Difference between revisions of "2021 April MIMC 10 Problems/Problem 20"

(Created page with "Given that <math>y=24\cdot 34\cdot 67\cdot 89</math>. Given that the product of the even divisors is <math>a</math>, and the product of the odd divisors is <math>b</math>. Fin...")
 
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Given that <math>y=24\cdot 34\cdot 67\cdot 89</math>. Given that the product of the even divisors is <math>a</math>, and the product of the odd divisors is <math>b</math>. Find <math>a \colon b^4</math>.
 
Given that <math>y=24\cdot 34\cdot 67\cdot 89</math>. Given that the product of the even divisors is <math>a</math>, and the product of the odd divisors is <math>b</math>. Find <math>a \colon b^4</math>.
  
<math>\textbf{(A)} ~512:1 \qquad\textbf{(B)} ~1024:1 \qquad\textbf{(C)} ~2^{64}:1 \qquad\textbf{(D)} ~2^{80}:1 \qquad\textbf{(E)} 2^{160}:1 \qquad</math>
+
<math>\textbf{(A)} ~512:1 \qquad\textbf{(B)} ~1024:1 \qquad\textbf{(C)} ~2^{64}:1 \qquad\textbf{(D)} ~2^{80}:1 \qquad\textbf{(E)} ~2^{160}:1 \qquad</math>
 
==Solution==
 
==Solution==
 
To be Released on April 26th.
 
To be Released on April 26th.

Revision as of 17:42, 22 April 2021

Given that $y=24\cdot 34\cdot 67\cdot 89$. Given that the product of the even divisors is $a$, and the product of the odd divisors is $b$. Find $a \colon b^4$.

$\textbf{(A)} ~512:1 \qquad\textbf{(B)} ~1024:1 \qquad\textbf{(C)} ~2^{64}:1 \qquad\textbf{(D)} ~2^{80}:1 \qquad\textbf{(E)} ~2^{160}:1 \qquad$

Solution

To be Released on April 26th.

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