There is a typo in the problem above.
The problem should read as follows:
oquiella 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?
560
616
672
728
784
When one positive integer is divided by another, we typically represent what's left over either 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 representations: 5/2 = 2.5.
Remainder/Divisor = 1/2.
Decimal = .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.
In the problem above:
Remainder = R.
Divisor = y.
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 R must be a MULTIPLE OF 8.
The prompt asks for the sum of all possible 2-DIGIT remainders.
2-digit multiples of 8:
16, 24, 32, 40, 48,
56, 64, 72, 80, 88, 96.
The values above constitute an EVENLY SPACED SET.
Sum of an evenly spaced set = (number of terms)(median).
Median of the 11 terms above = 56.
Thus:
Sum = (11)(56) = 616.
The correct answer is
B.
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