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.
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