Question

97) If the average of 3a and 4b is less than 50 and a is twice b, what

Answer 1

The average of $3a$ and $2b$ satisfies

$\dfrac{3a+4b}2$

Then

$a=2b\implies\dfrac{3(2b)+4b}2=5b$

$a=2b$, so if $a$ must be an integer, then the largest integer value it can take on is 19 if $b$ can be a rational number (in which case $b=9.5$) or 18 if $b$ must also be an integer.

Given that none of the provided answer choices lists 18 or 19, I'd bet there's a typo and you're supposed to find the maximum integer value of $b$, in which case the answer would be B as the largest integer value would be 9.