SOLUTION: The units digit, or the ones digit, of the product of any six consecutive positive whole numbers always equals which number? (A) 8 (B) 6 (C) 4 (D) 2 (E) 0

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Question 244881: The units digit, or the ones digit, of the product of any six consecutive positive whole numbers always equals which number?
(A) 8 (B) 6 (C) 4 (D) 2 (E) 0
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
The answer is E. The reasons are:
  • Any sequaence of six consecutive positive whole numbers will include at least one (actually 3 but we only need 1) even number
  • Any sequaence of six consecutive positive whole numbers will include at least one multiple of 5
  • Since multiplication is commutative and associative it is OK to consider multiplying the even number by the multiple of 5 first.
  • What do you get when you multiply an even number by a multiple of 5? Answer: A multiple of 10.
  • Multiplying this multiple of 10 by the other 4 numbers, whatever they are, just gives us a larger multiple of 10.
  • And what is the ones digit of all mutliples of 10? Answer: 0!