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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Is 1/(x - y) < y - x tagged by: M7MBA ##### This topic has 1 expert reply and 0 member replies ### Top Member ## Is 1/(x - y) < y - x $$Is\ \ \ \ \frac{1}{x-y} < y-x\ .$$ $$(1)\ \ \ \frac{1}{x} < \frac{1}{y}$$ $$(2)\ \ \ 2x = 3y$$ The OA is the option C. Experts, can you help me here? How can I show that each statement alone is not sufficient? Thanks. ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 M7MBA wrote: $$Is\ \ \ \ \frac{1}{x-y} < y-x\ .$$ $$(1)\ \ \ \frac{1}{x} < \frac{1}{y}$$ $$(2)\ \ \ 2x = 3y$$ The OA is the option C. Experts, can you help me here? How can I show that each statement alone is not sufficient? Thanks. Let's rephrase the question. If x > y, then x - y > 0 and y -x < 0. The left side of the inequality would be larger than the right side. If x < y, then x - y < 0, and y - x > 0. Now the left side of the inequality would be smaller than the right side - this is exactly what we're asked. Thus, our rephrased question: Is x < y? 1) 1/x < 1/y Case 1: x = 2 and y = 1. x is not less than y, so the answer is NO Case 2: x = -1 and y = 1. x is less than y, so the answer is YES. Not Sufficient. 2) 2x = 3y x = (3/2)y Case 1: y = 1 and x = 3/2. x < y? NO Case 2: y = -1 and x = -3/2. x < y? YES. Not Sufficient. Together: Substitute x = (3/2)y into 1/x < 1/y to give us 1/[(3/2)y] < 1/y (2/3) * 1/y < 1/y This will only be true if y is positive. (If y were negative, 1/y would also be negative, and multiplying that value by 2/3 would make the result less negative.) If y is positive, then and x = (3/2)y, x will be a larger positive number. If we know that x > y, the answer to the question is a definitive NO, and thus the statements together are sufficient to answer the question. The answer is C _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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