is this divisibility solution a fluke !!

[rajkapoor]

This following question simulates OG PS-82..

to test whether the expression below is divisible by 4 , given n is an integer and greater than 5

(n)(n +2 )(n +5)(n-5)

to solve this problem, i kept two things in mind
a) this expression will be divisible by 4 if these four numbers are consecutive or if at least two of these are even
b) n+ 5 divided by 4 is same as n+1 divided by 4 in terms of remainder...
so replacing (n+5) by (n + 1) and similarly n - 5 will leave the same remainder as (n-1)

so the above expression evaluates to
(n)(n+2)(n+1)(n-1) = > (n-1)(n)(n+1)(n+2) = four consecutive integers and hence divisible by 4.

i applied the same approach in the original question and got the correct answer

Question to instructors : is (b) the right approach or was it just a lucky strike ...

[esledge]

That is not only a valid approach, but also the concept I think the writers intended to test with that one.

It's probably worth noting that you could answer by plugging in several values for x (e.g. x = 5, 6, 7, 8, 9) and seeing that a pattern emerges.