Answer: C

Add $2$ to all three parts: $6 < 3a < 15$. Divide by $3$: $2 < a < 5$. Since $b = 2a + 1$, $2(2) + 1 < b < 2(5) + 1$, or $5 < b < 11$. Of the choices, only $9$ is between $5$ and $11$.

Choices B and D are the endpoints of the range, but the inequalities are strict, so $b$ can't equal $5$ or $11$.

Why the other choices are wrong

• A. 2 is the lower bound for a, not for b. Since b = 2a + 1, b must be greater than 5.
• B. b = 5 would require a = 2, but a must be greater than 2.
• D. b = 11 would require a = 5, but a must be less than 5.