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2012 AMC 10B Problems/Problem 4: Difference between revisions

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In total, there were <math>3+4=7</math> marbles left from both Ringo and Paul. <math>7/6</math>=1R1. This means that that there is <math>\boxed{1}</math> marbles left or  
In total, there were <math>3+4=7</math> marbles left from both Ringo and Paul.We know that  <math>7 \equiv 1 \pmod{6}</math>. This means that there would be <math>1</math> marble left over, or <math>\boxed{A}</math> .
 
<math> \textbf{(A)}</math>

Revision as of 17:58, 6 January 2013

Problem 4

When Ringo places his marbles into bags with 6 marbles per bag, he has 4 marbles left over. When Paul does the same with his marbles, he has 3 marbles left over. Ringo and Paul pool their marbles and place them into as many bags as possible, with 6 marbles per bag. How many marbles will be left over?

$\textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5$


Solution

In total, there were $3+4=7$ marbles left from both Ringo and Paul.We know that $7 \equiv 1 \pmod{6}$. This means that there would be $1$ marble left over, or $\boxed{A}$ .

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