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# 1/x > 1/y? 1) x < y 2) xy > 0

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4460

Kudos [?]: 3141 [0], given: 0

GPA: 3.82
1/x > 1/y? 1) x < y 2) xy > 0 [#permalink]

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01 Nov 2017, 00:56
00:00

Difficulty:

55% (hard)

Question Stats:

55% (00:55) correct 45% (00:44) wrong based on 44 sessions

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[GMAT math practice question]

1/x > 1/y?

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

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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Kudos [?]: 3141 [0], given: 0

Director
Joined: 25 Feb 2013
Posts: 619

Kudos [?]: 304 [1], given: 39

Location: India
GPA: 3.82
1/x > 1/y? 1) x < y 2) xy > 0 [#permalink]

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01 Nov 2017, 01:28
1
KUDOS
MathRevolution wrote:
[GMAT math practice question]

1/x > 1/y?

1) x < y
2) xy > 0

$$\frac{1}{x} > \frac{1}{y}.$$ this is only possible when $$y>x$$ or $$x>0$$ and $$y<0$$

Statement 1: this provides one condition i.e $$y>x$$ but the other condition is not mentioned. Insufficient

Statement 2: this implies that either $$x>0$$ & $$y>0$$ or $$x<0$$ & $$y<0$$. non of the required condition can be arrived at. Insufficient

Combining 1 & 2 we know that $$y>x$$ and both $$x$$ & $$y$$ have the same sign, so $$x>0$$ & $$y<0$$ is not possible. Hence Sufficient

Option C

Kudos [?]: 304 [1], given: 39

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4460

Kudos [?]: 3141 [1], given: 0

GPA: 3.82
Re: 1/x > 1/y? 1) x < y 2) xy > 0 [#permalink]

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04 Nov 2017, 17:16
1
KUDOS
Expert's post
=>

Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.

When we modify the question, we can multiply both sides of the inequality by x^2y^2, we have x(y^2)>x^2y? or xy(y-x)>0. Condition 1) states y – x > 0 and condition 2) states xy > 0.

Thus, C is the answer as expected.

Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore, C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer, hence using 1) and 2) together. (It saves us time). Obviously, there may be cases where the answer is A, B, D or E.

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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Kudos [?]: 3141 [1], given: 0

Senior Manager
Joined: 02 Apr 2014
Posts: 255

Kudos [?]: 17 [0], given: 457

Re: 1/x > 1/y? 1) x < y 2) xy > 0 [#permalink]

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10 Dec 2017, 11:08
$$1/x > 1/y$$ ?

$$1/x - 1/y > 0$$ ?

$$(y - x)/ xy > 0$$?

($$y > x$$ AND $$xy > 0$$) OR ($$y < x$$ AND $$xy < 0$$) ?

Statement 1:
$$x < y$$, but we don't know if $$xy > 0$$ -> InSuff

Statement 2:
$$xy > 0$$, but we don't know if $$y > x$$ -> InSuff

(1)+(2) => $$y > x$$ AND $$xy > 0,$$ aligns with our question, sufficient

Kudos [?]: 17 [0], given: 457

Re: 1/x > 1/y? 1) x < y 2) xy > 0   [#permalink] 10 Dec 2017, 11:08
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