diegocuenca wrote:When positive integer x is divided by positive integer y, the reminder is 9. If x/y = 96.12, what is the value of y? Are there any alternative explanations besides the answer in the book?
Hey!
This is pretty analagous to the post that's already been linked to, but maybe I'll use a few different words
Whenever you're doing a long division problem and the divisor doesn't divide cleanly into the dividend, you have three options when it comes to expressing what's left over: (1) remainders, (2) fractions, and (3) decimals. For instance 5/3 can be expressed as "1 with a remainder of 2," or "1 and 2/3," or 1.66666.
(The remainder, when used by itself, is pretty clearly the least informative of these modes of expression, which is why we more or less abandon it after third grade, but the GMAT likes to throw it back into the mix
.) So, when you've got a remainder and want to transition into one of the other forms of expression, the fractional equivalent of that remainder is the same as remainder/divisor (and the decimal equivalent is just the decimal equivalent of that fraction). Here we know that the divisor is y and the remainder is 9, so the fractional equivalent must be 9/y, which apparently also equals .12 (in other words, the entire whole number component--in this case 96--is totally irrelevant to the problem).
9/y = .12 --> .12y = 9 --> y = 9/.12 = 900/12 = 75.
