A digit $n > 3$ is divisible by 3 but not divisible by 6. Which one of the following is divisible by 4?
A digit $n > 3$ is divisible by 3 but not divisible by 6. Which one of the following is divisible by 4?
$2n$
$3n$
$2n + 4$
$3n + 1$
Solution
A digit $n > 3$ divisible by 3 but not by 6 must be odd and a multiple of 3, so $n = 9$ (the only single digit greater than 3 that is a multiple of 3 and odd). Check: $2n = 18$ (not divisible by 4); $3n = 27$ (not divisible by 4); $2n + 4 = 22$ (not divisible by 4); $3n + 1 = 28$ (divisible by 4). Hence $3n + 1$ is divisible by 4.