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Question

Difference between the squares of two consecutive odd integers is always divisible by
Options:
A .  8
B .  7
C .  6
D .  3
Answer: Option A

Answer : Option A

Explanation :

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Solution 1
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Let two odd numbers be (2n - 1) and (2n + 1)
Difference between the squares
= (2n + 1)2 - (2n - 1)2
= [4n2 + 4n + 1] - [4n2 - 4n + 1]
= 8n which is always divisible by 8
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Solution 2
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Take any two odd numbers, say 1 and 3
Difference between the squares = 32 - 12 = 9 - 1 = 8
From the given choices, now you can easily figure out the answer as 8



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