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# If 0<2x+3y<50 and -50<3x+2y<0, then which of the following must be tr

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8167
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If 0<2x+3y<50 and -50<3x+2y<0, then which of the following must be tr  [#permalink]

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Updated on: 23 Nov 2017, 13:05
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55% (hard)

Question Stats:

53% (02:16) correct 47% (02:06) wrong based on 93 sessions

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[GMAT math practice question]
If $$0<2x+3y<50$$ and $$-50<3x+2y<0$$, then which of the following must be true?

I. $$x>0$$
II. $$y>0$$
III. $$x<y$$

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

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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 21 Nov 2017, 18:20. Last edited by MathRevolution on 23 Nov 2017, 13:05, edited 1 time in total. Intern Joined: 27 Apr 2015 Posts: 39 GMAT 1: 370 Q29 V13 Re: If 0<2x+3y<50 and -50<3x+2y<0, then which of the following must be tr [#permalink] ### Show Tags 17 Mar 2018, 10:11 4 MathRevolution wrote: [GMAT math practice question] If $$0<2x+3y<50$$ and $$-50<3x+2y<0$$, then which of the following must be true? I. $$x>0$$ II. $$y>0$$ III. $$x<y$$ A. I only B . II only C. III only D. I and III E. II, and III Given $$0<2x+3y<50$$ and $$-50<3x+2y<0$$ Since => $$0<2x+3y$$ and => $$3x+2y<0$$ Therefore => $$3x+2y<2x+3y$$ => OR $$3x-2x<3y-2y$$ => OR $$x<y$$ so satisfy III Now x,y =>both CANNOT be +ve since given $$3x+2y<0$$ and =>both CANNOT be -ve since given $$2x+3y>0$$ Therefore =>both are OPPOSITE sign =>AND Since $$x<y$$ THEREFORE $$x<0$$ AND $$y>0$$ so Satisfy II Option E Regards Dinesh Retired Moderator Joined: 25 Feb 2013 Posts: 1162 Location: India GPA: 3.82 If 0<2x+3y<50 and -50<3x+2y<0, then which of the following must be tr [#permalink] ### Show Tags Updated on: 23 Nov 2017, 21:28 1 MathRevolution wrote: [GMAT math practice question] If $$0<2x+3y<50$$ and $$-50<3x+2y<0$$, then which of the following must be true? I. $$x>0$$ II. $$y>0$$ III. $$x<y$$ A. I only B . II only C. III only D. I and III E. II and III $$0<2x+3y<50 => 2x+3y$$ is positive ---------(1) $$-50<3x+2y<0 =>3x+2y$$ is negative -----------(2) notice that by adding $$x-y$$ to equation (1) it becomes equation (2) i.e a negative value. so $$x-y<0 => x<y$$. Statement III must be true $$x$$ can be negative try values $$x=-1$$ & $$y=1$$. Statement I is not always true Statement II: As $$0<2x+3y<50$$ is positive and we have already derived that $$y>x$$, so if $$y$$ is negative then $$x$$ has to be negative which will mean that $$2x+3y<0$$ which is not possible. So we can say that $$y$$ must be positive. Statement II must be true. Option E Originally posted by niks18 on 22 Nov 2017, 09:50. Last edited by niks18 on 23 Nov 2017, 21:28, edited 2 times in total. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8167 GMAT 1: 760 Q51 V42 GPA: 3.82 If 0<2x+3y<50 and -50<3x+2y<0, then which of the following must be tr [#permalink] ### Show Tags Updated on: 23 Nov 2017, 13:09 => When we add the two inequalities $$0<2x+3y<50$$ and $$-50<3x+2y<0$$, we obtain $$-50<5x+5y<50$$, or $$-20<-2x-2y< 20$$. Statement I. Adding the two inequalities $$-50<3x+2y<0$$ and $$-20<-2x-2y< 20$$ yields $$-70<x<20$$. So x may not be greater than zero. Statement I may not be true. Statement II. By multiplying all sides of $$0<2x+3y<50$$ by $$-3$$, we have $$-150<-6x-9y< 0$$. By multiplying all sides of $$-50<3x+2y<0$$ by $$2$$, we have $$-100<6x+4y< 0$$. By adding the above inequalities, we have $$-250<-5y<0$$ or $$0<y<50$$. Statement II is true. Statement III. Since $$0<2x+3y<50$$ is equivalent to $$-50<-2x-3y<0$$ and $$-50<3x+2y<0$$, adding the two inequalities yields $$-100<x-y<0$$. This implies that $$x < y$$. Statement III must be true. Therefore, the answer is E. Answer : E _________________ 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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Originally posted by MathRevolution on 22 Nov 2017, 19:53.
Last edited by MathRevolution on 23 Nov 2017, 13:09, edited 1 time in total.
Retired Moderator
Joined: 25 Feb 2013
Posts: 1162
Location: India
GPA: 3.82
Re: If 0<2x+3y<50 and -50<3x+2y<0, then which of the following must be tr  [#permalink]

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23 Nov 2017, 11:26
MathRevolution wrote:
=>

When we add the two inequalities $$0<2x+3y<50$$ and $$-50<3x+2y<0$$, we obtain $$-50<5x+5y<50$$, or $$-20<-2x-2y< 20$$.

Statement I.
Adding the two inequalities $$-50<3x+2y<0$$ and $$-20<-2x-2y< 20$$ yields $$-70<x<20$$.
So x may not be greater than zero.
Statement I may not be true.

Statement II.
Adding the two inequalities $$0<2x+3y<50$$ and $$-20<-2x-2y< 20$$ yields $$-20<y<70$$.
So y may not be greater than zero.
Statement II may not be true, either.

Statement III.
Since $$0<2x+3y<50$$ is equivalent to $$-50<-2x-3y<0$$ and $$-50<3x+2y<0$$, adding the two inequalities yields
$$-100<x-y<0$$. This implies that $$x < y$$.
Statement III must be true.

Hi MathRevolution,

Need a clarity in Statement II.

if x & y both can be negative then how will they both satisfy $$0<2x+3y<50$$ and $$-50<3x+2y<0$$ simultaneously? Negative x & negative y will not satisfy the $$0<2x+3y<50$$
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8167
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If 0<2x+3y<50 and -50<3x+2y<0, then which of the following must be tr  [#permalink]

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23 Nov 2017, 13:10
niks18 wrote:
MathRevolution wrote:
=>

When we add the two inequalities $$0<2x+3y<50$$ and $$-50<3x+2y<0$$, we obtain $$-50<5x+5y<50$$, or $$-20<-2x-2y< 20$$.

Statement I.
Adding the two inequalities $$-50<3x+2y<0$$ and $$-20<-2x-2y< 20$$ yields $$-70<x<20$$.
So x may not be greater than zero.
Statement I may not be true.

Statement II.
Adding the two inequalities $$0<2x+3y<50$$ and $$-20<-2x-2y< 20$$ yields $$-20<y<70$$.
So y may not be greater than zero.
Statement II may not be true, either.

Statement III.
Since $$0<2x+3y<50$$ is equivalent to $$-50<-2x-3y<0$$ and $$-50<3x+2y<0$$, adding the two inequalities yields
$$-100<x-y<0$$. This implies that $$x < y$$.
Statement III must be true.

Hi MathRevolution,

Need a clarity in Statement II.

if x & y both can be negative then how will they both satisfy $$0<2x+3y<50$$ and $$-50<3x+2y<0$$ simultaneously? Negative x & negative y will not satisfy the $$0<2x+3y<50$$

Yes, you are right.
The solution is fixed. Please look at the above solution again.
_________________
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"
Retired Moderator
Joined: 25 Feb 2013
Posts: 1162
Location: India
GPA: 3.82
If 0<2x+3y<50 and -50<3x+2y<0, then which of the following must be tr  [#permalink]

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23 Nov 2017, 21:23
MathRevolution wrote:
niks18 wrote:
MathRevolution wrote:
=>

When we add the two inequalities $$0<2x+3y<50$$ and $$-50<3x+2y<0$$, we obtain $$-50<5x+5y<50$$, or $$-20<-2x-2y< 20$$.

Statement I.
Adding the two inequalities $$-50<3x+2y<0$$ and $$-20<-2x-2y< 20$$ yields $$-70<x<20$$.
So x may not be greater than zero.
Statement I may not be true.

Statement II.
Adding the two inequalities $$0<2x+3y<50$$ and $$-20<-2x-2y< 20$$ yields $$-20<y<70$$.
So y may not be greater than zero.
Statement II may not be true, either.

Statement III.
Since $$0<2x+3y<50$$ is equivalent to $$-50<-2x-3y<0$$ and $$-50<3x+2y<0$$, adding the two inequalities yields
$$-100<x-y<0$$. This implies that $$x < y$$.
Statement III must be true.

Hi MathRevolution,

Need a clarity in Statement II.

if x & y both can be negative then how will they both satisfy $$0<2x+3y<50$$ and $$-50<3x+2y<0$$ simultaneously? Negative x & negative y will not satisfy the $$0<2x+3y<50$$

Yes, you are right.
The solution is fixed. Please look at the above solution again.

Thanks MathRevolution for the reply and clarifying
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Re: If 0<2x+3y<50 and -50<3x+2y<0, then which of the following must be tr  [#permalink]

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Re: If 0<2x+3y<50 and -50<3x+2y<0, then which of the following must be tr   [#permalink] 24 Jul 2019, 07:12
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