Created page with "==Problem== Let <math>N = 34 \cdot 34 \cdot 63 \cdot 270</math>. What is the ratio of the sum of the odd divisors of <math>N</math> to the sum of the even divisors of <math>N<...")
 
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<math>\textbf{(A)} ~1 : 16 \qquad\textbf{(B)} ~1 : 15 \qquad\textbf{(C)} ~1 : 14 \qquad\textbf{(D)} ~1 : 8 \qquad\textbf{(E)} ~1 : 3</math>
 
<math>\textbf{(A)} ~1 : 16 \qquad\textbf{(B)} ~1 : 15 \qquad\textbf{(C)} ~1 : 14 \qquad\textbf{(D)} ~1 : 8 \qquad\textbf{(E)} ~1 : 3</math>
 
==Solution==
 
==Solution==
<math>\textbf{(C)} ~1 : 14</math>
+
<math>\boxed{\textbf{(C)} ~1 : 14}</math>

Revision as of 18:44, 11 February 2021

Problem

Let $N = 34 \cdot 34 \cdot 63 \cdot 270$. What is the ratio of the sum of the odd divisors of $N$ to the sum of the even divisors of $N$?

$\textbf{(A)} ~1 : 16 \qquad\textbf{(B)} ~1 : 15 \qquad\textbf{(C)} ~1 : 14 \qquad\textbf{(D)} ~1 : 8 \qquad\textbf{(E)} ~1 : 3$

Solution

$\boxed{\textbf{(C)} ~1 : 14}$

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