Question

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

is the largest integer value of a?
a) 8
b) 9
c)10
d)11​

Answer 1

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

`\frac{3a+4b}2<50`

Then

`a=2b\implies\frac{3(2b)+4b}2=5b<50\implies b<10`

`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.