Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
$\left(7^{19}+2\right)$ is divided by 6 . The remainder is
(a)1
(b)2
(c)3
(d)5
Answer
Answer (as printed): C
Explanation
$\left(x^{n}-a^{n}\right)$ is divisible by $(x-a)$ for all values of $n$. $$\begin{aligned} & \therefore\left(7^{19}-1^{19}\right) \text { is divisible by }(7-1) \\ & \Rightarrow\left(7^{19}-1\right) \text { is divisible by } 6 \\ & \Rightarrow \text { On dividing }\left(7^{19}+2\right) \text { by } 6, \text { remainder obtained }=3 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.