Question

15. Ms. Goldman is thinking of a number that is less than 20 and has three factor pairs. She says

that if she adds the factors in each factor pair the sums are 19, 11 and 9. What is her number?

Answer 1

Answer: 18

Given: the number is less than 20; three-factor pairs; each factor pair individually adds up to 19, 11, and 9

Solve for her number.

Explanation:

If you think about it for a little bit, you will eventually find that 18 + 1 = 19 and 18 × 1 = 18 which is less than 20.

Then we know 18 has 2 more factor pairs : 9 × 2 and 6 × 3 which add up to 11 and 9.

Therefore our answer is: 18

18 × 1

9 × 2

6 × 3

The trick is to pick the largest sum of one-factor pair (19 in this question) and then choose the number below it.