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# If x > y >0, a < 0 and b > 0, then which of the following is (are) tru

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8005
GMAT 1: 760 Q51 V42
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If x > y >0, a < 0 and b > 0, then which of the following is (are) tru  [#permalink]

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Updated on: 09 Apr 2018, 23:19
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Difficulty:

15% (low)

Question Stats:

81% (01:35) correct 19% (02:27) wrong based on 61 sessions

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[GMAT math practice question]

If $$x > y >0, a < 0$$ and $$b > 0$$, then which of the following is (are) true?

Ⅰ. $$ax+by > 0$$
Ⅱ. $$ax-by > 0$$
Ⅲ. $$by-ax > 0$$

A. Ⅰonly
B. Ⅱ only
C. Ⅲ only
D.Ⅰ& Ⅱ only
E. Ⅱ & Ⅲ only

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"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" Originally posted by MathRevolution on 05 Apr 2018, 04:36. Last edited by MathRevolution on 09 Apr 2018, 23:19, edited 2 times in total. Senior PS Moderator Status: It always seems impossible until it's done. Joined: 16 Sep 2016 Posts: 737 GMAT 1: 740 Q50 V40 GMAT 2: 770 Q51 V42 Re: If x > y >0, a < 0 and b > 0, then which of the following is (are) tru [#permalink] ### Show Tags 05 Apr 2018, 05:56 1 ...which of the following is (are) positive you mean? Best, Gladi _________________ Regards, Gladi “Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back) Retired Moderator Joined: 27 Oct 2017 Posts: 1256 Location: India Concentration: International Business, General Management GPA: 3.64 WE: Business Development (Energy and Utilities) Re: If x > y >0, a < 0 and b > 0, then which of the following is (are) tru [#permalink] ### Show Tags 05 Apr 2018, 06:34 Please recheck your question. It seems the question asks if the following is positive? 1)ax +by. Here ax is negative but we don't know the value of b. Hence it is not possible to define if ax+by is positive or not. 2)ax-by. Here ax is negative and by is positive. So ax-by is negative. 3) by-ax Here by is positive and ax is negative. Hence by -ax = positive. Answer C, only III gives positive value. MathRevolution wrote: [GMAT math practice question] If $$x > y >0, a < 0$$ and $$b > 0$$, then which of the following is (are) true? Ⅰ. $$ax+by$$ Ⅱ.$$ax-by$$ Ⅲ. $$by-ax$$ A. Ⅰonly B. Ⅱ only C. Ⅲ only D.Ⅰ& Ⅱ only E. Ⅱ & Ⅲ only _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8005 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x > y >0, a < 0 and b > 0, then which of the following is (are) tru [#permalink] ### Show Tags 08 Apr 2018, 18:14 => Statement I. $$x = 2, y = 1, a = -1, b = 1$$: False Statement II. $$x = 2, y = 1, a = -1, b = 1$$: False Statement III. Since $$a < 0$$ and $$x > 0, -ax > 0.$$ And by $$> 0$$ since $$b > 0$$ and $$y > 0$$. $$by – ax = by + (-ax) > 0$$. True Therefore, C is the answer. 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$79 for 1 month Online Course"
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Retired Moderator
Joined: 27 Oct 2017
Posts: 1256
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: If x > y >0, a < 0 and b > 0, then which of the following is (are) tru  [#permalink]

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08 Apr 2018, 19:02
Kindly revise the question.
"Positive" is missing in question stem.

Regards

MathRevolution wrote:
=>

Statement I.
$$x = 2, y = 1, a = -1, b = 1$$: False

Statement II.
$$x = 2, y = 1, a = -1, b = 1$$: False

Statement III.
Since $$a < 0$$ and $$x > 0, -ax > 0.$$ And by $$> 0$$ since $$b > 0$$ and $$y > 0$$.
$$by – ax = by + (-ax) > 0$$. True

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Re: If x > y >0, a < 0 and b > 0, then which of the following is (are) tru   [#permalink] 08 Apr 2018, 19:02
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