Fun With Multiples!

Number Theory Level 1

Last year, Kiara’s age was a multiple of 7. This year it’s a multiple of 5.
If she is currently under 20, after how many years will she turn 20?

1 solution

Soha Farhin Pine Pine
Jul 15, 2016

Let Kiara's age be $k$ , which must be within 1 and 19.

We know that $k$ is a multiple of 5 and $k-1$ is a multiple of 7.

Listing the possible values of $k$ :

Multiples of 5 — $5$ , $10$ , $15$

Multiples of 7 — $7$ , $14$

(All multiples below 20.)

Just eyeballing it, we can say that Kiara's age is $15$ . $20-15$ yields $\boxed{5}$ which is the required answer.