It is currently 24 Nov 2017, 06:39

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

19 KUDOS received
Current Student
avatar
Joined: 07 Sep 2011
Posts: 74

Kudos [?]: 50 [19], given: 13

GMAT 1: 660 Q41 V40
GMAT 2: 720 Q49 V39
WE: Analyst (Mutual Funds and Brokerage)
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

Show Tags

New post 24 Aug 2012, 13:30
19
This post received
KUDOS
14
This post was
BOOKMARKED
Are x and y both positive?

1) 2x-2y=1
2(x-y)=1
x-y=1/2
-->3/4-1/4=1/2....YES
-->-1/4-(-3/4)=1/2...NO
INSUFFICIENT

2) x/y>1
This just means that x and y have the same sign. They're either both positive or both negative.
INSUFFICIENT

1&2)
x=1/2+y

(1/2+y)/y>1
y/2 + 1 > 1
y/2 > 0 which means that Y is greater than 0. And since both x and y have the same sign, both x and y are Positive. YES.

Answer is C.

Kudos [?]: 50 [19], given: 13

1 KUDOS received
Board of Directors
User avatar
G
Joined: 01 Sep 2010
Posts: 3381

Kudos [?]: 9315 [1], given: 1169

Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

Show Tags

New post 02 Oct 2012, 19:42
1
This post received
KUDOS
7
This post was
BOOKMARKED
Bunuel wrote:
Are x and y both positive?
(1) 2x-2y=1
(2) x/y>1

(1) 2x-2y=1. Well this one is clearly insufficient. You can do it with number plugging OR consider the following: x and y both positive means that point (x,y) is in the I quadrant. 2x-2y=1 --> y=x-1/2, we know it's an equation of a line and basically question asks whether this line (all (x,y) points of this line) is only in I quadrant. It's just not possible. Not sufficient.

(2) x/y>1 --> x and y have the same sign. But we don't know whether they are both positive or both negative. Not sufficient.

(1)+(2) Again it can be done with different approaches. You should just find the one which is the less time-consuming and comfortable for you personally.

One of the approaches:
\(2x-2y=1\) --> \(x=y+\frac{1}{2}\)
\(\frac{x}{y}>1\) --> \(\frac{x-y}{y}>0\) --> substitute x --> \(\frac{1}{y}>0\) --> \(y\) is positive, and as \(x=y+\frac{1}{2}\), \(x\) is positive too. Sufficient.

Answer: C.

Discussed here: ds1-93964.html?hilit=number%20plugging%20consider%20approaches and also here along with other hard inequality problems: inequality-and-absolute-value-questions-from-my-collection-86939.html

Hope it helps.



Bunuel i would like tto know how \(\frac{1}{y}>0\) have this : if I have ( y + 1 - y / 2 ) / y > 0 the result should be \(\frac{1}{2y}>0\) and not \(\frac{1}{y}> 0\)

can you please explain ??'

thanks

@edited ............I have seen the explanation in another answer by you :)) Ok
_________________

COLLECTION OF QUESTIONS AND RESOURCES
Quant: 1. ALL GMATPrep questions Quant/Verbal 2. Bunuel Signature Collection - The Next Generation 3. Bunuel Signature Collection ALL-IN-ONE WITH SOLUTIONS 4. Veritas Prep Blog PDF Version 5. MGMAT Study Hall Thursdays with Ron Quant Videos
Verbal:1. Verbal question bank and directories by Carcass 2. MGMAT Study Hall Thursdays with Ron Verbal Videos 3. Critical Reasoning_Oldy but goldy question banks 4. Sentence Correction_Oldy but goldy question banks 5. Reading-comprehension_Oldy but goldy question banks

Kudos [?]: 9315 [1], given: 1169

1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 458

Kudos [?]: 558 [1], given: 11

Concentration: Marketing, Finance
GPA: 3.23
GMAT ToolKit User
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

Show Tags

New post 17 Jan 2013, 04:55
1
This post received
KUDOS
3
This post was
BOOKMARKED
Manbehindthecurtain wrote:
Are x and y both positive?

(1) 2x-2y = 1
(2) x/y > 1


1. x-y = 1/2
This means that the distance between x and y is 1/2 unit and that x is greater than y.
But x and y could be positive such as x=5 and y=4.5, OR
x and y could be both negative such as x=-4 and y=-4.5

INSUFFICIENT.

2. x/y > 1
This shows that x and y must be positive meaning they are either both (+) or both (-).
ex) x/y = 5/2 OR x/y = -5/-2 = 5/2 still > 1

INSUFFICIENT.

Combine.
Let x = 5 and y=9/2: 5/(9/2) = 10/9 > 1 - This means when x and y are both positive it could be a solution to x/y > 1
Let x = -4 and y=-9/2: -4/(-9/2) = 8/9 < 1 - This means when x and y are negative it could not be a solution to x/y > 1

Thus, SUFFICIENT that x and y are both positive.

Answer: C
_________________

Impossible is nothing to God.

Kudos [?]: 558 [1], given: 11

1 KUDOS received
Intern
Intern
avatar
Joined: 02 Apr 2013
Posts: 2

Kudos [?]: 1 [1], given: 3

Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

Show Tags

New post 02 Apr 2013, 08:25
1
This post received
KUDOS
chris558 wrote:
Are x and y both positive?

1) 2x-2y=1
2(x-y)=1
x-y=1/2
-->3/4-1/4=1/2....YES
-->-1/4-(-3/4)=1/2...NO
INSUFFICIENT

2) x/y>1
This just means that x and y have the same sign. They're either both positive or both negative.
INSUFFICIENT

1&2)
x=1/2+y

(1/2+y)/y>1
y/2 + 1 > 1
y/2 > 0 which means that Y is greater than 0. And since both x and y have the same sign, both x and y are Positive. YES.

Answer is C.



Shouldn't (1/2+y)/y>1 simplify to (1/2y) + 1 > 1 ? Or am I missing something? Still get the right answer following this logic but I believe this step is off.

Kudos [?]: 1 [1], given: 3

1 KUDOS received
Manager
Manager
avatar
Joined: 24 Jul 2010
Posts: 88

Kudos [?]: 12 [1], given: 43

Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

Show Tags

New post 11 Apr 2013, 10:06
1
This post received
KUDOS
1
This post was
BOOKMARKED
Bunuel wrote:
Are x and y both positive?
(1) 2x-2y=1
(2) x/y>1

(1) 2x-2y=1. Well this one is clearly insufficient. You can do it with number plugging OR consider the following: x and y both positive means that point (x,y) is in the I quadrant. 2x-2y=1 --> y=x-1/2, we know it's an equation of a line and basically question asks whether this line (all (x,y) points of this line) is only in I quadrant. It's just not possible. Not sufficient.

(2) x/y>1 --> x and y have the same sign. But we don't know whether they are both positive or both negative. Not sufficient.

(1)+(2) Again it can be done with different approaches. You should just find the one which is the less time-consuming and comfortable for you personally.

One of the approaches:
\(2x-2y=1\) --> \(x=y+\frac{1}{2}\)
\(\frac{x}{y}>1\) --> \(\frac{x-y}{y}>0\) --> substitute x --> \(\frac{1}{y}>0\) --> \(y\) is positive, and as \(x=y+\frac{1}{2}\), \(x\) is positive too. Sufficient.

Answer: C.

Discussed here: ds1-93964.html?hilit=number%20plugging%20consider%20approaches and also here along with other hard inequality problems: inequality-and-absolute-value-questions-from-my-collection-86939.html

Hope it helps.


From 1- X=Y+1/2. Divide both sides by Y you get X/Y=1+1/2Y --> 1+1/2Y>1 --> 1/2Y>0 then Y>0. Then consequently X>0.
Is the reasoning sound?

Kudos [?]: 12 [1], given: 43

Expert Post
8 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42356

Kudos [?]: 133204 [8], given: 12439

Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

Show Tags

New post 12 Apr 2013, 02:15
8
This post received
KUDOS
Expert's post
10
This post was
BOOKMARKED
score780 wrote:
Bunuel wrote:
Are x and y both positive?
(1) 2x-2y=1
(2) x/y>1

(1) 2x-2y=1. Well this one is clearly insufficient. You can do it with number plugging OR consider the following: x and y both positive means that point (x,y) is in the I quadrant. 2x-2y=1 --> y=x-1/2, we know it's an equation of a line and basically question asks whether this line (all (x,y) points of this line) is only in I quadrant. It's just not possible. Not sufficient.

(2) x/y>1 --> x and y have the same sign. But we don't know whether they are both positive or both negative. Not sufficient.

(1)+(2) Again it can be done with different approaches. You should just find the one which is the less time-consuming and comfortable for you personally.

One of the approaches:
\(2x-2y=1\) --> \(x=y+\frac{1}{2}\)
\(\frac{x}{y}>1\) --> \(\frac{x-y}{y}>0\) --> substitute x --> \(\frac{1}{y}>0\) --> \(y\) is positive, and as \(x=y+\frac{1}{2}\), \(x\) is positive too. Sufficient.

Answer: C.

Discussed here: ds1-93964.html?hilit=number%20plugging%20consider%20approaches and also here along with other hard inequality problems: inequality-and-absolute-value-questions-from-my-collection-86939.html

Hope it helps.


From 1- X=Y+1/2. Divide both sides by Y you get X/Y=1+1/2Y --> 1+1/2Y>1 --> 1/2Y>0 then Y>0. Then consequently X>0.
Is the reasoning sound?


Yes, your approach is correct.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 133204 [8], given: 12439

Senior Manager
Senior Manager
avatar
Joined: 07 Sep 2010
Posts: 330

Kudos [?]: 1055 [0], given: 136

Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

Show Tags

New post 14 Sep 2013, 22:23
Hello Bunuel,
Request you to please provide your comments on the doubt posted here-

Usually, whenever I see combining an inequality and equation, I substitute the value of one of the variable in the inequality and then analyze the effect.
So, going by that approach;

x-y=1/2 ---(1)
x/y>1 --(2)
Substituting the value of x in equation(2)

(y+1/2)/y>1

Lets assume that y is positive-

(y+1/2) > y

1/2>0 --This means that our assumption is true since 1/2 is greater than Zero. Hence, y > 0

Now, Lets assume that y is negative-

Now, here I'm stuck, I know that multiplying by a negative number changes the sign of the inequality.
I'm sure that the sign will be changed but what would be the resulting equation. I mean, do we need to replace y with "-y" in the whole equation. Please clarify. Which of the following would be correct then

a) y+1/2 <y
b) y+1/2 < -y
c) -y+1/2 < -y

Please help.
Thanks
_________________

+1 Kudos me, Help me unlocking GMAT Club Tests

Kudos [?]: 1055 [0], given: 136

2 KUDOS received
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 627

Kudos [?]: 1390 [2], given: 136

Premium Member
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

Show Tags

New post 14 Sep 2013, 22:39
2
This post received
KUDOS
imhimanshu wrote:
Hello Bunuel,
Request you to please provide your comments on the doubt posted here-

Usually, whenever I see combining an inequality and equation, I substitute the value of one of the variable in the inequality and then analyze the effect.
So, going by that approach;

x-y=1/2 ---(1)
x/y>1 --(2)
Substituting the value of x in equation(2)

(y+1/2)/y>1

Lets assume that y is positive-

(y+1/2) > y

1/2>0 --This means that our assumption is true since 1/2 is greater than Zero. Hence, y > 0

Now, Lets assume that y is negative-

Now, here I'm stuck, I know that multiplying by a negative number changes the sign of the inequality.
I'm sure that the sign will be changed but what would be the resulting equation. I mean, do we need to replace y with "-y" in the whole equation. Please clarify. Which of the following would be correct then

a) y+1/2 <y
b) y+1/2 < -y
c) -y+1/2 < -y

Please help.
Thanks


Refer to the highlighted portion : Actually you don't have to take 2 cases at this point: The expression you have is : \(\frac{y+0.5}{y}>1 \to 1+\frac{0.5}{y}>1 \to \frac{1}{y}>0\)--> Hence, y>0.

As for your doubt, if y is negative, we cross-multiply it and get : \(y+0.5<y \to 0>0.5\), which is absurd.

If y is negative, then -y would be positive, and for multiplying a positive quantity, you don't need to flip signs. So , yes expression a is correct.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

Kudos [?]: 1390 [2], given: 136

Manager
Manager
avatar
Joined: 18 Oct 2013
Posts: 83

Kudos [?]: 58 [0], given: 36

Location: India
Concentration: Technology, Finance
GMAT 1: 580 Q48 V21
GMAT 2: 530 Q49 V13
GMAT 3: 590 Q49 V21
WE: Information Technology (Computer Software)
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

Show Tags

New post 19 Nov 2013, 11:29
Hi
I get confused in this question.
I understand A,B,D are not answer bu confuse in C and E.However,official answer is C.

My approach
1) x=y+(1/2) Not sufficient
2) x/y>1 Not sufficient
1+2) x=y+(1/2) So plugging in a value of y which makes x>y by statement 2 . So
If,y=-2.5 which gives x=-2 then No
If, y=2 x=2.5 then Yes
So answer is E.
Please correct me where I am wrong.

Kudos [?]: 58 [0], given: 36

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42356

Kudos [?]: 133204 [1], given: 12439

Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

Show Tags

New post 19 Nov 2013, 15:34
1
This post received
KUDOS
Expert's post
vikrantgulia wrote:
Hi
I get confused in this question.
I understand A,B,D are not answer bu confuse in C and E.However,official answer is C.

My approach
1) x=y+(1/2) Not sufficient
2) x/y>1 Not sufficient
1+2) x=y+(1/2) So plugging in a value of y which makes x>y by statement 2 . So
If,y=-2.5 which gives x=-2 then No
If, y=2 x=2.5 then Yes
So answer is E.
Please correct me where I am wrong.


x=-2 and y=-2.5 do not satisfy x/y>1.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 133204 [1], given: 12439

4 KUDOS received
Intern
Intern
avatar
Joined: 23 Oct 2012
Posts: 29

Kudos [?]: 16 [4], given: 3

Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

Show Tags

New post 03 Dec 2013, 23:07
4
This post received
KUDOS
St 1) 2x-2y = 1 => 2 (x-y) = 1 => x-y =1/2 => all this tells us is that x > y (could be positive or negative) == hence INSUFF

St 2) x/y > 1 => we don't know if y is (+) or (-) . So we have two cases:

if y positive, then x>y; if y negative, then x<y (again INSUFF)

Combining 1) and 2) we get x>y (from 1) ...which means y is positive (from 2)

Hence, if y is positive, and x >y, then x is also positive. SUFF!!

Hope this was reasoned properly.

Kudos [?]: 16 [4], given: 3

Intern
Intern
avatar
Joined: 16 Oct 2013
Posts: 8

Kudos [?]: 5 [0], given: 0

Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

Show Tags

New post 22 Dec 2013, 00:27
Bunuel wrote:
Are x and y both positive?

\(2x-2y=1\) --> \(x=y+\frac{1}{2}\)
\(\frac{x}{y}>1\) --> \(\frac{x-y}{y}>0\) --> substitute x --> \(\frac{1}{y}>0\) --> \(y\) is positive, and as \(x=y+\frac{1}{2}\), \(x\) is positive too. Sufficient.


Hope it helps.



Sorry for the bump but could you elaborate on the last part where you go from x/y>1 to (x-y)/y>0 to 1/y>0 ..?

I don't quite follow this algebra

Kudos [?]: 5 [0], given: 0

Expert Post
3 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42356

Kudos [?]: 133204 [3], given: 12439

Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

Show Tags

New post 22 Dec 2013, 04:47
3
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
kartboybo wrote:
Bunuel wrote:
Are x and y both positive?

\(2x-2y=1\) --> \(x=y+\frac{1}{2}\)
\(\frac{x}{y}>1\) --> \(\frac{x-y}{y}>0\) --> substitute x --> \(\frac{1}{y}>0\) --> \(y\) is positive, and as \(x=y+\frac{1}{2}\), \(x\) is positive too. Sufficient.


Hope it helps.



Sorry for the bump but could you elaborate on the last part where you go from x/y>1 to (x-y)/y>0 to 1/y>0 ..?

I don't quite follow this algebra


\(\frac{x}{y}>1\) --> \(\frac{x}{y}-1>\) --> \(\frac{x-y}{y}>0\). Now, substitute \(x=y+\frac{1}{2}\) there to get \(\frac{1}{2y}>0\), which further simplifies to \(\frac{1}{y}>0\).

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 133204 [3], given: 12439

Expert Post
1 KUDOS received
Director
Director
User avatar
B
Joined: 17 Dec 2012
Posts: 623

Kudos [?]: 535 [1], given: 16

Location: India
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

Show Tags

New post 23 Dec 2013, 03:53
1
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
Manbehindthecurtain wrote:
Are x and y both positive?

(1) 2x-2y = 1
(2) x/y > 1


Plug in approach that can be used without thinking much and very likely arrive at the correct answer.

Values to be taken: x positive and negative and find the corresponding values for y based on the statements
Note: x and y cannot be of different signs and also x cannot be zero as they will not satisfy (ii)

(i) x=10, we have y =9.5 .Both positive satisfied And now x=-10, we have y=-9.5. Both negative also satisfied .Different results. So (i) alone not sufficient

(ii) x=10, y can be positive. Both positive satisfied . And now x=-10, y can be negative. Both negative also satisfied. So (ii) alone not sufficient

(i) + (ii) x=10, y=9.5 satisfies both the statements . Both positive satisfied . And now x=-10. Value of y is found from (i) and is negative , but we see it does not satisfy (ii). So both cannot be negative .

So we can answer the question using (i) and (ii) together
_________________

Srinivasan Vaidyaraman
Sravna
http://www.sravnatestprep.com/regularcourse.php

Premium Material
Standardized Approaches

Kudos [?]: 535 [1], given: 16

Manager
Manager
User avatar
Joined: 11 Jan 2014
Posts: 94

Kudos [?]: 74 [0], given: 11

Concentration: Finance, Statistics
GMAT Date: 03-04-2014
GPA: 3.77
WE: Analyst (Retail Banking)
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

Show Tags

New post 29 Jan 2014, 22:28
Is it safe to solve this kind of questions based on logic?

I didn't jump into calculations/plug-ins, since statement (1) is clearly insufficient. And statement (2) states that x & y both have the same sign, so combining them together, the result of subtraction is a positive number, and given from (2) that they have the same sign, then they both must be positive.

Kudos [?]: 74 [0], given: 11

Manager
Manager
avatar
Joined: 26 Feb 2015
Posts: 124

Kudos [?]: 28 [0], given: 43

Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

Show Tags

New post 09 Jun 2015, 23:22
Bunuel wrote:
Are x and y both positive?
(1) 2x-2y=1
(2) x/y>1

(1) 2x-2y=1. Well this one is clearly insufficient. You can do it with number plugging OR consider the following: x and y both positive means that point (x,y) is in the I quadrant. 2x-2y=1 --> y=x-1/2, we know it's an equation of a line and basically question asks whether this line (all (x,y) points of this line) is only in I quadrant. It's just not possible. Not sufficient.

(2) x/y>1 --> x and y have the same sign. But we don't know whether they are both positive or both negative. Not sufficient.

(1)+(2) Again it can be done with different approaches. You should just find the one which is the less time-consuming and comfortable for you personally.

One of the approaches:
\(2x-2y=1\) --> \(x=y+\frac{1}{2}\)
\(\frac{x}{y}>1\) --> \(\frac{x-y}{y}>0\) --> substitute x --> \(\frac{1}{y}>0\) --> \(y\) is positive, and as \(x=y+\frac{1}{2}\), \(x\) is positive too. Sufficient.

Answer: C.

Discussed here: ds1-93964.html?hilit=number%20plugging%20consider%20approaches and also here along with other hard inequality problems: inequality-and-absolute-value-questions-from-my-collection-86939.html

Hope it helps.



Question: Whenever I graph it, and get to statement two that says "\(\frac{x}{y}> 1\)" I can make \(x > y\) and \(x < y\) depending on if they are both positive or both negative. Is there some connection to absolute values here? If they are both positive, say: \(\frac{10}{5}\)

Then 10 > 5. But if x = -10 and y = -5. -5 > -10.

So, without absolue values, they can be in either the first quadrant or third quadrant

Kudos [?]: 28 [0], given: 43

Intern
Intern
avatar
Joined: 27 Apr 2014
Posts: 3

Kudos [?]: 1 [0], given: 0

Concentration: General Management, Leadership
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

Show Tags

New post 14 Jun 2015, 16:46
Bunuel, what if
x=3/8 and y=-1/8

It satisfies, x-y=1/2--> 3/8+1/8=4/8-->1/2
And also satisfies x>y-->3/8>-1/8,

Could someone tell me what I am doing wrong??

best regards,

Kudos [?]: 1 [0], given: 0

Retired Moderator
User avatar
Joined: 06 Jul 2014
Posts: 1271

Kudos [?]: 2390 [0], given: 178

Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
GMAT ToolKit User Premium Member
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

Show Tags

New post 14 Jun 2015, 23:06
fcojcruz wrote:
Bunuel, what if
x=3/8 and y=-1/8

It satisfies, x-y=1/2--> 3/8+1/8=4/8-->1/2
And also satisfies x>y-->3/8>-1/8,

Could someone tell me what I am doing wrong??

best regards,


Hello fcojcruz
Here is mistake: "And also satisfies x>y-->3/8>-1/8"

if \(x=\frac{3}{8}\) and \(y = -\frac{1}{8}\) than inequality \(\frac{x}{y}> 1\) is wrong \(\frac{3}{8}\) divided by \(-\frac{1}{8}\) can't be bigger than \(1\)

if \(y < 0\) than you should change sign of inequality then you multiply or divide inequality on \(y\)

so if \(x>y\)-->\(\frac{3}{8}>-\frac{1}{8}\) than \(\frac{x}{y} < 1\) and this enaqulity contradicts to second statement
_________________

Simple way to always control time during the quant part.
How to solve main idea questions without full understanding of RC.
660 (Q48, V33) - unpleasant surprise
740 (Q50, V40, IR3) - anti-debrief ;)

Kudos [?]: 2390 [0], given: 178

Current Student
avatar
Joined: 14 May 2014
Posts: 45

Kudos [?]: 2 [0], given: 39

Schools: Broad '18 (WA)
GMAT 1: 700 Q44 V41
GPA: 3.11
GMAT ToolKit User Reviews Badge
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

Show Tags

New post 23 Jul 2015, 04:40
dauntingmcgee wrote:
I found this one easiest to solve by drawing a graph. Clearly 1) and 2) alone are not sufficient as discussed, so what remains to be seen is if 2) adds enough information to 1) to determine if both x and y are positive.

Drawing a quick graph of the line y=x-1/2 we find that the x-intercept of the line is (0.5,0) and the y-intercept is (0,-0.5). From this graph we can clearly see that we don't need to worry about anything in the 4th quadrant (+x/-y is not >1)or the 3rd quadrant (|x|<|y|, therefore x/y is not >1). All that is left is the 1st quadrant, in which x and y are both positive.

Sufficient.


i did not understand the highlighted portion. why is that we dont have to worry about 3 rd qdrt. the line passes thr it. pls help to understand..?

Kudos [?]: 2 [0], given: 39

Current Student
avatar
B
Joined: 20 Mar 2014
Posts: 2672

Kudos [?]: 1776 [0], given: 794

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

Show Tags

New post 23 Jul 2015, 05:35
riyazgilani wrote:
dauntingmcgee wrote:
I found this one easiest to solve by drawing a graph. Clearly 1) and 2) alone are not sufficient as discussed, so what remains to be seen is if 2) adds enough information to 1) to determine if both x and y are positive.

Drawing a quick graph of the line y=x-1/2 we find that the x-intercept of the line is (0.5,0) and the y-intercept is (0,-0.5). From this graph we can clearly see that we don't need to worry about anything in the 4th quadrant (+x/-y is not >1)or the 3rd quadrant (|x|<|y|, therefore x/y is not >1). All that is left is the 1st quadrant, in which x and y are both positive.

Sufficient.


i did not understand the highlighted portion. why is that we dont have to worry about 3 rd qdrt. the line passes thr it. pls help to understand..?



What this means is that when we combine the statements for the 3rd quadrant with y<0 , x= y+0.5 , we get x/y <1 (goes against statement 2) . You can see that , when both x,y <0, |x| < |y| and this will give you |x|/|y| < 1

Consider 2 cases:

y = -2.5 , x = y+0.5 = -2, but x/y < 1 (goes against statement 2)

or y = -0.5, x = -0.5+0.5 = 0 , but x/y = 0/-0.5 = 0 < 1 (goes against statement 2)

Thus 3rd quadrant values are not allowed/possible.

Hope this helps.

Kudos [?]: 1776 [0], given: 794

Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1   [#permalink] 23 Jul 2015, 05:35

Go to page   Previous    1   2   3   4    Next  [ 78 posts ] 

Display posts from previous: Sort by

Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.