Two positive integers $a$ and $b$ have the property that if $a$ is increased by $25 \%$, the result will be greater than five times the value of $b$. What is the minimum possible value for $a+b$ ?
(A) 3
(B) 6
(C) 10
(D) 9
(E) 21
When $a$ is increased by $25 \%$, the result is $1.25 a$ or $\frac{5}{4} a$.

Thus, we would like $\frac{5}{4} a>5 b$ or $5 a>20 b$ or $a>4 b$.

We would like to find the smallest possible positive integers $a$ and $b$ that satisfy this inequality. (If $a$ and $b$ are as small as possible, then their sum $a+b$ will be as small as possible.)

Since $b$ is a positive integer, $4 b \geq 4$, so since $a>4 b$, then $a>4$.

Thus, the smallest possible value of $a$ is 5 when $b=1$.

Since $b$ cannot be smaller, then $a$ cannot be smaller.

Therefore, the minimum possible value for $a+b$ is $5+1=6$.

ANSWER: (B)

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