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

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Question 257909: If 100 is divided by the positive integer x, the remainder is 2. What is the remainder when 198 is divided by x?
Found 2 solutions by ankor@dixie-net.com, jsmallt9:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
If 100 is divided by the positive integer x, the remainder is 2.
What is the remainder when 198 is divided by x?
:
The positive integer: %28%28100-2%29%29%2Fx = 98/x
:
"What is the remainder when 198 is divided by x?
Let r = the remainder, divide 198 by 2x
%28198-r%29%2F%282x%29 = 98%2Fx
Cross multiply
x(198-r) = 2x(98)
x(198-r) = 196x
Divide both sides by x
198 - r = 196
198 - 196 = r
r = 2 is the remainder when 198 is divided by x
:

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
If the remainder is 2 when 100 is divided by x then x must divide evenly into 98. The prime factorization of 98 is 2*7*7. X could be any combination of these factors except 2. (X cannot be two or it would divide evenly into 100.) X could be 7, 2*7, 7*7 or 2*7*7.

Now let's see what the remainders are when each of these x's are divided into 198:
198/7 = 28 (Reminder 2)
198/14 = 14 (Remainder 2)
198/49 = 4 (Remainder 2)
198/98 = 2 (Remainder 2)

So no matter what x is, the remainder is 2 after you divide it into 198.

Actually we could have figured this out pretty quickly:
198%2Fx+=+%2898%2B100%29%2Fx+=+98%2Fx+%2B+100%2Fx Since x divides evenly into 98, 98/x is a whole number. That leaves 100/x which, we already knew, has a remainder of 2!.