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Last Updated on May 11, 2023
GMAT OFFICIAL GUIDE PS
Solution:
Let’s simplify the given expression:
(k + 2)(k^3 – k) = (k + 2)[k(k^2 – 1)] = (k + 2)(k)(k + 1)(k – 1)
Reordering the factors in the expression, we have:
(k – 1)(k)(k + 1)(k + 2), which is a product of 4 consecutive integers. Since the product of n consecutive integers is always divisible by n!, the product of 4 consecutive integers is always divisible by 4! = 24 and hence by 6. Thus, the remainder when (k + 2)(k^3 – k) is divided by 6 is 0.
Answer: A
