Question

If a and b are positive integers, neither of which is divisible by 10, and if a × b = 10,000 then what is the sum a + b?

Answer 1

Answer:

a+b=641

Step-by-step explanation:

10000 = 10 x 10 x 10 x 10

= 2 x 5 x 2 x 5 x 2 x 5 x 2 x 5

If you include a 2 and 5 factor together, you'll make a multiple of 10. So put all the twos in one number and all the fives in the other.

For example:

a = 2 x 2 x 2 x 2 = 16

b = 5 x 5 x 5 x 5 = 625

Answer:

a + b = 641

P.S. The alternate answer is a = 625, b = 16, but the sum is still the same.