Difference between revisions of "2003 AMC 10A Problems/Problem 14"
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Revision as of 15:36, 27 May 2021
Problem
Let be the largest integer that is the product of exactly 3 distinct prime numbers
,
, and
, where
and
are single digits. What is the sum of the digits of
?
Solution 1
Since you want to be the largest number possible, you will want
in
to be as large as possible. So
.Then,
cannot be
because
which is not prime. So
.
.
So, the sum of the digits of
is
~ MathGenius_
Solution 2
Since is a single digit prime number, the set of possible values of
is
.
Since is a single digit prime number and is the units digit of the prime number
, the set of possible values of
is
.
Using these values for and
, the set of possible values of
is
Out of this set, the prime values are
Therefore the possible values of are:
The largest possible value of is
.
So, the sum of the digits of is
Video Solution by WhyMath
~savannahsolver
See Also
2003 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.