Ryan Ziemba wrote:Are there any standard rules one should keep in mind when solving quant problems involving remainders? I had some difficulty with Problem 106 in the Problem Solving section of the Official Guide and was wondering if there is a quick and easy approach to remember when tackling these types of questions. For instance, should I start by picking numbers or backsolving?
106. When positive integer x is divided by positive integer y, the remainder is 9. If x/y=96.12, what is the value of y?
(a) 96
(b) 75
(c) 48
(d) 25
(e) 12
When one number doesn't divide evenly into another number, we can represent what's left over 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 y, and the remainder is 9. So .12y = 9, y = 9/.12 = 900/12 = 75.
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