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goalevan wrote:A problem of this type appears very difficult to test numbers, so I would always start by rephrasing the question.
In many remainder problems, the formula dividend/divisor = quotient + remainder/divisor can be used to discover basic relationships between the inputs of the problem.
In this case, we have a/b = 3 + R/b. But the question stem also states that a/b = 3.45 = 3 + 45/100, so R/b = 45/100.
In problems testing integer properties of a variable, I like to isolate the other variable in the problem and identify possible values that create an integer.
Isolating the other variable, b, we see:
b = 100R/45,
b = 25R/9
We are told that b is an integer, and 25 is not divisible by 9, so R must be divisible by 9. In other words, 9 must be factor of R, or R is a multiple of 9.
It can be seen clearly that 3 is the only answer choice that is not a multiple of 9.
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