Discussion
A single digit number \(n \gt 2\) is divisible by 2 but not divisible by 4. Which one of the following is divisible by 6?
Answer: C
The number divisible by 6 is 9n.
The single-digit numbers greater than 2 that are even are 4, 6 and 8. Of these, 4 and 8 are divisible by 4, so n = 6.
\[ \begin{aligned} 9n &= 54 = 6 \times 9 \\ 9n + 4 &= 58,\ \ 6n + 7 = 43,\ \ 5n + 3 = 33 \end{aligned} \]
Only 54 is divisible by 6. 58 and 43 are not divisible by 3 (43 is not even even), and 33 is odd, so it fails the test for 2.
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