# Problem of the Day

If , is an integer?

(1)

(2) is an integer

E. Statements 1 and 2 together are not sufficient.

See the Solution

### Solution

[latexpage]

If $ab=c$, is $\displaystyle \frac {72}{b}$ an integer?

Statement 1: $c=36$. If $a=9$ and $b=4$, then $\frac{72}{b}=\frac{72}{4}=18$. If $a=\frac{36}{7}$ and $b=7$, thenÂ $\frac{72}{b}=\frac{72}{7}$, which is not an integer. INSUFFICIENT.

Statement 2: $\displaystyle \frac{72}{a}$ is an integer. This tells us nothing about $b$. INSUFFICIENT.

Statements 1&2: The examples used to prove Statement 1 insufficient also apply here. INSUFFICIENT.