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?
Number 15.

Answer 1

Answer:

18

Step-by-step explanation:

Let x be the unknown number.

Given information:

• x < 20
• x has 3 factor pairs with sums of 19, 11 and 9

Factor Pair:  

A pair of numbers that multiply together to give the original number.

We can immediately discount prime numbers since prime numbers only have one factor pair:  itself and one.

Remaining numbers: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18.

Of the remaining numbers, only 12, 16 and 18 have more than 2 pairs of factors:

Factors of 12:   1 and 12, 2 and 6, 3 and 4

Factors of 16:   1 and 16, 2 and 8, 4 and 4

Factors of 18:   1 and 18, 2 and 9, 3 and 6

If the pairs of factors sum to 19, 11 and 9, then the number must be 18.