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The difference of the squares of two consecutive even integers is divisible by which of the following integers ?
Answer & Solution
Correct Answer:
Option
B
Let the two consecutive even integers be 2n and (2n + 2). Then,
(2n + 2)2 - (2n)2 = (2n + 2 + 2n) (2n + 2 - 2n)
= 2(4n + 2)
= 4(2n + 1), which is divisible by 4
(2n + 2)2 - (2n)2 = (2n + 2 + 2n) (2n + 2 - 2n)
= 2(4n + 2)
= 4(2n + 1), which is divisible by 4
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