Difference between revisions of "2012 AMC 10B Problems/Problem 4"
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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> . | 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> . | ||
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| + | ==See Also== | ||
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| + | {{AMC10 box|year=2012|ab=B|num-b=3|num-a=5}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 21:09, 8 February 2014
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?
Solution
In total, there were 
marbles left from both Ringo and Paul.We know that 
. This means that there would be 
marble left over, or 
.
See Also
| 2012 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
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