ccassel wrote:Hi,

How would you explain the answer to this question?

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

When one number doesn't divide evenly into another number, we can represent what's left over either as a decimal (5/2 = 2.5) or as a remainder (5/2 = 2 R 1). The problem above is testing the relationship between the decimal representation and the remainder representation. Here's the relationship:

decimal * divisor = remainder

Let's revisit 5/2 = 2.5. If we multiply the decimal (.5) by the divisor (2), we get .5 * 2 = 1, which is the remainder if we represent the division as 5/2 = 2 R1.

In the problem above the decimal is .12, the divisor is t, and the remainder is one of the answer choices. So .12t = answer choice. The problem stipulates that t must be an integer. Which answer choice yields an integer value for t?

Only answer choice E works:
.12t = 45
t =45/.12 = 4500/12 = 375.

The correct answer is E.

You explained that very well. Thank you very much!

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?

s = tq + r
s/t = q + r/t

64.12 = 64 + 0.12
64.12 = 64 + r/t HENCE r/t = 0.12

r/t = 12/100
r/t = 3/25
3t = 25r
t = 25r/3
Because t must be an integer, then r must be a multiple of 3.

If we divide (s = tq + r) by t, we know that the "tq" part will yield a remainder of 0, thus the remainder of s/t would be r, which must be a multiple of 3 (for "t" to be an integer)

[spoiler]The only multiple of 3 in the answer choices is (E) which is the correct answer[/spoiler]