Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
If $n$ is even, $\left(6^{n}-1\right)$ is divisible by
(a)6
(b)30
(c)35
(d)37
Answer
Answer (as printed): C
Explanation
When $n$ is even, $\left(x^{n}-a^{n}\right)$ is divisible by both $(x-a)$ and $(x+a)$. So, $\left(6^{n}-1\right)$ is divisible by both $(6-1)$ and $(6+1)$ $$\begin{aligned} & \Rightarrow\left(6^{n}-1\right) \text { is divisible by both } 5 \text { and } 7 \\ & \Rightarrow\left(6^{n}-1\right) \text { is divisible by }(5 \times 7) \text {, i.e. } 35 . \end{aligned}$$ [ $\because 5$ and 7 are co-primes]
Explanation as extracted from the printed page; notation may be imperfect.