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# Is x<1/y?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5296
GMAT 1: 800 Q59 V59
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24 Aug 2016, 19:21
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KUDOS
Expert's post
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Difficulty:

45% (medium)

Question Stats:

61% (00:52) correct 39% (00:45) wrong based on 153 sessions

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

*An answer will be posted in 2 days.
[Reveal] Spoiler: OA

_________________

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 $79 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 15 Sep 2011 Posts: 347 Location: United States WE: Corporate Finance (Manufacturing) Re: Is x<1/y? [#permalink] ### Show Tags 24 Aug 2016, 19:38 Top Contributor There is no information about x or y so nothing can be done to reduce the initial statement...at first. Statement 1: y>0, explains nothing about x. NSUF Statement 2: xy<1, x and y could be different signs or x and y could be fractions or a combination of the two. NSUF Statement 1 & 2: if y>0 and xy<1 then divide the equation by y and you have the statement. SUF Intern Joined: 27 Dec 2010 Posts: 4 Re: Is x<1/y? [#permalink] ### Show Tags 25 Aug 2016, 15:36 S1)$$y>0$$ Pick $$y=1$$ and $$x=2$$; =>$$2<\frac{1}{1}$$ =>No Pick $$y=2$$ and $$x=-2$$ =>$$-2<\frac{1}{2}$$ =>Yes So S1 is insufficient BCE S2)$$xy<1$$ Pick $$x=\frac{1}{2}$$ and $$y=\frac{1}{2}$$ =>$$\frac{1}{2}<2$$ => Yes Pick $$x=\frac{1}{2}$$ and $$y=\frac{-1}{2}$$ =>$$\frac{1}{2}<-2$$ =>No So S2 is insufficient (Note: This statement could be a trap if inequality in question stem is just cross multiplied without checking possible values that $$y$$ could take.) CE S1 and S2) Pick $$x=\frac{1}{2}$$ and $$y=\frac{1}{2}$$;This meets both the statements =>$$\frac{1}{2}<2$$ =>Yes Pick $$x=-2$$ and $$y=1$$; This meets both the statements => $$-2<\frac{1}{1}$$ =>Yes Here $$y>0$$ is satisfied from statement 1; both positive and negative values (integer and fraction as well) for $$x$$ are tried and that should cover all possible values for $$x$$ and the output is an YES in both the cases. Hence Statements 1 and 2 taken together is sufficient. Answer is C. (S1 says that $$y>0$$; So if $$y$$, which is greater than 0, is divided both sides of statement 2, then it will not change the sign of the inequality and we get $$x<\frac{1}{y}$$ which is exactly what the question stem is asking. Hence C) SVP Joined: 12 Sep 2015 Posts: 2325 Location: Canada Re: Is x<1/y? [#permalink] ### Show Tags 26 Aug 2016, 06:08 1 This post received KUDOS Expert's post Top Contributor 3 This post was BOOKMARKED MathRevolution wrote: Is x < 1/y? 1) y > 0 2) xy < 1 Target question: Is x < 1/y? Statement 1: y > 0 No information about x, so statement 1 is NOT SUFFICIENT Statement 2: xy < 1 IMPORTANT: some students will want to divide both sides by y to get x < 1/y, HOWEVER doing so is incorrect, because we don't know whether y is POSITIVE or NEGATIVE. If y is POSITIVE, then dividing both sides by y gives us x < 1/y If y is NEGATIVE, then dividing both sides by y gives us x > 1/y [when we divide both sides by a negative value, we must REVERSE the direction of the inequality] Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Statements 1 and 2 combined Statement 1 tells us that y is POSITIVE Statement 2 tells us that xy < 1 Since we know that y is POSITIVE, we can safely divide both sides by y to get the inequality x < 1/y. Since we can answer the target question with certainty, the combined statements are SUFFICIENT Answer = [Reveal] Spoiler: C RELATED VIDEO _________________ Brent Hanneson – Founder of gmatprepnow.com Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5296 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: Is x<1/y? [#permalink] ### Show Tags 27 Aug 2016, 05:21 If we modify the original condition and the question, in case of inequality, square is very important. If we multiply y^2 to both sides, we get xy^2<y?, xy^2-y<0?, y(xy-1)<0?. There are 2 variables (x and y) and there is a high chance that C is the correct answer. Using 1) & 2), the answer is always yes and the condition is sufficient. Thus, the correct answer is 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$79 for 3 month Online Course"
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12 Dec 2017, 12:28
$$x < 1/y$$ ?
Re-arranging,
=> $$x - (1/y) < 0$$ ?
=> $$(xy - 1)/y < 0$$ ?
For this term to be negative, ($$xy < 1$$ AND $$y > 0$$) OR ($$xy > 1$$ AND $$y < 0$$) ?
Question becomes => ($$xy < 1$$ AND $$y > 0$$) OR ($$xy > 1$$ AND $$y < 0$$) ?

Statement 1: $$y > 0$$, but we don't know if $$xy < 1$$ => InSufficient
Statement 2: $$xy < 1$$, but we don't know if $$y > 0$$ => InSufficient

Statement 1 + 2: $$y > 0$$ AND $$xy < 1$$ => Answers our question

Is x<1/y?   [#permalink] 12 Dec 2017, 12:28
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