Which Numbers Always Divides the Difference Between the Squares of two Consecutive Odd Integers?

  1. 7
  2. 3
  3. 8
  4. 6
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1 Answer(s)

Answer: (3) 8
Explanation:-

Let be the two consecutive numbers = (2X – 1) and (2X + 1)
Difference between their square = (2X + 1)2 – (2X – 1)2
= {(2x)2 + 12 + 4X} – {(2X)2 + 12 – 4X}
= 4X2 + 4X + 1 – 4X2 – 1 + 4X
= 8X

Hence, the answer is 8.

Anurag Mishra Professor Answered on 3rd June 2015.
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