When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the value of y ?
(A) 96 (B) 75 (C) 48 (D) 25 (E) 12
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 = 9.
Divisor = y.
Decimal = .12 = 12/100 = 3/25.
Plugging these values into
remainder/divisor = decimal, we get:
9/y = 3/25
y = 75.
The correct answer is
B.
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