2016 AMC 8 Problems/Problem 5
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 ?
Contents
[hide]Video Solution
https://youtu.be/7an5wU9Q5hk?t=574
Solution
From the second bullet point, we know that the second digit must be . Because there is a remainder of when it is divided by , the multiple of must end in a in order for it to have the desired remainder We now look for this one:
The number satisfies both conditions. We subtract the biggest multiple of less than to get the remainder. Thus, .
Solution 2
33
Video Solution
https://www.youtube.com/watch?v=LqnQQcUVJmA (has questions 1-5)
2016 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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