henilshaht wrote:P and Q are integers, and r is the remainder when P is divided by Q. If P = 3.16Q, which of the following must divide evenly into r?
I. 2
II. 4
III. 8
A. I Only
B. II Only
C. I and II
D. II and III
E. I, II, and III
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 = 0.5
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 = Q
Decimal = 0.16 = 16/100 = 8/50 = 4/25
R/Q = 4/25
Since R/Q is in its most reduced form, we know that Q must be a multiple of 25 and that R must be a multiple of 4.
Options I and II (2 and 4) will divide evenly into every multiple of 4.
Option III (8) will not divide evenly into R if R = 4, 12, 20, etc.
The correct answer is
C.
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