Question

The product of two whole numbers is 1000. If neither of the numbers is a multiple of 10, what is their sum?

Answer 1

133

Explanation:

We are given that the product of two numbers is 1000. Let's first list out the factors of 1000 (factors are numbers that evenly divide into 1000):

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000

We see that the pairs are:

(1, 1000)

(2, 500)

(4, 250)

(5, 200)

(8, 125)

(10, 100)

(20, 50)

(25, 40)

An easy way to see if a number is divisible by 1000 is to check is it has a zero at the end. Notice that all of the pairs have at least one number that ends with at least 1 zero except (8, 125), so this is the pair of numbers we're looking for.

The sum is thus 8 + 125 = 133.

~ an aesthetics lover

Answer 2

133

Explanation:

1000 = 2 * 2 * 2 * 5 * 5 * 5

To not have a multiple of 10, you cannot have 2 and 5 as factors of the same number.

One number is 2^3 = 8.

The other number is 5^3 = 125.

8 * 125 = 1000, so the two do multiply to 1000.

Neither 8 nor 125 is a multiple of 10.

8 + 125 = 133