100000

The variables a \textup{ and }b represent positive integers, neither of which are divisible by 10 yet the product of a\textup{ and }b is 100000.  Find the sum of a\textup{ and }b.
Source: mathcontest.olemiss.edu 1/12/2009

SOLUTION
This problem is similar to the problem titled “Product of X and Y” dated 12/1/2008.
100000=10\times 10\times 10\times 10\times 10
=2\times 5\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\times 5
=a\times b

Since we want a \textup{ and }b not divisible by 10, we should keep the 2’s and the 5’s separate when we form the two factors a \textup{ and }b of 100000. Thus,
a=2\times 2\times 2\times 2\times 2
=32

b=5\times 5\times 5\times 5\times 5
=3125

The sum a+b=32+3125=3157.

Answer: 3157.

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About mvtrinh

Retired high school math teacher.
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