Last visit was: 20 Jun 2024, 02:19 It is currently 20 Jun 2024, 02:19
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 93832
Own Kudos [?]: 633252 [78]
Given Kudos: 82387
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6808
Own Kudos [?]: 30592 [21]
Given Kudos: 799
CEO
Joined: 26 Feb 2016
Posts: 2867
Own Kudos [?]: 5265 [13]
Given Kudos: 47
Location: India
GPA: 3.12
General Discussion
examPAL Representative
Joined: 07 Dec 2017
Posts: 1048
Own Kudos [?]: 1793 [8]
Given Kudos: 26
Re: Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 [#permalink]
3
Kudos
5
Bookmarks
Bunuel wrote:
Is $$\frac{x + 1}{y + 1} > \frac{x}{y}$$?

(1) $$0 < x < y$$

(2) $$xy > 0$$

NEW question from GMAT® Official Guide 2019

(DS09315)

We'll simplify the inequalities so we understand what we need to do.
This is a Precise approach.

(1) Multiplying both sides by y(y+1) (note that both are positive), gives yx+y > yx+x and cancelling out yx gives y > x.
This is exactly what we're told in our statement!
Sufficient.

(2) If y(y+1) is positive we can repeat the same process as above to get y > x, but since all we know is that both x,y are positive or both are negative but do not know which is larger we cannot answer.
If y(y+1) is negative we'll get the expression y < x, but, for the same reason as above, we still cannot answer.
Insufficient

Originally posted by DavidTutorexamPAL on 24 Jun 2018, 11:50.
Last edited by DavidTutorexamPAL on 24 Jun 2018, 11:59, edited 2 times in total.
Intern
Joined: 01 May 2017
Posts: 28
Own Kudos [?]: 47 [0]
Given Kudos: 40
Re: Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 [#permalink]
Dear Bunuel DavidTutorexamPAL GMATPrepNow pushpitkc

How can we cross multiply in this question, when we are not aware of the signs of x and y?

Warm Regards,
FANJ
examPAL Representative
Joined: 07 Dec 2017
Posts: 1048
Own Kudos [?]: 1793 [0]
Given Kudos: 26
Re: Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 [#permalink]
FANewJersey wrote:
Dear Bunuel DavidTutorexamPAL GMATPrepNow pushpitkc

How can we cross multiply in this question, when we are not aware of the signs of x and y?

Warm Regards,
FANJ
Hey FANewJersey, good question! In 1) we do know the sign: we are told that 0 < x < y - this means they are both bigger than 0 - they are positive!
Intern
Joined: 01 May 2017
Posts: 28
Own Kudos [?]: 47 [0]
Given Kudos: 40
Re: Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 [#permalink]
Hi DavidTutorexamPAL,
So basically you are reading ahead to get an idea and then applying something from the statements to firm up your stem question (is x less than y). Correct?
Warmly,
FANJ

DavidTutorexamPAL wrote:
FANewJersey wrote:
Dear Bunuel DavidTutorexamPAL GMATPrepNow pushpitkc

How can we cross multiply in this question, when we are not aware of the signs of x and y?

Warm Regards,
FANJ
Hey FANewJersey, good question! In 1) we do know the sign: we are told that 0 < x < y - this means they are both bigger than 0 - they are positive!
examPAL Representative
Joined: 07 Dec 2017
Posts: 1048
Own Kudos [?]: 1793 [2]
Given Kudos: 26
Re: Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 [#permalink]
1
Bookmarks
FANewJersey wrote:
Hi DavidTutorexamPAL,
So basically you are reading ahead to get an idea and then applying something from the statements to firm up your stem question (is x less than y). Correct?
Warmly,
FANJ

DavidTutorexamPAL wrote:
FANewJersey wrote:
Dear Bunuel DavidTutorexamPAL GMATPrepNow pushpitkc

How can we cross multiply in this question, when we are not aware of the signs of x and y?

Warm Regards,
FANJ
Hey FANewJersey, good question! In 1) we do know the sign: we are told that 0 < x < y - this means they are both bigger than 0 - they are positive!

You could say that, I suppose... I don't think of it as "reading ahead" since solving with statement (1) is the first thing we are supposed to try and do anyway. The question stem on its own isn't going to give us the answer....
Intern
Joined: 01 May 2017
Posts: 28
Own Kudos [?]: 47 [0]
Given Kudos: 40
Re: Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 [#permalink]
Thanks DavidTutorexamPAL, But we will have to nail down a goal, which we drive from the stem question (value vs. Yes/No, what is being asked etc. etc.). But I believe I got the idea here. Thanks
Intern
Joined: 14 Dec 2017
Posts: 2
Own Kudos [?]: 4 [4]
Given Kudos: 78
Re: Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 [#permalink]
3
Kudos
1
Bookmarks
Bunuel wrote:
Is $$\frac{x + 1}{y + 1} > \frac{x}{y}$$?

(1) $$0 < x < y$$

(2) $$xy > 0$$

NEW question from GMAT® Official Guide 2019

(DS09315)

SIMPLIFY THE EQUATION QUESTION:
(X+1)/(Y+1) > X/Y
Y(X+1) > X(Y+1)
XY+Y>XY+X (cancel out "XY" from both sides of the inequality)
Y>X

RESTATING THE QUESTION: IS Y>X?
STATEMENT 1: $$0 < x < y$$
YES. SUFFICIENT

STATEMENT 2 : $$xy > 0$$
This statement leaves 2 variables unknown.
Therefore, it could be a YES or a NO case. IN-SUFFICIENT
Intern
Joined: 30 Mar 2018
Posts: 30
Own Kudos [?]: 25 [0]
Given Kudos: 116
Location: United Kingdom
GMAT 1: 660 Q42 V38
GPA: 4
Re: Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 [#permalink]
BrentGMATPrepNow wrote:
Bunuel wrote:
Is $$\frac{x + 1}{y + 1} > \frac{x}{y}$$?

(1) $$0 < x < y$$

(2) $$xy > 0$$

Target question: Is (x+1)/(y+1) > x/y ?

Statement 1: 0 < x < y
This tells us that y is POSITIVE, which means y+1 is also POSITIVE.
This means we can safely take the inequality (x+1)/(y+1) > x/y and safely multiply both sides by y
When we do so, we get: (y)(x+1)/(y+1) > x
We can also multiply both sides by y+1 to get: (y)(x+1) > (x)(y+1)
Expand to get: xy + y > xy + x
Subtract xy from both sides to get: y > x
So, with the help of statement 1, our original target question Is (x+1)/(y+1) > x/y ? becomes Is y > x ?
Since statement 1 tells us that y > x, the answer to the target question is a definitive YES
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: xy > 0
Let's TEST some values
There are several values of x and y that satisfy statement 2 (xy > 0). Here are two:
Case a: x = 1 and y = 1. In this case, (x+1)/(y+1) = (1+1)/(1+1) = 2/2 = 1, and x/y = 1/1 = 1. So, the answer to the target question is NO, (x+1)/(y+1) is NOT greater than x/y ?
Case b: x = -3 and y = -2. In this case, (x+1)/(y+1) = (-3 +1)/(-2 +1) = -2/-1 = 2, and x/y = -3/-2 = 3/2. So, the answer to the target question is YES, (x+1)/(y+1) IS greater than x/y ?
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

RELATED VIDEO FROM OUR COURSE

Hi BrentGMATPrepNow
Why do we need to make sure that x and y are positive before we simplify the inequality? Couldn't we simplify the inequality first and then change the truth of the inequality if we find out that x or y are negative?

i.e. can we not just simplify the question stem to say: "is y>x?" before being given the information in (1)?

Thanks
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6808
Own Kudos [?]: 30592 [1]
Given Kudos: 799
Re: Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 [#permalink]
1
Kudos
Top Contributor
silverprince wrote:

Hi BrentGMATPrepNow
Why do we need to make sure that x and y are positive before we simplify the inequality? Couldn't we simplify the inequality first and then change the truth of the inequality if we find out that x or y are negative?

i.e. can we not just simplify the question stem to say: "is y>x?" before being given the information in (1)?

Thanks

Hi silverprince,

Can you show me what you mean?

Cheers,
Brent
Intern
Joined: 30 Mar 2018
Posts: 30
Own Kudos [?]: 25 [0]
Given Kudos: 116
Location: United Kingdom
GMAT 1: 660 Q42 V38
GPA: 4
Re: Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 [#permalink]
BrentGMATPrepNow wrote:
silverprince wrote:

Hi BrentGMATPrepNow
Why do we need to make sure that x and y are positive before we simplify the inequality? Couldn't we simplify the inequality first and then change the truth of the inequality if we find out that x or y are negative?

i.e. can we not just simplify the question stem to say: "is y>x?" before being given the information in (1)?

Thanks

Hi silverprince,

Can you show me what you mean?

Cheers,
Brent

Hi BrentGMATPrepNow

Sure, so here's how I approached solving the problem.

The question initially asks: is $$\frac{x+1}{y+1}>\frac{x}{y}$$?

I eliminated the fraction by initially multiplying both sides first by $$y$$ and then by $$(y+1)$$.

This results in: is $$y(x+1) > x(y+1)$$?

Finally expanding the brackets gives: is $$xy+y > xy+x$$?

$$xy$$ cancels out on both sides of the inequality and the question stem can be rephrased as: is $$y>x$$?

Now when we look at the data provided, we're searching specifically for evidence that proves or disproves that y is greater than x.

(1) clearly shows that y is greater than x --> SUFFICIENT

(2) shows that either x and y are both positive or both negative. Since the combinations x=1;y=2 and x=-1 y=-2 satisfy this condition but yield different results, then INSUFFICIENT

Would you agree with the initial approach of simplifying the inequality given in the question stem?

Thanks
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6808
Own Kudos [?]: 30592 [1]
Given Kudos: 799
Re: Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 [#permalink]
1
Kudos
Top Contributor
silverprince wrote:

Hi BrentGMATPrepNow

Sure, so here's how I approached solving the problem.

The question initially asks: is $$\frac{x+1}{y+1}>\frac{x}{y}$$?

I eliminated the fraction by initially multiplying both sides first by $$y$$ and then by $$(y+1)$$.

This results in: is $$y(x+1) > x(y+1)$$?

Finally expanding the brackets gives: is $$xy+y > xy+x$$?

$$xy$$ cancels out on both sides of the inequality and the question stem can be rephrased as: is $$y>x$$?

Now when we look at the data provided, we're searching specifically for evidence that proves or disproves that y is greater than x.

(1) clearly shows that y is greater than x --> SUFFICIENT

(2) shows that either x and y are both positive or both negative. Since the combinations x=1;y=2 and x=-1 y=-2 satisfy this condition but yield different results, then INSUFFICIENT

Would you agree with the initial approach of simplifying the inequality given in the question stem?

Thanks

That approach seems valid for this particular question.
I have a feeling it could cause issues with other questions (but I can't think of an example at the moment)
Also, the hard part is remembering that the rephrased target question may or may not be accurate.
GMAT Club Reviews PM Intern
Joined: 10 Apr 2018
Posts: 532
Own Kudos [?]: 759 [0]
Given Kudos: 522
Location: India
Schools: ISB'22 (D)
GMAT 1: 680 Q48 V34
GPA: 3.3
Re: Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 [#permalink]
BrentGMATPrepNow and DavidTutorexamPAL, what would be the answer and the approach if statement 1 was just x<y instead of 0<x<y? I want to understand how to solve this question if the sign of x and y is not given anywhere. Thank you.
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6808
Own Kudos [?]: 30592 [2]
Given Kudos: 799
Re: Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 [#permalink]
1
Kudos
1
Bookmarks
Top Contributor
siddharthkapoor wrote:
BrentGMATPrepNow and DavidTutorexamPAL, what would be the answer and the approach if statement 1 was just x<y instead of 0<x<y? I want to understand how to solve this question if the sign of x and y is not given anywhere. Thank you.

If we ignore the condition that 0 < x < y and go with just x < y, then the correct answer is E.
Once we lose the fact that x and y are both positive, I'd start testing various negative values.
If x = -0.5 and y = -0.1, then (x + 1)/(y + 1) < x/y
Conversely, if x = 1 and y = 2, then (x + 1)/(y + 1) > x/y
VP
Joined: 11 Aug 2020
Posts: 1252
Own Kudos [?]: 205 [0]
Given Kudos: 332
Re: Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 [#permalink]
Is x+1/y+1> x/y?

Rephrase the target question:

x+1/y+1> x/y ---> y > x?

(1) 0<x<y
Sufficient

(2) xy>0
Insufficient

A.
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6019
Own Kudos [?]: 13645 [2]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Re: Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 [#permalink]
2
Bookmarks
Bunuel wrote:
Is $$\frac{x + 1}{y + 1} > \frac{x}{y}$$?

(1) $$0 < x < y$$

(2) $$xy > 0$$

NEW question from GMAT® Official Guide 2019

(DS09315)

Wanna make solving the Official Questions interesting???

Click here and solve 1000+ Official Questions with Video solutions as Timed Sectional Tests
and Dedicated Data Sufficiency (DS) Course

Video solution by GMATinsight

Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK HERE.
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub
Intern
Joined: 21 Jul 2019
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 4
Re: Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 [#permalink]
I solved this a different way. Can someone let me know if this approach is correct? Thanks!

From statement 1: Since we know X and Y are positive, we know X+1/Y+1 tends to 1 while X/Y would be closer to 0. Hence, X+Y/Y+1 is greater. SUFFICIENT.

From statement 2: xy>0 - this tells us nothing about X & Y (both could be positive or both could be negative, giving different results). Hence, INSUFFICIENT.
Tutor
Joined: 17 Jul 2019
Posts: 1304
Own Kudos [?]: 1746 [1]
Given Kudos: 66
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Re: Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 [#permalink]
1
Bookmarks