Author 
Message 
TAGS:

Hide Tags

Director
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 554
Location: Bangladesh
Concentration: Finance, Leadership
GPA: 2.81
WE: Business Development (Real Estate)

If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ? [#permalink]
Show Tags
Updated on: 12 Aug 2017, 08:52
Question Stats:
42% (01:25) correct 58% (01:36) wrong based on 227 sessions
HideShow timer Statistics
If \(x<0\) and \(0 < \frac{x}{y} + 1<1\), which of the following must be true ? I. \(y > 0\) II. \(\frac{x}{y}>1\) III. \(\frac{1}{x}+\frac{1}{y}<0\) A. I only B. I and II only C. I and III only D. II and III only E. I, II and III
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Md. Abdur Rakib
Please Press +1 Kudos,If it helps Sentence CorrectionCollection of Ron Purewal's "elliptical construction/analogies" for SC Challenges
Originally posted by AbdurRakib on 06 May 2017, 01:26.
Last edited by Mahmud6 on 12 Aug 2017, 08:52, edited 2 times in total.
Edited the question.



Intern
Joined: 29 Apr 2017
Posts: 30
Location: India
Concentration: General Management, Other
WE: Engineering (Computer Software)

Re: If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ? [#permalink]
Show Tags
06 May 2017, 02:11
AbdurRakib wrote: If x<0 and 0 < \(\frac{x}{y}\) + 1<1 ,which of the following must be true ?
I. y > 0
II. \(\frac{x}{y}\)>1
III. \(\frac{1}{x}\)+\(\frac{1}{y}\)<0
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I,II and III IMO, (D) should be the answer. If statement I is true, then y > 0. Let us choose y = 1. And it is given that, x<0 and 0 < \(\frac{x}{y}\) + 1<1 Putting y = 1, and taking any value of x < 0 (say, x = 1) , we find that, \(\frac{x}{y}\) + 1 = 0. Now it is NOT given that 0 <= \(\frac{x}{y}\) + 1<1, but 0 < \(\frac{x}{y}\) + 1<1. Therefore statement I cannot be true. Only option (D) is present which does not contain statement I. So, IMO (D) is the answer. If you like my post, please encourage by giving KUDOS.



Intern
Joined: 29 Apr 2017
Posts: 16

Re: If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ? [#permalink]
Show Tags
06 May 2017, 04:40
moutikli wrote: AbdurRakib wrote: If x<0 and 0 < \(\frac{x}{y}\) + 1<1 ,which of the following must be true ?
I. y > 0
II. \(\frac{x}{y}\)>1
III. \(\frac{1}{x}\)+\(\frac{1}{y}\)<0
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I,II and III IMO, (D) should be the answer. If statement I is true, then y > 0. Let us choose y = 1. And it is given that, x<0 and 0 < \(\frac{x}{y}\) + 1<1 Putting y = 1, and taking any value of x < 0 (say, x = 1) , we find that, \(\frac{x}{y}\) + 1 = 0. Now it is NOT given that 0 <= \(\frac{x}{y}\) + 1<1, but 0 < \(\frac{x}{y}\) + 1<1. Therefore statement I cannot be true. Only option (D) is present which does not contain statement I. So, IMO (D) is the answer. If you like my post, please encourage by giving KUDOS. Hello If we simplify the given equation 0<x/y +1 < 1 It equals 0<x+y < y Which implies y>0 Hence I is true Is this correct? Or am i doing something wrong Thanks Sent from my SMN9200 using GMAT Club Forum mobile app



Intern
Joined: 23 Apr 2017
Posts: 21
Location: India
WE: Marketing (Manufacturing)

Re: If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ? [#permalink]
Show Tags
06 May 2017, 06:54
IMO the answer is E 0<x/y +1<1 1<x/y<0 As x<0 and x/y <0 Y must be positive As mod value of x/y lesser than 1, mod value of y is greater than mod value of x So mod value of 1/x is greater than mod value of 1/y x < 0, so 1/x < 0 As 1/x >1/y 1/x+1/y<0 So all the conditions are correct Ans E Sent from my BLNL22 using GMAT Club Forum mobile app



Math Expert
Joined: 02 Sep 2009
Posts: 46215

Re: If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ? [#permalink]
Show Tags
06 May 2017, 10:00



Manager
Joined: 11 Sep 2016
Posts: 61
Location: India
GPA: 3
WE: Sales (Manufacturing)

Re: If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ? [#permalink]
Show Tags
13 May 2017, 23:57
Bunuel Please let me know whether my method of deriving III as true is valid ? From the question stem we know that x<0 and and \(\frac{x}{y}\) lies between 0 and 1 i.e. 1<\(\frac{x}{y}\)<0 Hence we necessarily have to have y>0 Multiplying Y on both sides (without changing signs because y>0) \(x>y\) result 1 Given in III is \(\frac{1}{x}+\frac{1}{y}<0\) Therefore, \(\frac{1}{x}<\frac{1}{y}\) Taking resiprocals \(\frac{x}{1}\)>\(\frac{y}{1}\) Hence \(x >y\) result 2 result 1 and result 2 are the same Hence III is correct



Math Expert
Joined: 02 Sep 2009
Posts: 46215

Re: If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ? [#permalink]
Show Tags
14 May 2017, 01:43



Manager
Joined: 11 Sep 2016
Posts: 61
Location: India
GPA: 3
WE: Sales (Manufacturing)

Re: If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ? [#permalink]
Show Tags
14 May 2017, 04:01
Bunuel wrote: KM2018AA wrote: Bunuel Please let me know whether my method of deriving III as true is valid ? From the question stem we know that x<0 and and \(\frac{x}{y}\) lies between 0 and 1 i.e. 1<\(\frac{x}{y}\)<0 Hence we necessarily have to have y>0 Multiplying Y on both sides (without changing signs because y>0) \(x>y\) result 1 Given in III is \(\frac{1}{x}+\frac{1}{y}<0\) Therefore, \(\frac{1}{x}<\frac{1}{y}\) Taking resiprocals
\(\frac{x}{1}\)>\(\frac{y}{1}\)Hence \(x >y\) result 2 result 1 and result 2 are the same Hence III is correct Your solution missing steps. In the highlighted part, do you know the sign of y? How? If not then you cannot do that. So then what is the rule with taking reciprocals in inequalities? (if any)



Math Expert
Joined: 02 Sep 2009
Posts: 46215

Re: If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ? [#permalink]
Show Tags
14 May 2017, 05:36



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2758
Location: United States (CA)

Re: If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ? [#permalink]
Show Tags
18 May 2017, 20:02
AbdurRakib wrote: If \(x<0\) and \(0 < \frac{x}{y} + 1<1\), which of the following must be true ?
I. \(y > 0\)
II. \(\frac{x}{y}>1\)
III. \(\frac{1}{x}+\frac{1}{y}<0\)
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I,II and III We can simplify the given inequality: 0 < x/y + 1 < 1 1 < x/y < 0 Since x is negative, y must be positive. Let’s now analyze our Roman numeral answer choices: I. y > 0 Since we’ve mentioned y must be positive, Roman numeral I is correct. II. x/y > 1 Since 1 < x/y < 0 also means that x/y > 1, Roman numeral II is correct. III. 1/x + 1/y < 0 We can multiply both sides of the inequality by x to obtain: 1 + x/y > 0 Notice that we switch the inequality sign since x is negative. Now let’s subtract 1 from both sides: x/y > 1 Roman numeral III is correct also. Answer: E
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Manager
Joined: 14 Dec 2017
Posts: 171

Re: If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ? [#permalink]
Show Tags
16 Jun 2018, 12:31
AbdurRakib wrote: If \(x<0\) and \(0 < \frac{x}{y} + 1<1\), which of the following must be true ?
I. \(y > 0\)
II. \(\frac{x}{y}>1\)
III. \(\frac{1}{x}+\frac{1}{y}<0\)
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III Given \(x<0\) .............(i) & \(0 < \frac{x}{y} + 1<1\)......(ii) can be simplified as, \(1 < \frac{x}{y} < 0\) ................(iii) I. \(y > 0\)  from (iii), we can say since \(x<0\), \(y>0\) is true II. \(\frac{x}{y}>1\)  from (iii), we can say this is true III. \(\frac{1}{x}+\frac{1}{y}<0\)  multiply (ii) with \(\frac{1}{x}\) & since \(x<0\), we need to flip the signs. Hence III is also true. Answer E. Thanks, GyM




Re: If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ?
[#permalink]
16 Jun 2018, 12:31






