Which of the following is true for every integer ?

Answer and explanation

Correct answer: C. is divisible by

  1. Step 1: is a product of three consecutive integers, so it contains a multiple of and a multiple of , hence a multiple of .
  2. Step 2: The others fail: gives ; gives ; gives ; gives .
Answer
is divisible by .
Why not the others: The products of consecutive integers guarantee only factors of and ; extra factors such as , or are not guaranteed.

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