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1. The difference of the squares of two consecutive odd integers is divisible by which of the following integers?
- A. 3
- B. 3
- C. 3
- D. 3
Answer: Option D
Explanation:
Let the two consecutive odd integers be (2x+1) and (2x+3)
Then according to the question
⇒(2x+3)2−(2x+1)2=4x2+12x+9−4x2−4x−1
⇒8x+8
⇒8(x+1)
Hence the difference between the squares of two consecutive odd integers is always divisible by 8
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