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Question

Every even and odd integers can be represented as ________ and ________

A
2q and 2q+1
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B
3q and 3q+2
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C
3q and 3q+1
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D
2q and q+1
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Solution

The correct option is A 2q and 2q+1
Let 'a' be any positive integer and b=2.
By euclid's division algorithm,
a=bq + r 0 ≤ r < b
a=2q + r 0 ≤ r < 2 or r =0,1
If r=0 , then a=2q+0
a=2q, then a is an even integer
If r=1, then a=2q+1
a=2q+1, then a is an odd integer

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