ABC26GN0296 · Number System
Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
If $n$ is any odd number greater than 1 , then $n\left(n^{2}-1\right)$ is
(a)divisible by 24 always
(b)divisible by 48 always
(c)divisible by 96 always
(d)None of these
Answer
Explanation
Let $n = (2m+1)$. Then, $N = n(n^2-1) = n(n-1)(n+1) = (2m+1)(2m)(2m+2) = 4m(m+1)(2m+1)$. Now, $m=1 \Rightarrow N = (4 \times 1 \times 2 \times 3) = 24$. So, $N$ is always divisible by 24.
Explanation as extracted from the printed page; notation may be imperfect.
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