2016 AMC 8 Problems/Problem 5
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The number is a two-digit number.
• When is divided by
, the remainder is
.
• When is divided by
, the remainder is
.
What is the remainder when is divided by
?
Solution
From the second bullet point, we know that the second digit must be 3. Because there is a remainder of 1 when it is divided by three, the multiple of 9 must end in a 2. We now look for this one:
The number satisfies both conditions. We subtract the biggest multiple of 11 less than 73 to get the remainder. Thus,
.
2016 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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