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Question
The difference of the squares of two consecutive odd integers is divisible by which of the following integers?
The difference of the squares of two consecutive odd integers is divisible by which of the following integers?
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Solution
The correct option is D 8
Let the two consecutive odd integers be (2n+1) and (2n+3). Then,
(2n+3)2−(2n−1)2=(2n+3+2n+1)(2n+3−2n−1)
=(4n+4)×2
=8(n+1), which is divisible by 8.
Let the two consecutive odd integers be (2n+1) and (2n+3). Then,
(2n+3)2−(2n−1)2=(2n+3+2n+1)(2n+3−2n−1)
=(4n+4)×2
=8(n+1), which is divisible by 8.
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