Difference between revisions of "2021 AMC 10B Problems/Problem 13"
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Let <math>n</math> be a positive integer and <math>d</math> be a digit such that the value of the numeral <math>\underline{32d}</math> in base <math>n</math> equals <math>263</math>, and the value of the numeral <math>\underline{324}</math> in base <math>n</math> equals the value of the numeral <math>\underline{11d1}</math> in base six. What is <math>n + d ?</math> | Let <math>n</math> be a positive integer and <math>d</math> be a digit such that the value of the numeral <math>\underline{32d}</math> in base <math>n</math> equals <math>263</math>, and the value of the numeral <math>\underline{324}</math> in base <math>n</math> equals the value of the numeral <math>\underline{11d1}</math> in base six. What is <math>n + d ?</math> | ||
<math>\textbf{(A)} ~10 \qquad\textbf{(B)} ~11 \qquad\textbf{(C)} ~13 \qquad\textbf{(D)} ~15 \qquad\textbf{(E)} ~16</math> | <math>\textbf{(A)} ~10 \qquad\textbf{(B)} ~11 \qquad\textbf{(C)} ~13 \qquad\textbf{(D)} ~15 \qquad\textbf{(E)} ~16</math> | ||
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==Solution== | ==Solution== | ||
B | B | ||
Revision as of 19:49, 11 February 2021
Problem
Let 
be a positive integer and 
be a digit such that the value of the numeral 
in base equals 
, and the value of the numeral 
in base equals the value of the numeral 
in base six. What is 
Solution
B
