division of positive integers?

Question

If 100 is divided by the positive integer x, the remainder is 2. What is the remainder when 198 is divided by x?

Answer 1

Two (2)

Answer 2

To put your question another way
100 = 2 + qx
That means that x goes into 100 q times with a remainder of 2.
Now multiply by 2:

200 = 4 + 2qx
is a divisor of 2*98 or 196.
So198 = 2 + 2qx
So x goes into 198 2q times with a remainder of 2.
The answer is 2.
Another way:
100 = 2 + qx
So 98 = qx,
196 = 2qx
198 = 2 + 2qx
So the remainder is 2, as before.

Answer 3

You're told that 100 divided by x has a remainder y. Let the quotient by y, then that means

(100/x) = y + (2/x)

100 = xy + 2

Multiply both sides by 2:

200 = 2xy + 4

Subtract 2:

200 - 2 = 2xy + 4 - 2

198 = 2xy + 2

(198/x) = 2y + (2/x)

So, the remainder is 2. You could probably have worked this out without the algebra - see if you can figure out how.

Answer 4

x is 7. So the remainder when 198 is divided by x is 2.