# Possible percent problem

Algebra Level 3

Consider numbers $a$ and $b$ such that $\frac{a}{b}=24\%$ when rounded to the nearest whole percent.

$b$ could be 63 since if $a=15$ we would have $\frac{15}{63}\approx .2381$ which rounds to $24\%$

$b$ could not be 10 however since no fraction of the form $\frac{a}{10}$ rounds to $24\%$

Let $x=$ the least possible value of $b$ for which there is a value of $a$ that makes $\frac{a}{b}=24\%$ when rounded to the nearest whole percent.

Let $y=$ the greatest possible value of $b$ for which there is no value of $a$ that makes $\frac{a}{b}=24\%$ when rounded to the nearest whole percent.

Give the value of $x+y$.

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