Last visit was: 09 Jul 2025, 17:46 It is currently 09 Jul 2025, 17:46
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
avatar
LamaSalah
Joined: 10 Feb 2017
Last visit: 03 Nov 2017
Posts: 1
Own Kudos:
52
 [52]
Given Kudos: 78
Posts: 1
Kudos: 52
 [52]
1
Kudos
Add Kudos
51
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 09 Jul 2025
Posts: 21,066
Own Kudos:
26,121
 [11]
Given Kudos: 296
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 21,066
Kudos: 26,121
 [11]
7
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
General Discussion
User avatar
Kurtosis
User avatar
Current Student
Joined: 13 Apr 2015
Last visit: 10 Nov 2021
Posts: 1,400
Own Kudos:
4,976
 [3]
Given Kudos: 1,228
Location: India
Products:
Posts: 1,400
Kudos: 4,976
 [3]
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
User avatar
broall
User avatar
Retired Moderator
Joined: 10 Oct 2016
Last visit: 07 Apr 2021
Posts: 1,138
Own Kudos:
6,936
 [2]
Given Kudos: 65
Status:Long way to go!
Location: Viet Nam
Posts: 1,138
Kudos: 6,936
 [2]
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
LamaSalah
Is x < y ?

(1) x^2 - y^2 < 0
(2) -x - y < 0

(1) \(x^2 < y^2 \iff |x| < |y|\)

We have \(3^2 < 5^2 \implies 3 < 5\)
However \(3^2 < (-5)^2 \implies 3 > - 5\).

Hence, insufficient.

(2) \(-x-y < 0 \implies x+y > 0\)

If x=5, y=2 then \(x+y>0\) and \(x>y\)
If x=-2, y=5 then \(x+y>0\) and \(x<y\).

Hence, insufficient.

Combine (1) and (2):
\((2) \implies x+y > 0\)
\((1) \implies (x-y)(x+y) < 0 \implies x-y < 0 \implies x<y\). Sufficient

The answer is C
User avatar
HKD1710
User avatar
Retired Moderator
Joined: 22 Jun 2014
Last visit: 26 Feb 2021
Posts: 963
Own Kudos:
Given Kudos: 182
Location: India
Concentration: General Management, Technology
GMAT 1: 540 Q45 V20
GPA: 2.49
WE:Information Technology (Computer Software)
GMAT 1: 540 Q45 V20
Posts: 963
Kudos: 4,383
Kudos
Add Kudos
Bookmarks
Bookmark this Post
x < y?

stmt-1:
x^2 - y^2 < 0
|x| < |y|
here x or y or both can be postitive or negative. so we cannot decide if x < y or not.

stmt-2:
-x-y < 0
-x < y

say x=2, y=1 then -2 < 1, so x>y. so answer to the given question is NO.
say x=-1, y=2 then 1 < 2, but here x < y. so answer to the given question is Yes.

stmt-1 + stmt-2:
|x| < |y| AND -x < y then is x < y?
x=1, y=2 satisfies both |x| < |y| AND -x < y. in this case x < y (1<2). so answer is YES.
x=-1,y=2 satisfies both |x| < |y| AND -x < y. in this case x < y (-1<2). so answer is YES.

Sufficient!
avatar
manimadhuri
Joined: 24 May 2015
Last visit: 01 Apr 2018
Posts: 3
Own Kudos:
4
 [2]
Given Kudos: 57
Location: India
GMAT 1: 570 Q42 V26
GPA: 3.85
GMAT 1: 570 Q42 V26
Posts: 3
Kudos: 4
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
broall
LamaSalah
Is x < y ?

(1) x^2 - y^2 < 0
(2) -x - y < 0

(1) \(x^2 < y^2 \iff |x| < |y|\)

We have \(3^2 < 5^2 \implies 3 < 5\)
However \(3^2 < (-5)^2 \implies 3 > - 5\).

Hence, insufficient.

(2) \(-x-y < 0 \implies x+y > 0\)

If x=5, y=2 then \(x+y>0\) and \(x>y\)
If x=-2, y=5 then \(x+y>0\) and \(x<y\).

Hence, insufficient.

Combine (1) and (2):
\((2) \implies x+y > 0\)
\((1) \implies (x-y)(x+y) < 0 \implies x-y < 0 \implies x<y\). Sufficient

The answer is C

-----------------------------------------

Can we write the first statement as -y<x<y
since (x+y)(x-y)<0, x falls in the range of -y and y.

This would make statement 1 alone sufficient to answer the question.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 09 Jul 2025
Posts: 102,609
Own Kudos:
739,908
 [2]
Given Kudos: 97,813
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,609
Kudos: 739,908
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
manimadhuri
broall
LamaSalah
Is x < y ?

(1) x^2 - y^2 < 0
(2) -x - y < 0

(1) \(x^2 < y^2 \iff |x| < |y|\)

We have \(3^2 < 5^2 \implies 3 < 5\)
However \(3^2 < (-5)^2 \implies 3 > - 5\).

Hence, insufficient.

(2) \(-x-y < 0 \implies x+y > 0\)

If x=5, y=2 then \(x+y>0\) and \(x>y\)
If x=-2, y=5 then \(x+y>0\) and \(x<y\).

Hence, insufficient.

Combine (1) and (2):
\((2) \implies x+y > 0\)
\((1) \implies (x-y)(x+y) < 0 \implies x-y < 0 \implies x<y\). Sufficient

The answer is C

-----------------------------------------

Can we write the first statement as -y<x<y
since (x+y)(x-y)<0, x falls in the range of -y and y.

This would make statement 1 alone sufficient to answer the question.

x^2 - y^2 < 0;

x^2 < y^2;

|x| < |y|.

This means that y is further from 0 than x is. Which is not enough to get whether x < y. Basically we can have the following cases:

----y----x----0--------------
----y---------0----x---------
---------x----0---------y----
--------------0----x----y----
User avatar
rishabhmishra
Joined: 23 Sep 2016
Last visit: 16 Aug 2019
Posts: 181
Own Kudos:
Given Kudos: 29
Products:
Posts: 181
Kudos: 413
Kudos
Add Kudos
Bookmarks
Bookmark this Post
LamaSalah
Is x < y ?

(1) x^2 - y^2 < 0
(2) -x - y < 0
i will also go with c as by using both the statement we can conclude whether x and y are positive and negative and then we can say x<y.
User avatar
dcummins
Joined: 14 Feb 2017
Last visit: 17 Jun 2025
Posts: 1,069
Own Kudos:
Given Kudos: 368
Location: Australia
Concentration: Technology, Strategy
GMAT 1: 560 Q41 V26
GMAT 2: 550 Q43 V23
GMAT 3: 650 Q47 V33
GMAT 4: 650 Q44 V36
GMAT 5: 600 Q38 V35
GMAT 6: 710 Q47 V41
WE:Management Consulting (Consulting)
Products:
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi ScottTargetTestPrep and Bunuel, thanks for your explanations.

What values could we plug into statement 2 to make it agree with the constraints?

I didn't think to multiply by -1, making it easier to eliminate statement 2, so I'm trying to see what I missed in my plug-in approach
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 09 Jul 2025
Posts: 102,609
Own Kudos:
Given Kudos: 97,813
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,609
Kudos: 739,908
Kudos
Add Kudos
Bookmarks
Bookmark this Post
dcummins
Hi ScottTargetTestPrep and Bunuel, thanks for your explanations.

What values could we plug into statement 2 to make it agree with the constraints?

I didn't think to multiply by -1, making it easier to eliminate statement 2, so I'm trying to see what I missed in my plug-in approach


For (2) x = 1 and y = 2 gives an YES answer, while x = 2 and y = 1 gives a NO answer.
User avatar
dcummins
Joined: 14 Feb 2017
Last visit: 17 Jun 2025
Posts: 1,069
Own Kudos:
Given Kudos: 368
Location: Australia
Concentration: Technology, Strategy
GMAT 1: 560 Q41 V26
GMAT 2: 550 Q43 V23
GMAT 3: 650 Q47 V33
GMAT 4: 650 Q44 V36
GMAT 5: 600 Q38 V35
GMAT 6: 710 Q47 V41
WE:Management Consulting (Consulting)
Products:
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
dcummins
Hi ScottTargetTestPrep and Bunuel, thanks for your explanations.

What values could we plug into statement 2 to make it agree with the constraints?

I didn't think to multiply by -1, making it easier to eliminate statement 2, so I'm trying to see what I missed in my plug-in approach


For (2) x = 1 and y = 2 gives an YES answer, while x = 2 and y = 1 gives a NO answer.


Damn. I realise how silly this mistake was. I didn't write "-" in front of the x i.e. -x-y so was wondering how the hell you could get x-y<0
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 09 Jul 2025
Posts: 21,066
Own Kudos:
Given Kudos: 296
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 21,066
Kudos: 26,121
Kudos
Add Kudos
Bookmarks
Bookmark this Post
dcummins
Hi ScottTargetTestPrep and Bunuel, thanks for your explanations.

What values could we plug into statement 2 to make it agree with the constraints?

I didn't think to multiply by -1, making it easier to eliminate statement 2, so I'm trying to see what I missed in my plug-in approach

I actually addressed your question in my solution:

Statement Two Alone:

-x - y < 0

We can multiply the inequality in statement two by -1, remembering to reverse the inequality sign, and obtain:

x + y > 0, or equivalently, 0 < x + y. However, we still cannot determine whether x > y.

For instance if x = 2 and y = 1, then x is greater than y; however if x = 1 and y = 2, then x is less than y. Statement two alone is not sufficient to answer the question.
User avatar
J2S2019
Joined: 10 Jan 2017
Last visit: 24 Sep 2022
Posts: 270
Own Kudos:
265
 [1]
Given Kudos: 371
Location: India
Products:
Posts: 270
Kudos: 265
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ScottTargetTestPrep
dcummins
Hi ScottTargetTestPrep and Bunuel, thanks for your explanations.

What values could we plug into statement 2 to make it agree with the constraints?

I didn't think to multiply by -1, making it easier to eliminate statement 2, so I'm trying to see what I missed in my plug-in approach

I actually addressed your question in my solution:

Statement Two Alone:

-x - y < 0

We can multiply the inequality in statement two by -1, remembering to reverse the inequality sign, and obtain:

x + y > 0, or equivalently, 0 < x + y. However, we still cannot determine whether x > y.

For instance if x = 2 and y = 1, then x is greater than y; however if x = 1 and y = 2, then x is less than y. Statement two alone is not sufficient to answer the question.


@ScottTargetTestPrep@Bunuel

Please evaluate the attached problem, the work done on this same question. I tried not to do it by putting values.
Attachments

IMG_20190821_222100.jpg
IMG_20190821_222100.jpg [ 1.66 MiB | Viewed 18108 times ]

User avatar
dcummins
Joined: 14 Feb 2017
Last visit: 17 Jun 2025
Posts: 1,069
Own Kudos:
Given Kudos: 368
Location: Australia
Concentration: Technology, Strategy
GMAT 1: 560 Q41 V26
GMAT 2: 550 Q43 V23
GMAT 3: 650 Q47 V33
GMAT 4: 650 Q44 V36
GMAT 5: 600 Q38 V35
GMAT 6: 710 Q47 V41
WE:Management Consulting (Consulting)
Products:
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ScottTargetTestPrep
dcummins
Hi ScottTargetTestPrep and Bunuel, thanks for your explanations.

What values could we plug into statement 2 to make it agree with the constraints?

I didn't think to multiply by -1, making it easier to eliminate statement 2, so I'm trying to see what I missed in my plug-in approach

I actually addressed your question in my solution:

Statement Two Alone:

-x - y < 0

We can multiply the inequality in statement two by -1, remembering to reverse the inequality sign, and obtain:

x + y > 0, or equivalently, 0 < x + y. However, we still cannot determine whether x > y.

For instance if x = 2 and y = 1, then x is greater than y; however if x = 1 and y = 2, then x is less than y. Statement two alone is not sufficient to answer the question.

Thanks Scott, I must have overlooked this.
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 09 Jul 2025
Posts: 21,066
Own Kudos:
Given Kudos: 296
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 21,066
Kudos: 26,121
Kudos
Add Kudos
Bookmarks
Bookmark this Post
dcummins
ScottTargetTestPrep
dcummins
Hi ScottTargetTestPrep and Bunuel, thanks for your explanations.

What values could we plug into statement 2 to make it agree with the constraints?

I didn't think to multiply by -1, making it easier to eliminate statement 2, so I'm trying to see what I missed in my plug-in approach

I actually addressed your question in my solution:

Statement Two Alone:

-x - y < 0

We can multiply the inequality in statement two by -1, remembering to reverse the inequality sign, and obtain:

x + y > 0, or equivalently, 0 < x + y. However, we still cannot determine whether x > y.

For instance if x = 2 and y = 1, then x is greater than y; however if x = 1 and y = 2, then x is less than y. Statement two alone is not sufficient to answer the question.

Thanks Scott, I must have overlooked this.

My pleasure.
avatar
JiddiHuMain
Joined: 06 May 2019
Last visit: 09 Jan 2020
Posts: 82
Own Kudos:
Given Kudos: 7
Location: India
Concentration: Leadership, Finance
Schools: LBS '22
GMAT 1: 710 Q51 V35
GPA: 4
WE:Information Technology (Computer Software)
Schools: LBS '22
GMAT 1: 710 Q51 V35
Posts: 82
Kudos: 111
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Detail Solution -

1) x2- y2 < 0 ----->(x-y)(x+y) <0, -----------> either x-y>0 and x+y<0 or x-y<0 and x+y>0 -----------> hen x>y or x<y both possible----Not Sufficient - A,D rejected
2)-x-y<0 -------------> x+y>0 Not ufficient----B rejected.

combining 1+2 ---------> x+y>0 hence x-y<0 ---->x<y ...sufficient ----option C is correct.

you can also solve by putting random -ve +ve values.
User avatar
aniket16c
User avatar
Current Student
Joined: 20 Oct 2018
Last visit: 05 Feb 2024
Posts: 180
Own Kudos:
153
 [1]
Given Kudos: 57
Location: India
GMAT 1: 690 Q49 V34
GMAT 2: 740 Q50 V40
GPA: 4
GMAT 2: 740 Q50 V40
Posts: 180
Kudos: 153
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Official explanation

Explanation: (1) The values 2 and 3 will give us a YES answer to the question stem, but the values 2 and -3 will give us a response of NO. Another way to approach this is to realize that you can factor the left hand side of the inequality to get (x - y)(x + y) < 0. This means that either the first term, (x - y), is negative or the second term, (x + y), is negative, but not both. If the first term is negative, then YES is answer to the question. However, if the second term is negative, the answer could be YES or NO. Accordingly, this statement is insufficient.

(2) You can simplify this by multiplying both sides by -1, which means you need to flip the direction of the inequality. You'll now have x + y > 0. This, however, doesn't tell us which value is larger, and this statement is insufficient.

Together, we know that (x - y)(x + y) < 0 and x + y > 0. This means that x - y < 0 . Remember, for the product of two values to be negative, one of them and only one of them must be negative. Because we know that (x + y) must be positive, then (x - y) < 0. Simply adding to each side of that inequality, we find that x < y, and know that the statements together are sufficient. Accordingly, the answer is C.
User avatar
ProfChaos
Joined: 11 Apr 2020
Last visit: 06 Dec 2020
Posts: 122
Own Kudos:
Given Kudos: 630
GMAT 1: 660 Q49 V31
GMAT 1: 660 Q49 V31
Posts: 122
Kudos: 313
Kudos
Add Kudos
Bookmarks
Bookmark this Post
LamaSalah
Is x < y ?

(1) x^2 - y^2 < 0
(2) -x - y < 0

S1:
(x+y)(x-y)<0
Since the product of two expressions is less than zero i.e negative
Thus
either
(x+y) is positive and (x-y) is negative
OR
(x+y) is negative and (x-y) is positive
INSUFFICIENT

S2:
(x+y)>0
i.e (x+y) is positive
INSUFFICIENT

S1&S2:
Combining, we get (x+y) is positive and (x-y) is negative, thus x<y

Ans : C
User avatar
Basshead
Joined: 09 Jan 2020
Last visit: 07 Feb 2024
Posts: 927
Own Kudos:
Given Kudos: 432
Location: United States
Posts: 927
Kudos: 286
Kudos
Add Kudos
Bookmarks
Bookmark this Post
LamaSalah
Is x < y ?

(1) x^2 - y^2 < 0
(2) -x - y < 0

Is \(x - y < 0\)?

(1) \((x+y)(x-y) < 0\)

We can't say for certain; INSUFFICIENT.

(2) \(-x - y <0\)
\(0 < x + y\)

INSUFFICIENT.

(1&2) Combined,

\(x + y > 0\), therefore \(x - y < 0\).

SUFFICIENT.

Answer is C.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,365
Own Kudos:
Posts: 37,365
Kudos: 1,010
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderator:
Math Expert
102609 posts