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The Divisibility Test...

This question will test basic general understanding. This question can be solved by students over 8th class onwards very easily.

Consider two numbers a & b which when divided by 6, leave remainder 3 and 2 respectively. So what will be the remainder when each one of the following is divided by 6:
(i) a+b
(ii) a-b
(iii) a*b
(iv) b-a
(v) b*b

Solution :

The answers are (i) 5 (ii) 1 (iii) 0 (iv) 5 (v) 4
How ?
Just take these two numbers a and b as 6x+3 and 6y+2 so that they leave the remainder 3 & 2 respectively when divided by 6.
Now you can see that a+b= 6(x+y)+5
a-b = 6(x+y)+1
a*b=(6x+3)*(6y+2)=36xy+18y+12x+6 is divisible by 6
b-a = 6(y-x)-1 = 6(y-x-1)+ 6-1=6(y-x-1)+5
b*b= (6y+2)*(6y+2) = 36yy+12y+12y+4

I hope now you get how we arrived at the solution.

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