Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
$\left(9^{6}+1\right)$ when divided by 8, would leave a remainder of
(a)0
(b)1
(c)2
(d)3
Answer
Answer (as printed): C
Explanation
$\left(x^{n}-a^{n}\right)$ is divisible by $(x-a)$ for all values of $n$ $$\begin{aligned} & \therefore\left(9^{6}-1^{6}\right) \text { is divisible by }(9-1) \\ & \Rightarrow\left(9^{6}-1\right) \text { is divisible by } 8 \\ & \Rightarrow \text { On dividing }\left(9^{6}+1\right) \text { by } 8, \text { we get } 2 \text { as remainder. } \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.