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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: 6390
GMAT 1: 760 Q51 V42
GPA: 3.82
1/x > 1/y? 1) x < y 2) xy > 0  [#permalink]

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01 Nov 2017, 01:56
00:00

Difficulty:

55% (hard)

Question Stats:

55% (01:16) correct 45% (01:12) wrong based on 69 sessions

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[GMAT math practice question]

1/x > 1/y?

1) x < y
2) xy > 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 $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" PS Forum Moderator Joined: 25 Feb 2013 Posts: 1216 Location: India GPA: 3.82 1/x > 1/y? 1) x < y 2) xy > 0 [#permalink] ### Show Tags 01 Nov 2017, 02:28 1 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 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6390 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: 1/x > 1/y? 1) x < y 2) xy > 0 [#permalink] ### Show Tags 04 Nov 2017, 18:16 1 => 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. Answer: C _________________ 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$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
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Joined: 02 Apr 2014
Posts: 471
GMAT 1: 700 Q50 V34
Re: 1/x > 1/y? 1) x < y 2) xy > 0  [#permalink]

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10 Dec 2017, 12:08
$$1/x > 1/y$$ ?

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

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

($$y > x$$ 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

Re: 1/x > 1/y? 1) x < y 2) xy > 0 &nbs [#permalink] 10 Dec 2017, 12:08
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