SAT Prep

Category - Math

The difference of squares of any two consecutive odd numbers is divisible by:
  1. 6
  2. 7
  3. 8
  4. 9
  5. 10
Explanation
Answer: C - The difference of squares of any two consecutive odd numbers is divisible by 8. Denote consecutive odd integers with 2n-1 and 2n + 1.
(2n + 1)2-(2n-1)2 = 4n2 + 4n + 1-(4n2-4n + 1) = 4n2 + 4n + 1-4n2 + 4n-1 =
= 8n
Since one of the factors is 8, the whole expression is divisible by 8.
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