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# M61-07

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6027
GMAT 1: 760 Q51 V42
GPA: 3.82

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18 Jun 2018, 01:25
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Question Stats:

50% (01:09) correct 50% (02:59) wrong based on 4 sessions

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If $$0 < 2x + 3y < 10$$ and $$-10 < 3x+2y < 0$$, then which of the following must be true?

I. $$x < 0$$

II. $$y < 0$$

III. $$x < y$$

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

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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" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6027 GMAT 1: 760 Q51 V42 GPA: 3.82 M61-07 [#permalink] ### Show Tags Updated on: 05 Aug 2018, 23:05 Official Solution: If $$0 < 2x + 3y < 10$$ and $$-10 < 3x+2y < 0$$, then which of the following must be true? I. $$x < 0$$ II. $$y < 0$$ III. $$x < y$$ A. I only B. II only C. I and II only D. I and III only E. I, II, and III Label the inequalities as follows: $$0 < 2x+3y < 10$$ --- (1) $$-10 < 3x+2y < 0$$ --- (2) We consider each statement individually. Statement I: Multiplying (1) by -2 yields $$-20 < -4x – 6y < 0$$, and multiplying (2) by 3 yields $$-30 < 9x + 6y < 0$$. Adding these inequalities gives $$-50 < 5x < 0$$ or $$-10 < x < 0$$. This statement is true. Statement II: Multiplying (1) by 3 yields $$0 < 6x + 9y < 30$$, and multiplying (2) by -2 yields $$0 < -6x – 4y < 20$$. Adding these inequalities gives $$0 < 5y < 50$$ or $$0 < y < 10$$. This statement is false. Statement III: Multiplying (1) by – 1 yields $$-10 < -2x – 3y < 0$$. Adding this to inequality (2) yields $$-20 < x – y < 0$$. This implies that $$x < y$$, and statement III is true. Answer: D _________________ 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"

Originally posted by MathRevolution on 18 Jun 2018, 01:26.
Last edited by MathRevolution on 05 Aug 2018, 23:05, edited 1 time in total.
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Joined: 14 Jul 2018
Posts: 2

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01 Aug 2018, 04:16
Must do before exam. It teaches a lot of concepts. This is an easy question. If someone has command over inequalities can surely do it correctly.
Re: M61-07 &nbs [#permalink] 01 Aug 2018, 04:16
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# M61-07

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