2019 AMC 10B Problems/Problem 19

Revision as of 16:50, 14 February 2019 by Greersc (talk | contribs) (I wrote the solution using LaTeX.)

Problem

Solution

To find the number of numbers that are the product of two distinct elements of $S$, we first square $S$ and factor it. Factoring, we find $S^2 = 2^{10} \cdot 5^{10}$. Therefore, $S^2$ has $(10 + 1)(10 + 1) = 121$ distinct factors. Each of these can be achieved by multiplying two factors of $S$. However, the factors must be distinct, so we eliminate $1$ and $S^2$, so the answer is $121 - 1 - 1 = 119$.

Solution by greersc.

See Also

2019 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 18
Followed by
Problem 20
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. AMC logo.png