If x is divided by y and the result is 120.15, which of the following could be the remainder of x/y?
28
42
58
88
92
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.
We should write the decimal representation AS A FRACTION IN ITS MOST REDUCED FORM.
In the problem above:
Remainder = R
Divisor = y
Decimal = .15 = 15/100 = 3/20.
Plugging these values into
remainder/divisor = decimal, we get:
R/y = 3/20.
Since R/y is in its most reduced form, we know that y must be a multiple of 20 and that R must be a multiple of 3.
Only answer choice
B is a multiple of 3.
The correct answer is
B.
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