Product of X and Y

X \textup{ and }Y are whole numbers and neither of which are divisible by 10. If the product of X \textup{ and }Y equals 20000, find the absolute value of the difference of X \textup{ and }Y.
Source: mathcontest.olemiss.edu 12/1/2008

SOLUTION
This problem is similar to the problem titled “100000” dated 1/12/2009.
20000=2\times 10\times 10\times 10\times 10
=2\times 2\times 5\times 2\times 5\times 2\times 5\times 2\times 5
=2\times 2\times 2\times 2\times 2\times 5\times 5\times 5\times 5
= X\times Y

Since we want X \textup { and }Y not divisible by 10, we should keep the 2’s and 5’s separate when we form the two factors X\textup{ and }Y of 20000. Thus,
X=2\times 2\times 2\times 2\times 2
=32
Y=5\times 5\times 5\times 5
=625

\left |X-Y\right |=\left |32-625\right |
=\left |-593\right |
=593.

Answer: 593.

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About mvtrinh

Retired high school math teacher.
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