Foundation
Mathematics Foundation
Real Number Properties
Question
If any positive even integer is of the form 4q or 4q+2, then q belongs to:
irrational number
whole number
Both A & B
none of these
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Solution
Let a be any positive even integer and b=4.Then by division algorithm,
a=4q+r for some integer q0 and r=0,1,2,3
So,
a=4q or, 
4q+1,
4q+2
4q+3
Because 0r 4
Now,
4q i.e 2(2q) is an even number
4q+1 is an odd number
4q+2 i.e. 2(2q+1) is an even number
(4q+2)+1=4q+3 is an odd number
Thus, We can say that any positive even integer can be written as in the form of 4q,4q+2 where q is the whole number