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

It is currently 24 Jun 2018, 17:28

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

If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1

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

Hide Tags

5 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 25 Jun 2009
Posts: 258
Reviews Badge
If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 [#permalink]

Show Tags

New post 20 May 2012, 19:02
5
22
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

51% (01:19) correct 49% (01:25) wrong based on 891 sessions

HideShow timer Statistics

If x^2 = y^2, is true that x > 0 ?

(1) x = 2y+1

(2) y <= -1
Expert Post
17 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46319
Re: If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 [#permalink]

Show Tags

New post 21 May 2012, 00:38
17
13
If x^2 = y^2, is true that x>0?

\(x^2 = y^2\) --> \(|x|=|y|\) --> either \(y=x\) or \(y=-x\).

(1) x=2y+1 --> if \(y=x\) then we would have: \(x=2x+1\) --> \(x=-1<0\) (notice that in this case \(y=x=-1\)) but if \(y=-x\) then we would have: \(x=-2x+1\) --> \(x=\frac{1}{3}>0\) (notice that in this case \(y=-x=-\frac{1}{3}\)). Not sufficient.

(2) y<= -1. Clearly insufficient.

(1)+(2) Since from (2) \(y\leq{-1}\) then from (1) \(y=x=-1\), so the answer to the question is NO. Sufficient.

Answer: C.

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

4 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 13 Jan 2012
Posts: 290
Weight: 170lbs
GMAT 1: 740 Q48 V42
GMAT 2: 760 Q50 V42
WE: Analyst (Other)
Re: If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 [#permalink]

Show Tags

New post 18 Jun 2012, 17:16
4
The way I usually approach these problems is with plugging in examples, like -1, 0, and 1 to see when the equations hold true.

1)
x = 2y +1

Here, we actually don't need to do anything. Obviously we can't know if x>0 if we don't know the value of y.

2) y<=-1

Alone, this obviously tells us nothing about x! Insufficient. Answer is either C or E.

1+2)

Let's plug a few values of y that are <= -1 into the equation from situation #1 to see how they affect x:

x=2y+1
x=2(-1)+1 = -1
x=2(-2)+1 = -3
x=2(-3)+1 = -5
Obviously, this will continue as a series.

Therefore, we clearly know that x will never be >0 and therefore, C is the answer.
Senior Manager
Senior Manager
avatar
Joined: 28 Jul 2011
Posts: 410
Location: United States
Concentration: International Business, General Management
GPA: 3.86
WE: Accounting (Commercial Banking)
Re: If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 [#permalink]

Show Tags

New post 31 Aug 2012, 07:48
Bunuel wrote:
If x^2 = y^2, is true that x>0?

\(x^2 = y^2\) --> \(|x|=|y|\) --> either \(y=x\) or \(y=-x\).

(1) x=2y+1 --> if \(y=x\) then we would have: \(x=2x+1\) --> \(x=-1<0\) (notice that in this case \(y=x=-1\)) but if \(y=-x\) then we would have: \(x=-2x+1\) --> \(x=\frac{1}{3}>0\) (notice that in this case \(y=-x=-\frac{1}{3}\)). Not sufficient.

(2) y<= -1. Clearly insufficient.

(1)+(2) Since from (2) \(y\leq{-1}\) then from (1) \(y=x=-1\), so the answer to the question is NO. Sufficient.

Answer: C.

Hope it's clear.


Hi Bunnel,

I need a clarification here, when i put statement 1 in X^2 = Y^2 i get the below

3Y^2= -4Y-1,

and since LHS is positive so the RHS needs to be positive so in order to RHS to be positive Y should be "-ve" and when Y is negative, Now

considering statement 1 we can get to know that X is negative.....

So my point is again statement 2 needed?

Please clarify me if i am wrong?
_________________

+1 Kudos If found helpful..

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46319
Re: If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 [#permalink]

Show Tags

New post 31 Aug 2012, 08:17
kotela wrote:
Bunuel wrote:
If x^2 = y^2, is true that x>0?

\(x^2 = y^2\) --> \(|x|=|y|\) --> either \(y=x\) or \(y=-x\).

(1) x=2y+1 --> if \(y=x\) then we would have: \(x=2x+1\) --> \(x=-1<0\) (notice that in this case \(y=x=-1\)) but if \(y=-x\) then we would have: \(x=-2x+1\) --> \(x=\frac{1}{3}>0\) (notice that in this case \(y=-x=-\frac{1}{3}\)). Not sufficient.

(2) y<= -1. Clearly insufficient.

(1)+(2) Since from (2) \(y\leq{-1}\) then from (1) \(y=x=-1\), so the answer to the question is NO. Sufficient.

Answer: C.

Hope it's clear.


Hi Bunnel,

I need a clarification here, when i put statement 1 in X^2 = Y^2 i get the below

3Y^2= -4Y-1,

and since LHS is positive so the RHS needs to be positive so in order to RHS to be positive Y should be "-ve" and when Y is negative, Now

considering statement 1 we can get to know that X is negative.....

So my point is again statement 2 needed?

Please clarify me if i am wrong?


How did you get that if y is negative x must be positive?

For (1) we have:
\(x^2 = y^2\) and \(x=2y+1\). Solving gives: \(x=-1\) and \(y=-1\) OR \(x=\frac{1}{3}\) and \(y=-\frac{1}{3}\), just substitute these values to check that they satisfy both equations.
_________________

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

Intern
Intern
avatar
Joined: 18 Mar 2012
Posts: 47
GPA: 3.7
Re: If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 [#permalink]

Show Tags

New post 02 Mar 2013, 10:38
Bunuel wrote:
If x^2 = y^2, is true that x>0?

\(x^2 = y^2\) --> \(|x|=|y|\) --> either \(y=x\) or \(y=-x\).

(1) x=2y+1 --> if \(y=x\) then we would have: \(x=2x+1\) --> \(x=-1<0\) (notice that in this case \(y=x=-1\)) but if \(y=-x\) then we would have: \(x=-2x+1\) --> \(x=\frac{1}{3}>0\) (notice that in this case \(y=-x=-\frac{1}{3}\)). Not sufficient.

(2) y<= -1. Clearly insufficient.

(1)+(2) Since from (2) \(y\leq{-1}\) then from (1) \(y=x=-1\), so the answer to the question is NO. Sufficient.

Answer: C.

Hope it's clear.


Hi!

I did a bit of a unnecessarily long way but got to the wrong answer and was hoping someone could tell me what my logical error is.

i squared both sides of statement 1 and got to \(x^2 = 4y^2 + 4y +1\)

then I replaced \(x^2\) with \(y^2\) and got the same as everyone else that y = -1 or y = -(1/3) NOT sufficient

Using statement B i eliminated y=-(1/3) but where I got it wrong is that I thought that since y = -1 then x could be equal to +/- 1 so I chose E

Am i missing something?

Thank you in advance or any responses!
2 KUDOS received
Manager
Manager
User avatar
Joined: 24 Sep 2012
Posts: 85
Location: United States
Concentration: Entrepreneurship, International Business
GMAT 1: 730 Q50 V39
GPA: 3.2
WE: Education (Education)
Re: If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 [#permalink]

Show Tags

New post 02 Mar 2013, 14:10
2
Hello Alexpavlos,

You are right in assuming that since y=-1 and x^2=y^2, x=+/-1. However, remember that equation in statement 1 also gives you a relationship between statement x and y. The correct answer should satisfy all the data. Now the question you should ask yourself is whether it is possible to use the information in statement 2 and 1 together to get a single value for x.

Statement 1 mentions that
x=2y+1
Substituting y=-1 in the this equation, we get

x=-1 and hence, x<0. Hence, together the two statements suffice.

Answer-C

Hope this helps! Let me know if you need any further clarification.

alexpavlos wrote:
Bunuel wrote:
If x^2 = y^2, is true that x>0?

\(x^2 = y^2\) --> \(|x|=|y|\) --> either \(y=x\) or \(y=-x\).

(1) x=2y+1 --> if \(y=x\) then we would have: \(x=2x+1\) --> \(x=-1<0\) (notice that in this case \(y=x=-1\)) but if \(y=-x\) then we would have: \(x=-2x+1\) --> \(x=\frac{1}{3}>0\) (notice that in this case \(y=-x=-\frac{1}{3}\)). Not sufficient.

(2) y<= -1. Clearly insufficient.

(1)+(2) Since from (2) \(y\leq{-1}\) then from (1) \(y=x=-1\), so the answer to the question is NO. Sufficient.

Answer: C.

Hope it's clear.


Hi!

I did a bit of a unnecessarily long way but got to the wrong answer and was hoping someone could tell me what my logical error is.

i squared both sides of statement 1 and got to \(x^2 = 4y^2 + 4y +1\)

then I replaced \(x^2\) with \(y^2\) and got the same as everyone else that y = -1 or y = -(1/3) NOT sufficient

Using statement B i eliminated y=-(1/3) but where I got it wrong is that I thought that since y = -1 then x could be equal to +/- 1 so I chose E

Am i missing something?

Thank you in advance or any responses!
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 620
Premium Member
Re: If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 [#permalink]

Show Tags

New post 10 May 2013, 22:50
1
burnttwinky wrote:
If x^2 = y^2, is true that x>0?

(1) x=2y+1

(2) y<= -1


Nothing new to add. Maybe another approach:

From F.S 1, we know that x = 2y+1.
Also \(x^2 = y^2\)
Upon adding,\(x^2+x = (y+1)^2\).Thus, x(x+1)> 0--> x>0 OR x<-1.Insufficient.

From F.S 2, we know that y<-1. Clearly Insufficient.

On combining both, we know that y = (x-1)/2 --> (x-1)/2<-1-->x<-1. Sufficient.

C.
_________________

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

Hit and Trial for Integral Solutions

1 KUDOS received
Retired Moderator
User avatar
B
Joined: 05 Jul 2006
Posts: 1734
GMAT ToolKit User Premium Member
Re: If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 [#permalink]

Show Tags

New post 19 May 2013, 11:08
1
If x^2 = y^2, is it true that x > 0?

1. x = 2y + 1
2. y <= -1

from 1

x^2 = 4y^2 + 4y+1 so now 4y^2 + 4y+1 = y^2 therefore 3y^2 + 4y+1 = 0 ..... (3y + 1) (y+1) = 0 and thus y is either -1/3 or y = -1

subst in 1

x = -2/3 + 1 > 0 or x = -2+1<0 ......insuff

from 2 alone obviously not suff

both ........ y = -1 ........x = -1 too ....suff.......C
Senior Manager
Senior Manager
User avatar
Joined: 13 May 2013
Posts: 430
Re: If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 [#permalink]

Show Tags

New post 11 Jun 2013, 18:03
Can someone tell me if my reasoning is sound?

x^2=y^2 and thus, x=y or x=-y

1.)

I.) x=2y+1

y=2y+1
-y=1
y=-1

y=2(-1)+1
x=-1


II.) x=2y+1

-y=2y+1
-3y=1
y=-1/3

x=2(-1/3)+1
x=1/3

Insufficient because we have two values for x. (however, using the same reasoning to arrive at c. cant we say that both answers we arrive at show that x ≠ 0 and thus, a is sufficient?)

2. y≤-1 Not sufficent

1+2 2. says that y≤-1. In #1, the only case where y≤-1 is y=2y+1

-y=1
y=-1

y=2(-1)+1
x=-1


Here we get an answer of x=-1 which is obviously ≠ to 0.
Expert Post
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8102
Location: Pune, India
Re: If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 [#permalink]

Show Tags

New post 11 Jun 2013, 22:33
WholeLottaLove wrote:
Can someone tell me if my reasoning is sound?

x^2=y^2 and thus, x=y or x=-y

1.)

I.) x=2y+1

y=2y+1
-y=1
y=-1

y=2(-1)+1
x=-1


II.) x=2y+1

-y=2y+1
-3y=1
y=-1/3

x=2(-1/3)+1
x=1/3

Insufficient because we have two values for x. (however, using the same reasoning to arrive at c. cant we say that both answers we arrive at show that x ≠ 0 and thus, a is sufficient?)

2. y≤-1 Not sufficent

1+2 2. says that y≤-1. In #1, the only case where y≤-1 is y=2y+1

-y=1
y=-1

y=2(-1)+1
x=-1


Here we get an answer of x=-1 which is obviously ≠ to 0.


Everything you did is correct except that you misunderstood the question.
The question is:

Is x positive? Is x > 0?
It does not ask you whether x is equal to 0.

Statement I tells you that x could be positive or negative. So not sufficient.
Both statements together tell you that x is negative. Hence it is not positive. It answers the question with 'No'. Sufficient.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Senior Manager
Senior Manager
User avatar
Joined: 13 May 2013
Posts: 430
Re: If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 [#permalink]

Show Tags

New post 20 Jun 2013, 16:45
Question time:

for #2.) we are given y<=-1. This is not sufficient because of the following:

|x| = |y|

x=y
OR
x=-y

x=-y
OR
x=-(-y) x=y

Correct?

Another thing that has bothered me is this. If x=-y, and for example, y=5, then would x=(-5)?

As always, thanks for the help!
Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8102
Location: Pune, India
Re: If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 [#permalink]

Show Tags

New post 20 Jun 2013, 20:55
1
WholeLottaLove wrote:
Question time:

for #2.) we are given y<=-1. This is not sufficient because of the following:

|x| = |y|

x=y
OR
x=-y

x=-y
OR
x=-(-y) x=y

Correct?


I am not really sure what you have done here. The 4 cases will be
x = y
x = -y
-x = y
-x = -y
which are equivalent to just two cases: x = y or x = -y.
Statement 2 is not sufficient because all we know now is that y is negative. IF x = y, x is negative. If x = -y, x is positive. So we still don't know whether x is positive or not.

WholeLottaLove wrote:
Another thing that has bothered me is this. If x=-y, and for example, y=5, then would x=(-5)?

As always, thanks for the help!


Yes. If x = -y and y = 5, then x = -5
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Manager
Manager
avatar
B
Joined: 27 Aug 2014
Posts: 82
Re: If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 [#permalink]

Show Tags

New post 12 Nov 2014, 05:48
Bunuel wrote:
If x^2 = y^2, is true that x>0?

\(x^2 = y^2\) --> \(|x|=|y|\) --> either \(y=x\) or \(y=-x\).

(1) x=2y+1 --> if \(y=x\) then we would have: \(x=2x+1\) --> \(x=-1<0\) (notice that in this case \(y=x=-1\)) but if \(y=-x\) then we would have: \(x=-2x+1\) --> \(x=\frac{1}{3}>0\) (notice that in this case \(y=-x=-\frac{1}{3}\)). Not sufficient.

(2) y<= -1. Clearly insufficient.

(1)+(2) Since from (2) \(y\leq{-1}\) then from (1) \(y=x=-1\), so the answer to the question is NO. Sufficient.

Answer: C.

Hope it's clear.


Hi Bunuel

Why cant answer be B

From x^2=y^2
x and y can take the following values:
1 and -1 or
-1 and 1
as x and y different so not considering same integers like both positive or both negative

from 1st statement none of the values satisfy the given equation
from 2nd statement, y is negative which makes x as positive. Where am I wrong?
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46319
Re: If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 [#permalink]

Show Tags

New post 12 Nov 2014, 06:29
sinhap07 wrote:
Bunuel wrote:
If x^2 = y^2, is true that x>0?

\(x^2 = y^2\) --> \(|x|=|y|\) --> either \(y=x\) or \(y=-x\).

(1) x=2y+1 --> if \(y=x\) then we would have: \(x=2x+1\) --> \(x=-1<0\) (notice that in this case \(y=x=-1\)) but if \(y=-x\) then we would have: \(x=-2x+1\) --> \(x=\frac{1}{3}>0\) (notice that in this case \(y=-x=-\frac{1}{3}\)). Not sufficient.

(2) y<= -1. Clearly insufficient.

(1)+(2) Since from (2) \(y\leq{-1}\) then from (1) \(y=x=-1\), so the answer to the question is NO. Sufficient.

Answer: C.

Hope it's clear.


Hi Bunuel

Why cant answer be B

From x^2=y^2
x and y can take the following values:
1 and -1 or
-1 and 1
as x and y different so not considering same integers like both positive or both negative

from 1st statement none of the values satisfy the given equation
from 2nd statement, y is negative which makes x as positive. Where am I wrong?


x and y can be the same number. Generally, unless it is explicitly stated otherwise, different variables CAN represent the same number.

So, for (2) it's possible that x = y = -1, or x= 1 and y = -1, or x = y = -2, or x = y = -1.5, or x = 100 and y = -100...
_________________

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

Manager
Manager
avatar
B
Joined: 27 Aug 2014
Posts: 82
Re: If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 [#permalink]

Show Tags

New post 12 Nov 2014, 10:39
Bunuel wrote:
sinhap07 wrote:
Bunuel wrote:
If x^2 = y^2, is true that x>0?

\(x^2 = y^2\) --> \(|x|=|y|\) --> either \(y=x\) or \(y=-x\).

(1) x=2y+1 --> if \(y=x\) then we would have: \(x=2x+1\) --> \(x=-1<0\) (notice that in this case \(y=x=-1\)) but if \(y=-x\) then we would have: \(x=-2x+1\) --> \(x=\frac{1}{3}>0\) (notice that in this case \(y=-x=-\frac{1}{3}\)). Not sufficient.

(2) y<= -1. Clearly insufficient.

(1)+(2) Since from (2) \(y\leq{-1}\) then from (1) \(y=x=-1\), so the answer to the question is NO. Sufficient.

Answer: C.

Hope it's clear.


Hi Bunuel

Why cant answer be B

From x^2=y^2
x and y can take the following values:
1 and -1 or
-1 and 1
as x and y different so not considering same integers like both positive or both negative

from 1st statement none of the values satisfy the given equation
from 2nd statement, y is negative which makes x as positive. Where am I wrong?


x and y can be the same number. Generally, unless it is explicitly stated otherwise, different variables CAN represent the same number.

So, for (2) it's possible that x = y = -1, or x= 1 and y = -1, or x = y = -2, or x = y = -1.5, or x = 100 and y = -100...


Agreed Bunuel. Tried that too. But by that logic, Statement 1 holds true only when both x and y are negative and hence we could get A as the answer as we would know that y is negative along with x.
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46319
Re: If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 [#permalink]

Show Tags

New post 12 Nov 2014, 10:48
sinhap07 wrote:
Bunuel wrote:
sinhap07 wrote:

Hi Bunuel

Why cant answer be B

From x^2=y^2
x and y can take the following values:
1 and -1 or
-1 and 1
as x and y different so not considering same integers like both positive or both negative

from 1st statement none of the values satisfy the given equation
from 2nd statement, y is negative which makes x as positive. Where am I wrong?


x and y can be the same number. Generally, unless it is explicitly stated otherwise, different variables CAN represent the same number.

So, for (2) it's possible that x = y = -1, or x= 1 and y = -1, or x = y = -2, or x = y = -1.5, or x = 100 and y = -100...


Agreed Bunuel. Tried that too. But by that logic, Statement 1 holds true only when both x and y are negative and hence we could get A as the answer as we would know that y is negative along with x.


That's not correct.

For (1) it's possible that x = -1 and y = -1 or x = 1/3 and y = -1/3.

The correct answer is C, not B or A.
_________________

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

Manager
Manager
avatar
B
Joined: 27 Aug 2014
Posts: 82
Re: If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 [#permalink]

Show Tags

New post 29 Nov 2014, 06:57
VeritasPrepKarishma wrote:
WholeLottaLove wrote:
Question time:

for #2.) we are given y<=-1. This is not sufficient because of the following:

|x| = |y|

x=y
OR
x=-y

x=-y
OR
x=-(-y) x=y

Correct?


I am not really sure what you have done here. The 4 cases will be
x = y
x = -y
-x = y
-x = -y
which are equivalent to just two cases: x = y or x = -y.
Statement 2 is not sufficient because all we know now is that y is negative. IF x = y, x is negative. If x = -y, x is positive. So we still don't know whether x is positive or not.

WholeLottaLove wrote:
Another thing that has bothered me is this. If x=-y, and for example, y=5, then would x=(-5)?

As always, thanks for the help!


Yes. If x = -y and y = 5, then x = -5


Hi Karishma

I did get C as the answer applying the same method that you have indicated here. But if we solve through using variables, are we not getting x in the positive range? Applying the scenario where x=-y or y=-x
Expert Post
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8102
Location: Pune, India
Re: If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 [#permalink]

Show Tags

New post 30 Nov 2014, 22:24
sinhap07 wrote:

Hi Karishma

I did get C as the answer applying the same method that you have indicated here. But if we solve through using variables, are we not getting x in the positive range? Applying the scenario where x=-y or y=-x



|x| = |y| implies
either x = y or x = -y.
Which is the actual case, we do not know.

Stmnt 2 gives us y is negative. But do we know whether x = y or x = -y? No.
If x = y, x is negative.
If x = -y, x is positive.

So stmnt 2 alone is not sufficient to say whether x is positive or negative. It could be either.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Top Contributor
Senior Manager
Senior Manager
User avatar
B
Affiliations: SPG
Joined: 15 Nov 2006
Posts: 310
Re: If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 [#permalink]

Show Tags

New post 20 Jan 2017, 03:42
Top Contributor
Bunuel wrote:
If x^2 = y^2, is true that x>0?

\(x^2 = y^2\) --> \(|x|=|y|\) --> either \(y=x\) or \(y=-x\).

(1) x=2y+1 --> if \(y=x\) then we would have: \(x=2x+1\) --> \(x=-1<0\) (notice that in this case \(y=x=-1\)) but if \(y=-x\) then we would have: \(x=-2x+1\) --> \(x=\frac{1}{3}>0\) (notice that in this case \(y=-x=-\frac{1}{3}\)). Not sufficient.

(2) y<= -1. Clearly insufficient.

(1)+(2) Since from (2) \(y\leq{-1}\) then from (1) \(y=x=-1\), so the answer to the question is NO. Sufficient.

Answer: C.

Hope it's clear.


Hi Bunuel & Karishma, I will appreciate if you can comment:

1- How can we see this question and decide whether we need to pick numbers or not?

2- In other words, combining the two statements here is fairly easy, but how do we get it to a 50-50 between C and E in 5 to 10 seconds?

3 - In other words, how do we ensure that we don't waste time plugging in numbers in statement 1?
_________________

press kudos, if you like the explanation, appreciate the effort or encourage people to respond.

Download the Ultimate SC Flashcards

Re: If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1   [#permalink] 20 Jan 2017, 03:42

Go to page    1   2    Next  [ 32 posts ] 

Display posts from previous: Sort by

If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1

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


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.