Question
The difference of the squares of two consecutive even integers is divisible by which of the following numbers?
The difference of the squares of two consecutive even integers is divisible by which of the following numbers?
Answer: Option C
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Answer : Option C
Explanation :
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Solution 1
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Let the consecutive even integers are n and (n + 2)
difference of the squares = (n + 2)2 - n2 = (n2 + 4n + 4) - n2 = 4n + 4 = 4(n + 1)
which is divisible by 4
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Solution 2 (preferred way)
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Just take any of the two consecutive even integers say 2 and 4
difference of the squares = 42 - 22 = 16 - 4 = 12 which is divisible by 4
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