Bunuel wrote:
If s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t ?
(A) 2
(B) 4
(C) 8
(D) 20
(E) 45
This problem will be best solved using the remainder formula. Let’s first state the remainder formula:
When positive integer x is divided by positive integer y, if integer Q is the quotient and r is the remainder, then x/y = Q + r/y.
In this problem we are given the following:
s/t = 64.12
We can simplify this to read as the remainder formula:
s/t = 64 + 0.12
s/t = 64 + 0.12
s/t = 64 + 12/100
s/t = 64 + 3/25
Because Q is always an integer, we see that Q must be 64, and thus the remainder r/y must be 3/25. We can now equate r/y to 3/25 and determine a possible value for r.
r/y = 3/25
Note that some equivalent values for r/y could be 6/50 or 9/75 or 12/100, and so forth. Note that in all cases, the value of r is a multiple of 3.
Of the answer choices, the only multiple of 3 is 45, so that is a possible value of r.
Answer: E
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