2017 AMC 8 Problems/Problem 12
Problem
The smallest positive integer greater than 1 that leaves a remainder of 1 when divided by 4, 5, and 6 lies between which of the following pairs of numbers?
Solution 1
Since the remainder is the same for all numbers, then we will only need to find the lowest common multiple of the three given numbers, and add the given remainder. The is
. Since
, and that is in the range of
Solution 2
Call the number we want to find . We can say that
We can also say that
is divisible by
and
Therefore,
, so
which is in the range of
Video Solution
See Also
2017 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
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