GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Jan 2019, 18:08

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### $450 Tuition Credit & Official CAT Packs FREE January 15, 2019 January 15, 2019 10:00 PM PST 11:00 PM PST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### The winning strategy for a high GRE score January 17, 2019 January 17, 2019 08:00 AM PST 09:00 AM PST Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL. # If 0<2x+3y<50 and -50<3x+2y<0, then which of the following must be tr  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6799 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, 12:05 3 4 00:00 Difficulty: 55% (hard) Question Stats: 50% (02:19) correct 50% (02:08) wrong based on 98 sessions ### HideShow timer Statistics [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 _________________ 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$149 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 21 Nov 2017, 17:20.
Last edited by MathRevolution on 23 Nov 2017, 12:05, edited 1 time in total.
Retired Moderator
Joined: 25 Feb 2013
Posts: 1220
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, 20:28
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, 08:50.
Last edited by niks18 on 23 Nov 2017, 20:28, edited 2 times in total.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6799
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, 12:09
=>

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.

_________________

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 $149 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 22 Nov 2017, 18:53. Last edited by MathRevolution on 23 Nov 2017, 12:09, edited 1 time in total. Retired Moderator Joined: 25 Feb 2013 Posts: 1220 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] ### Show Tags 23 Nov 2017, 10:26 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. Therefore, the answer is C. Answer : C 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: 6799 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] ### Show Tags 23 Nov 2017, 12:10 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. Therefore, the answer is C. Answer : C 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$149 for 3 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: 1220
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

23 Nov 2017, 20:23
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
Intern
Joined: 27 Apr 2015
Posts: 41
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, 09:11
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

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
Re: If 0<2x+3y<50 and -50<3x+2y<0, then which of the following must be tr &nbs [#permalink] 17 Mar 2018, 09:11
Display posts from previous: Sort by