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# Is xy< -(x/y)?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6815
GMAT 1: 760 Q51 V42
GPA: 3.82

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31 Jan 2018, 01:50
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Difficulty:

(N/A)

Question Stats:

76% (01:28) correct 24% (01:05) wrong based on 60 sessions

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[GMAT math practice question]

Is $$xy< -(\frac{x}{y})$$?

$$1) xy<0$$
$$2) y<0$$

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 30 Dec 2016 Posts: 230 GMAT 1: 650 Q42 V37 GPA: 4 WE: Business Development (Other) Re: Is xy< -(x/y)? [#permalink] ### Show Tags 31 Jan 2018, 02:07 1 its A. Since xy < 0 , either x or y is negative. therefore from given xy < - (x/y) L.H.S. will always be negative and R.H.S will always be positive. Anything-ve < Anything +ve. Hence A _________________ Regards SandySilva ____________ Please appreciate the efforts by pressing +1 KUDOS (: DS Forum Moderator Joined: 21 Aug 2013 Posts: 1432 Location: India Re: Is xy< -(x/y)? [#permalink] ### Show Tags 31 Jan 2018, 10:00 MathRevolution wrote: [GMAT math practice question] Is $$xy< -(\frac{x}{y})$$? $$1) xy<0$$ $$2) y<0$$ xy < -(x/y) can also be written as: xy + x/y < 0. So the question is asking whether sum of xy and x/y is negative or not. (1) xy < 0. This is only possible when x & y have opposite signs (one of them has to be positive, other has to be negative). But if x & y have opposite signs, then x/y will also be negative. So both xy and x/y are negative, hence their sum will also be negative. Sufficient. (2) y < 0. But nothing is given about x, we cannot deduce anything about xy or x/y. Not sufficient. Hence A answer Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6815 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is xy< -(x/y)? [#permalink] ### Show Tags 02 Feb 2018, 00:57 1 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question. Modifying the question: $$xy < -(\frac{x}{y})$$ $$⇔ xy^3 < -xy$$ (multiplying both sides by $$y^2$$) $$⇔ xy^3 + xy < 0$$ $$⇔ xy(y^2+1) < 0$$ $$⇔ xy < 0 since y^2+1 > 0$$ Condition 1): $$xy < 0$$ Condition 1) is same as the question. This condition is sufficient. Condition 2): Since this condition tells us nothing about $$x$$, it is not sufficient. Therefore, the answer is A. Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E. Answer: A _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Joined: 26 Mar 2013
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05 Feb 2018, 18:09
Is $$xy< -(\frac{x}{y})$$?

$$1) xy<0$$

It means that either x or y is negative......This makes the $$\frac{-x}{y}$$ always positive

The answer to the question is always YES

Sufficient

$$2) y<0$$

Let y = -1 & x = 1, It is same like case in statement 1......Answer is Yes

Let y = -1 & x =-1, $$(-1)(-1)< -(\frac{-1}{-1})$$......Answer is No

Insufficient

Is xy< -(x/y)? &nbs [#permalink] 05 Feb 2018, 18:09
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