Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
The remainder when $7^{84}$ is divided by 342 is
(a)0
(b)1
(c)49
(d)341
Answer
Answer (as printed): B
Explanation
$7^{84}=\left(7^{3}\right)^{28}=(343)^{28}$. Now, $\left(x^{n}-a^{n}\right)$ is divisible by $(x-a)$ for all values of $n$. $$\begin{aligned} & \therefore\left[(343)^{28}-1\right] \text { is divisible by }(343-1) \\ & \Rightarrow\left[(343)^{28}-1\right] \text { is divisible by } 342 \\ & \Rightarrow\left(7^{84}-1\right) \text { is divisible by } 342 \\ & \Rightarrow \text { On dividing } 7^{84} \text { by } 342, \text { we get } 1 \text { as remainder. } \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.