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Is x>x/y?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8005
GMAT 1: 760 Q51 V42
GPA: 3.82

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25 Sep 2018, 03:40
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Difficulty:

55% (hard)

Question Stats:

58% (01:31) correct 42% (01:34) wrong based on 52 sessions

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[Math Revolution GMAT math practice question]

$$Is x>\frac{x}{y}?$$

$$1) y>1$$
$$2) xy>0$$

_________________
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 $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 24 Dec 2017 Posts: 185 Location: India Concentration: Strategy, Real Estate Schools: Johnson '21 Re: Is x>x/y? [#permalink] Show Tags 25 Sep 2018, 04:26 Here is my take on this question x > x/y St 1: y >1 No information about x Case 1: x=2, y=2 2>2/2 2>1 (Yes) Case 2: x=-2, y=2 -2>-2/2 -2<-1 (No) AD/BCE St 2: xy>0 Case 1: x=2, y=2 2>2/2 2>1 (Yes) Case 2: x=-1,y=-2 -1>-1/-2 -1<1/2 (No) Hence Insufficient BCE St 1 + St2: y>1 and xy>0 so x and y have to be positive. So x will be always greater than x/y. Hence C is the answer Manager Joined: 01 Nov 2017 Posts: 95 GMAT 1: 700 Q50 V35 GMAT 2: 640 Q49 V28 GMAT 3: 680 Q47 V36 GMAT 4: 700 Q50 V35 GPA: 3.84 Re: Is x>x/y? [#permalink] Show Tags 25 Sep 2018, 06:47 Change the original condition x>x/y => x - x/y > 0 => x(1 - 1/y) > 0 (1) y > 1 -> we don't know anything about x so INSUFFICIENT (2) xy > 0, so we knkow x and y have same signs. Looking at the inequality we can for sure say that there must be cases when inequality is less than 0 for both positive or both negative x and y, and there must be cases when inequality is larger than 0 for both positive or both negative x and y. -> As both less and larger than 0 case happen, this option is insufficient. (1) (2) together, looking at 1 - 1/y, obviously as y is larger than 1, 1 - 1/y is always positive. Plus we have x is positive too as xy >0 -> Sufficient C is the answer Plz let rain the kudosssss GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 935 Re: Is x>x/y? [#permalink] Show Tags 25 Sep 2018, 09:13 MathRevolution wrote: [Math Revolution GMAT math practice question] Is $$x>\frac{x}{y}?$$ $$1) y>1$$ $$2) xy>0$$ $$x\,\,\mathop > \limits^? \,\,\frac{x}{y}$$ $$\left( 1 \right)\,\,\,y > 1\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,\left( {0,2} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \,\, \hfill \\ \,{\text{Take}}\,\,\left( {1,2} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \,\, \hfill \\ \end{gathered} \right.$$ $$\left( 2 \right)\,\,\,xy > 0\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,\left( {1,2} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\ \,{\text{Take}}\,\,\left( {1,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \,\,\,\, \hfill \\ \end{gathered} \right.$$ $$\left( {1 + 2} \right)\,\,\,\, \Rightarrow \,\,\,\,x,y\,\, > 0\,\,\,$$ $$x\,\,\mathop > \limits^? \,\,\frac{x}{y}\,\,\,\,\,\mathop \Leftrightarrow \limits^{:\,\,x\,\, > \,\,0} \,\,\,\,1\,\,\mathop > \limits^? \,\,\,\frac{1}{y}\,\,\,\,\,\mathop \Leftrightarrow \limits^{ \cdot \,\,y\,\, > \,\,0} \,\,\,\,y\,\,\mathop > \limits^? \,\,\,1\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle$$ The correct answer is therefore (C). This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8005 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is x>x/y? [#permalink] Show Tags 27 Sep 2018, 00:53 => 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. We then recheck the question. The question $$x>\frac{x}{y}$$ is equivalent to $$xy(y-1) > 0$$ as shown below: $$x>\frac{x}{y}$$ $$=> xy^2 > xy$$ since $$y^2 > 0$$ $$=> xy^2 – xy > 0$$ $$=> xy(y – 1) > 0$$ Condition 1) tells us that $$y – 1 > 0$$, and condition 2) tells us that $$xy > 0$$. Thus, both conditions together are sufficient. Therefore, C is the answer. _________________ 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 1 month Online Course"
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Re: Is x>x/y?   [#permalink] 27 Sep 2018, 00:53
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