2017 AMC 10B Problems/Problem 1
Contents
[hide]Problem
Mary thought of a positive two-digit number. She multiplied it by and added
. Then she switched the digits of the result, obtaining a number between
and
, inclusive. What was Mary's number?
Solution 1
We try out each answer choice. Multiplying by
, adding
, and reversing the digits yields
. Therefore the answer is
.
Solution 2
Working backwards, we reverse the digits of each number from ~
and subtract
from each, so we have
The only numbers from this list that are divisible by
are
and
. We divide both by
, yielding
and
. Since
is not a two-digit number, the answer is
.
See Also
2017 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
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All AMC 10 Problems and Solutions |
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