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# If xy ≠ 0, is x/y < 0 ?

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Math Expert
Joined: 02 Sep 2009
Posts: 58381
If xy ≠ 0, is x/y < 0 ?  [#permalink]

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31 Dec 2017, 12:14
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Difficulty:

25% (medium)

Question Stats:

79% (01:21) correct 21% (02:04) wrong based on 68 sessions

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If xy ≠ 0, is x/y < 0 ?

(1) x^2/y^2 > 0

(2) x^2/y^3 > 0

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Re: If xy ≠ 0, is x/y < 0 ?  [#permalink]

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31 Dec 2017, 14:07
1
Bunuel wrote:
If xy ≠ 0, is x/y < 0 ?

(1) x^2/y^2 > 0

(2) x^2/y^3 > 0

We're asked if x and y have different signs so we'll look for an answer that gives us this information.
This is a Logical approach.

(1) Since the square of a non-zero number is always positive, then (1) is always true and gives us no information.
Insufficient!

(2) Since x^2 is always positive then y^3 must also be positive meaning that y is positive.
But, without knowledge of x, we cannot know if x/y < 0 or not.
Insufficient!

Combined, we know that y is positive but still have no information on x.
Insufficient!

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Re: If xy ≠ 0, is x/y < 0 ?  [#permalink]

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20 Jan 2018, 22:57
Bunuel wrote:
If xy ≠ 0, is x/y < 0 ?

(1) x^2/y^2 > 0

(2) x^2/y^3 > 0

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.

Since we have 2 variables and 0 equations, E is most likely to be the answer. So, we should consider 1) & 2) first.

Conditions 1) & 2):

Case 1: x = 1, y = -1
x/y < 0 : Yes

Case 2: x = -1, y = -1
x/y > 0 : No

Both conditions together are 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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Re: If xy ≠ 0, is x/y < 0 ?   [#permalink] 20 Jan 2018, 22:57
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