Four Integers That are Divisible by $3$

Algebra Level 2

If $A, B ,C , \frac{B}{C}$ are four integers that are evenly divisible by $3$ , then which one of the given four must be evenly divisible by $9 ?$

B C A None of them.

1 solution

Hana Wehbi
Mar 5, 2018

We can write $A=3x, B=3y, C=3z, \text { and } \frac{B}{C}= 3w$ , for positive integers $w,x,y,z$ ,

$\implies \frac {B}{3z}= 3w,$

$\implies B= 9zw$ ,

then $B$ is evenly divisible by $9.$