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# Is xy< -(x/y)?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4898
GPA: 3.82

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31 Jan 2018, 01:50
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Difficulty:

35% (medium)

Question Stats:

76% (00:58) correct 24% (00:52) wrong based on 50 sessions

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[GMAT math practice question]

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

$$1) xy<0$$
$$2) y<0$$
[Reveal] Spoiler: OA

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Manager
Joined: 30 Dec 2016
Posts: 127

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31 Jan 2018, 02:07
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KUDOS
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

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SandySilva

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DS Forum Moderator
Joined: 21 Aug 2013
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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.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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02 Feb 2018, 00:57
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Expert's post
=>

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.

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.
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VP
Joined: 26 Mar 2013
Posts: 1431

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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)?   [#permalink] 05 Feb 2018, 18:09
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