Kevin wrote:Most Manhattan GMAT students are trying to break the 700 barrier. As a result, we've developed our own math problems written at the 700+ level; these are the types of questions you'll WANT to see, when you are working at that level. Try to solve this 700+ level problem (I'll post the solution next Monday).
Question:
When the integer x is divided by the integer y, the remainder is 60. Which of the following is a possible value of the quotient x/y?
I. 15.15
II. 18.16
III. 17.17
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
The easiest approach is to understand the following:
When one positive integer doesn't divide evenly into another positive integer, 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 remainder is 60, y is the divisor, and the answer choices give three possible decimal representations. For each answer choice, we should plug the given values into the formula
decimal * divisor = remainder to which yields an integer value for y.
I) .15y = 60.
y = 60/.15 = 6000/15 = 400.
Since y is an integer, the correct answer must include I. Eliminate B and C.
II) .16y = 60
y = 60/.16 = 6000/16 = 375.
Since y is an integer, the correct answer must include II. Eliminate A and E.
The correct answer is D.Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
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