# Problem of the Day

What percent of is ?

(1) (2) A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

See the Solution

### Solution

[latexpage]

To determine what percent of $b$ is $a$, we need to calculate $\displaystyle \frac{a}{b} \cdot 100$. The unknown part is $\displaystyle \frac{a}{b}$, so that’s what we need to focus on.

Statement 1: SUFFICIENT. The key is to rewrite the left side of the equation by separating the two parts of the numerator into separate fractions over the common denominator.

$\displaystyle \frac{b-a}{b}=\frac{b}{b}-\frac{a}{b} = 1-\frac{a}{b}$.

Then, set the new, equivalent version of the left side equal to the right side and solve for $\displaystyle \frac{a}{b}$:

$\displaystyle 1-\frac{a}{b}=\frac{2}{5}$

$\displaystyle \frac{a}{b}=\frac{3}{5}$

We have determined a unique value for $\displaystyle \frac{a}{b}$, so Statement 1 is sufficient.

Statement 2: INSUFFICIENT. This gives us no information about $a$, so we cannot determine $\displaystyle Â \frac{a}{b}$