n is a natural number. State whether n (n² - 1) is divisible by 24.
(1) 3 divides 'n' completely without leaving any remainder.
(2) 'n' is odd.
n (n² - 1) = n (n-1) (n+1) = 3 consecutive integers
Any three consecutive integers will be divisible by 24 if the middle integer is odd.
if n=1, then (n+1)=2 and (n-1)=0 => n (n-1) (n+1) = 0, which is divisible by any number
if n=3, then (n+1)=4 and (n-1)=2 => n (n-1) (n+1) = 24, which is divisible by 24
if n=5, then (n+1)=6 and (n-1)=4 => n (n-1) (n+1) = 120, which is divisible by 24
=> n (n-1) (n+1) is divisible by 24 for all odd values of n
Statement 1 states that n is a multiple of 3
if n=3 sufficient
if n=6 not sufficient ----> not sufficient
Statement 2 states that n is odd -> sufficient
Answer is B
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