Doubt in solution

GRE GRE Quant Problem Solving
1

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as per the solution we can add/remove 3 in general format - (x-1)x(x+1) and derive the formate that also division by 3
so why (x-5) does not work?
(x+1+ (-3)) → (x-2+ (-3)) → (x-5) so option B does work right? why solution says it doesn’t !

2

You can choose numbers to validate your hypothesis.

The questions says “always” a multiple of 3, so if you find a case where its not, then you can cross it out.

Assume x=1

(x-5)(x)(x+4)= (1-5)(1)(1+4) = (-4)(1)(5)

And this is not a multiple of 3. So you can cross out option B

3

definitely we can solve using numbers but it would become tedious ..
check out greg’s solution. as per his statement option B should work right?