Last visit was: 23 Apr 2026, 17:53 It is currently 23 Apr 2026, 17:53
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
 1   2   3   
705-805 (Hard)|   Algebra|   Inequalities|      
User avatar
burnttwinky
User avatar
Joined: 25 Jun 2009
Last visit: 11 Sep 2016
Posts: 195
Own Kudos:
1,647
 [177]
Given Kudos: 4
Products:
My Reviews
Schools: Duke '15 (A)
Posts: 195
Kudos: 1,647
 [177]
If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 20 May 2012, 19:02
15
Kudos
Add Kudos
161
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

56% (02:12) correct 44% (02:12) wrong based on 2634 sessions

History

Date
Time
Result
Not Attempted Yet
If x^2 = y^2, is true that x > 0 ?

(1) x = 2y+1

(2) y <= -1
ShowHide Answer
Official Answer
C
Every tricky question should trigger a follow up quiz. Build that habit with GMAT Club Forum Quiz →.
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,785
Own Kudos:
810,870
 [61]
Given Kudos: 105,853
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,785
Kudos: 810,870
 [61]
If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 21 May 2012, 00:38
30
Kudos
Add Kudos
31
Bookmarks
Bookmark this Post
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.
User avatar
geometric
User avatar
Joined: 13 Jan 2012
Last visit: 15 Feb 2017
Posts: 243
Own Kudos:
907
 [17]
Given Kudos: 38
Weight: 170lbs
GMAT 1: 740 Q48 V42
GMAT 2: 760 Q50 V42
WE:Analyst (Other)
GMAT 2: 760 Q50 V42
Posts: 243
Kudos: 907
 [17]
If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 18 Jun 2012, 17:16
11
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
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.
General Discussion
User avatar
mydreammba
User avatar
Joined: 28 Jul 2011
Last visit: 06 Dec 2013
Posts: 224
Own Kudos:
1,677
Given Kudos: 16
Location: United States
Concentration: International Business, General Management
GPA: 3.86
WE:Accounting (Commercial Banking)
Posts: 224
Kudos: 1,677
If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 31 Aug 2012, 07:48
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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.
Show more

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?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,785
Own Kudos:
810,870
Given Kudos: 105,853
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,785
Kudos: 810,870
If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 31 Aug 2012, 08:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
kotela
Bunuel
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?
Show more

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.
User avatar
alex1233
User avatar
Joined: 18 Mar 2012
Last visit: 01 Dec 2013
Posts: 38
Own Kudos:
1,380
Given Kudos: 117
Schools: CBS '16 (I) Insead '14 (II) HBS '16 (D) Wharton '16 (S) LBS '16 (II) Booth '16 (II)
GPA: 3.7
Schools: CBS '16 (I) Insead '14 (II) HBS '16 (D) Wharton '16 (S) LBS '16 (II) Booth '16 (II)
Posts: 38
Kudos: 1,380
If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 02 Mar 2013, 10:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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.
Show more

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!
User avatar
Kris01
User avatar
Joined: 24 Sep 2012
Last visit: 14 Apr 2013
Posts: 64
Own Kudos:
467
 [4]
Given Kudos: 3
Location: United States
Concentration: Entrepreneurship, International Business
GMAT 1: 730 Q50 V39
GPA: 3.2
WE:Education (Education)
GMAT 1: 730 Q50 V39
Posts: 64
Kudos: 467
 [4]
If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 02 Mar 2013, 14:10
4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
Bunuel
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!
Show more
User avatar
mau5
User avatar
Verbal Forum Moderator
Joined: 10 Oct 2012
Last visit: 31 Dec 2024
Posts: 478
Own Kudos:
3,386
 [2]
Given Kudos: 141
Posts: 478
Kudos: 3,386
 [2]
If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 10 May 2013, 22:50
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
burnttwinky
If x^2 = y^2, is true that x>0?

(1) x=2y+1

(2) y<= -1
Show more

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.
User avatar
yezz
User avatar
Retired Moderator
Joined: 05 Jul 2006
Last visit: 26 Apr 2022
Posts: 830
Own Kudos:
1,686
 [1]
Given Kudos: 49
Posts: 830
Kudos: 1,686
 [1]
If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 19 May 2013, 11:08
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
User avatar
WholeLottaLove
User avatar
Joined: 13 May 2013
Last visit: 13 Jan 2014
Posts: 301
Own Kudos:
640
Given Kudos: 134
Posts: 301
Kudos: 640
If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 11 Jun 2013, 18:03
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 23 Apr 2026
Posts: 16,441
Own Kudos:
79,396
Given Kudos: 484
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,441
Kudos: 79,396
If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 11 Jun 2013, 22:33
Kudos
Add Kudos
Bookmarks
Bookmark this Post
WholeLottaLove
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.
Show more

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.
User avatar
WholeLottaLove
User avatar
Joined: 13 May 2013
Last visit: 13 Jan 2014
Posts: 301
Own Kudos:
640
Given Kudos: 134
Posts: 301
Kudos: 640
If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 20 Jun 2013, 16:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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!
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 23 Apr 2026
Posts: 16,441
Own Kudos:
79,396
 [1]
Given Kudos: 484
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,441
Kudos: 79,396
 [1]
If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 20 Jun 2013, 20:55
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
WholeLottaLove
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?
Show more

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

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!
Show more

Yes. If x = -y and y = 5, then x = -5
User avatar
sinhap07
User avatar
Joined: 27 Aug 2014
Last visit: 09 Oct 2018
Posts: 48
Own Kudos:
30
Given Kudos: 3
Posts: 48
Kudos: 30
If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 12 Nov 2014, 05:48
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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.
Show more

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?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,785
Own Kudos:
810,870
Given Kudos: 105,853
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,785
Kudos: 810,870
If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 12 Nov 2014, 06:29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
sinhap07
Bunuel
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?
Show more

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...
User avatar
sinhap07
User avatar
Joined: 27 Aug 2014
Last visit: 09 Oct 2018
Posts: 48
Own Kudos:
30
Given Kudos: 3
Posts: 48
Kudos: 30
If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 12 Nov 2014, 10:39
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
sinhap07
Bunuel
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...
Show more

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.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,785
Own Kudos:
810,870
Given Kudos: 105,853
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,785
Kudos: 810,870
If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 12 Nov 2014, 10:48
Kudos
Add Kudos
Bookmarks
Bookmark this Post
sinhap07
Bunuel
sinhap07


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.
Show more

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.
User avatar
sinhap07
User avatar
Joined: 27 Aug 2014
Last visit: 09 Oct 2018
Posts: 48
Own Kudos:
30
Given Kudos: 3
Posts: 48
Kudos: 30
If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 29 Nov 2014, 06:57
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasPrepKarishma
WholeLottaLove
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

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
Show more

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
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 23 Apr 2026
Posts: 16,441
Own Kudos:
79,396
Given Kudos: 484
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,441
Kudos: 79,396
If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 30 Nov 2014, 22:24
Kudos
Add Kudos
Bookmarks
Bookmark this Post
sinhap07


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
Show more


|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.
User avatar
dimitri92
User avatar
Joined: 15 Nov 2006
Last visit: 18 May 2019
Posts: 229
Own Kudos:
3,651
Given Kudos: 34
Affiliations: SPG
Posts: 229
Kudos: 3,651
If x^2 = y^2, is true that x > 0 ? (1) x = 2y+1 (2) y <= -1 20 Jan 2017, 03:42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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.
Show more

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?
 1   2   3   
Moderators:
Bunuel
Math Expert
109785 posts
kingbucky
498 posts
Gmat860sanskar
212 posts