Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
Consider the following statements: For any positive integer $n$, the number $10^{n}-1$ is divisible by (1) 9 for $n=\mathrm{odd}$ only (2) 9 for $n=$ even only (3) 11 for $n=\mathrm{odd}$ only (4) 11 for $n=$ even only Which of the above statements are correct?
(a)1 and 3
(b)2 and 3
(c)1 and 4
(d)2 and 4
Answer
Answer (as printed): D
Explanation
We know that $\left(x^{n}-a^{n}\right)$ is divisible by ( $x-a$ ), when $n$ is even and $\left(x^{n}-a^{n}\right)$ is divisible by $(x+a)$, when $n$ is even. $\therefore\left(10^{n}-1\right)$ is divisible by $(10-1)=9$, when $n$ is even. And, $\left(10^{n}-1\right)$ is divisible by $(10+1)=11$, when $n$ is even. ∴ Statements 2 and 4 are correct.
Explanation as extracted from the printed page; notation may be imperfect.