When positive integer x is divided by positive interger y,

When one positive integer is divided by another, we typically represent what is left over as a REMAINDER or as a DECIMAL.
There is a relationship between the two representations:

Remainder/Divisor = Decimal.

When 5 is divided by 2:
Remainder representation: 5/2 = 2 R1
Decimal representation: 5/2 = 2.5
Remainder/Divisor = 1/2
Decimal = 0.5
Since the two values are equal:
Remainder/divisor = decimal

It can be helpful to write the decimal representation AS A FRACTION IN ITS MOST REDUCED FORM.

BTGmoderatorDC wrote:When positive integer x is divided by positive integer y, the result is 59.32. What is the sum of all possible 2-digit remainders for x/y?

A. 560
B. 616
C. 672
D. 728
E. 784

In the problem above:
Remainder = R
Divisor = 7
Decimal = 0.32 = 32/100 = 8/25
Plugging these values into remainder/divisor = decimal, we get:
R/y = 8/25

The resulting equation implies that the remainder must be a MULTIPLE OF 8.

For any EVENLY SPACED SET:
Count = (biggest - smallest)/(increment) + 1.
Average = (biggest + smallest)/2.
Sum = (count)(average).
The INCREMENT is the difference between successive values.

Here, we must sum the 2-digit multiples of 8 between 16 and 96, inclusive.
Since the integers are multiples of 8, the increment = 8.
Thus:
Count = (96-16)/8 + 1 = 11
Average = (96+16)/2= 56
Sum = (count)(average) = 11*56 = integer with a units digit of 6

The correct answer is B.

Similar remainder problems:

https://www.beatthegmat.com/dealing-with ... 69971.html
https://www.beatthegmat.com/quotient-rem ... 01371.html
https://www.beatthegmat.com/remainder-t176105.html
https://www.beatthegmat.com/remainder-t111428.html