SOLUTION: When 100 is divided by some positive integer x, the remainder is 10. What is the sum of the smallest and largest values of x?

Algebra ->  Divisibility and Prime Numbers -> SOLUTION: When 100 is divided by some positive integer x, the remainder is 10. What is the sum of the smallest and largest values of x?      Log On


   

Question 262678: When 100 is divided by some positive integer x, the remainder is 10. What is the sum of the smallest and largest values of x?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
x is the divisor
y is the result
r is the remainder

if the remainder is always 10, then the number of 100 - 10 = 90 must be divisible without a remainder.

our equation becomes:

90/x = y with no remainder.

multiply both sides of this equation by x to get:

90 = x*y

find all the factors of x and you will be able to find the anser.

90 equals:
1*90
2*45
3*30
6*15
9*10

now take these factors and divide them into 100.

100/1 = 100 with no remainder
100/90 = 1 with a remainder of 10
100/2 = 50 with no remainder
100/45 = 2 with a remainder of 10
100/3 = 33 with a remainder of 1
100/30 = 3 with a remainder of 10
100/6 = 16 with a remainder of 4
100/15 = 6 with a remainder of 10
100/9 = 11 with a remainder of 1
100/10 = 10 with a remainder of 0.

narrow it down to all those with a remainder of 10 and you get:

100/90
100/45
100/30
100/15

the divisor had to be greater than 10.

the smallest divisor is 15.

the largest divisor is 90.

your answer is:

the sum of the smallest and the largest divisor is 90 + 15 = 105.