Difference between revisions of "2011 AMC 12B Problems/Problem 4"
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Revision as of 18:38, 29 May 2011
Problem
In multiplying two positive integers and
, Ron reversed the digits of the two-digit number
. His erroneous product was
What is the correct value of the product of
and
?
Solution
Taking the prime factorization of reveals that it is equal to
Therefore, the only ways to represent
as a product of two positive integers is
and
Because neither
nor
is a two-digit number, we know that
and
are
and
Because
is a two-digit number, we know that a, with its two digits reversed, gives
Therefore,
and
Multiplying our two correct values of
and
yields
\[= \boxed{224\ \(\textbf{(E)}}\] (Error compiling LaTeX. Unknown error_msg)
See also
2011 AMC 12B (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 12 Problems and Solutions |