Last visit was: 19 Jul 2025, 14:39 It is currently 19 Jul 2025, 14:39
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
User avatar
hogann
Joined: 29 Jun 2009
Last visit: 21 Apr 2015
Posts: 117
Own Kudos:
1,332
 [79]
Given Kudos: 2
Affiliations: CFA Level 2 Candidate
Concentration: Finance
Schools:RD 2: Darden Class of 2012
 Q49  V35
Posts: 117
Kudos: 1,332
 [79]
10
Kudos
Add Kudos
68
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
AKProdigy87
Joined: 11 Sep 2009
Last visit: 11 Mar 2015
Posts: 80
Own Kudos:
1,102
 [13]
Given Kudos: 6
Posts: 80
Kudos: 1,102
 [13]
8
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
User avatar
truplayer257
Joined: 19 Jan 2017
Last visit: 06 May 2025
Posts: 27
Own Kudos:
28
 [5]
Given Kudos: 5
Posts: 27
Kudos: 28
 [5]
4
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
General Discussion
User avatar
Zarrolou
Joined: 02 Sep 2012
Last visit: 11 Dec 2013
Posts: 848
Own Kudos:
5,077
 [1]
Given Kudos: 219
Status:Far, far away!
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Posts: 848
Kudos: 5,077
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Is x negative?

(i) x^2 is a positive number
\(x^2>0\), so \(x\neq{0}\), not sufficient to say that it is negative.

(ii) x * |y| is not a positive number
\(x*|y|\leq{0}\), so y could be 0 and x could have any value (positive, negative, or zero) and this would be respected
Not sufficient.

1+2)Still y could be 0, and in this case x, which now we know cannot be zero, could still equal a positive or negative number.
Example \(2*0\leq{0}\) this respects both conditions and x is positive, or \(-2*0\leq{0}\) here x is negative.
Not sufficient
E
User avatar
summer101
Joined: 06 Jun 2012
Last visit: 16 Jun 2014
Posts: 106
Own Kudos:
Given Kudos: 37
Posts: 106
Kudos: 1,033
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Zarrolou
Is x negative?

(i) x^2 is a positive number
\(x^2>0\), so \(x\neq{0}\), not sufficient to say that it is negative.

(ii) x * |y| is not a positive number
\(x*|y|\leq{0}\), so y could be 0 and x could have any value (positive, negative, or zero) and this would be respected
Not sufficient.

1+2)Still y could be 0, and in this case x, which now we know cannot be zero, could still equal a positive or negative number.
Example \(2*0\leq{0}\) this respects both conditions and x is positive, or \(-2*0\leq{0}\) here x is negative.
Not sufficient
E

Hi Zarrolou,
I thought mod of Zero was illegal.
in (ii) x could be zero. But together we know x cannot be zero hence negative.
User avatar
Zarrolou
Joined: 02 Sep 2012
Last visit: 11 Dec 2013
Posts: 848
Own Kudos:
Given Kudos: 219
Status:Far, far away!
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Posts: 848
Kudos: 5,077
Kudos
Add Kudos
Bookmarks
Bookmark this Post
summer101
Hi Zarrolou,
I thought mod of Zero was illegal.
in (ii) x could be zero. But together we know x cannot be zero hence negative.

Mod of 0 is legit.

\(|0|=0\)
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 July 2025
Posts: 102,625
Own Kudos:
Given Kudos: 98,235
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,625
Kudos: 742,783
Kudos
Add Kudos
Bookmarks
Bookmark this Post
summer101
Zarrolou
Is x negative?

(i) x^2 is a positive number
\(x^2>0\), so \(x\neq{0}\), not sufficient to say that it is negative.

(ii) x * |y| is not a positive number
\(x*|y|\leq{0}\), so y could be 0 and x could have any value (positive, negative, or zero) and this would be respected
Not sufficient.

1+2)Still y could be 0, and in this case x, which now we know cannot be zero, could still equal a positive or negative number.
Example \(2*0\leq{0}\) this respects both conditions and x is positive, or \(-2*0\leq{0}\) here x is negative.
Not sufficient
E

Hi Zarrolou,
I thought mod of Zero was illegal.
in (ii) x could be zero. But together we know x cannot be zero hence negative.
\

|0|=0.

Is x negative?

(1) x^2 is a positive number. This statement implies that \(x\neq{0}\). Not sufficient.

(2) x * |y| is not a positive number --> \(x * |y|\leq{0}\). If \(y=0\), then \(x\) could be ANY number. Not sufficient.

(1)+(2) Again, if \(y=0\), then \(x\) could be ANY number but 0 (excluded because of the first statement). Not sufficient.

Answer: E.
User avatar
WholeLottaLove
Joined: 13 May 2013
Last visit: 13 Jan 2014
Posts: 305
Own Kudos:
Given Kudos: 134
Posts: 305
Kudos: 617
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Is x negative?


(1) x^2 is a positive number

x^2 = +
|x| = +
x could be any number aside from zero and |x| will be positive.
x = positive or negative
INSUFFICIENT

(2) x * |y| is not a positive number
|y| will always be a positive number so for x * |y| to be negative x must be negative.
HOWEVER, the answer could be zero too. 0 is not positive or negative. So, 0 * |y| = 0 OR x * |0| = 0.
x = positive, zero or negative
INSUFFICIENT

1+2) # 1 tells us that x could be positive or negative. # 2 tells us that c could be positive, negative or zero. In other words, x could be positive or negative.
INSUFFICIENT

(E)
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,788
Own Kudos:
12,504
 [2]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,788
Kudos: 12,504
 [2]
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Hi All,

This question can be solved by TESTing VALUES.

We're asked if X is a negative number. This is a YES/NO question.

Fact 1: X^2 is a positive number.

IF....
X = 2
X^2 = 4
The answer to the question is NO.

X = -2
X^2 = 4
The answer to the question is YES.
Fact 1 is INSUFFICIENT.

Fact 2: (X)|Y| is NOT a positive number.

IF....
Y = 0
X = 2
The answer to the question is NO.

Y = 0
X = -2
The answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, the two TESTs that we did in Fact 2 ALSO "fit" Fact 1, so we end up with NO and YES answers.
Combined, INSUFFICIENT

Final Answer:
GMAT assassins aren't born, they're made,
Rich
avatar
davidian22
Joined: 28 Mar 2019
Last visit: 10 Jan 2021
Posts: 6
Own Kudos:
8
 [1]
Given Kudos: 2
Location: Netherlands
GMAT 1: 750 Q49 V44
GPA: 4
GMAT 1: 750 Q49 V44
Posts: 6
Kudos: 8
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
1) x can be either positive or negative --> insufficient

2) if y = 0 --> then for any x, the product of x*|y| will not be positive. --> insufficient

Combined) no new information --> insufficient.

Hence, the answer is E.
avatar
Mayank1996
Joined: 20 Nov 2018
Last visit: 03 Mar 2020
Posts: 12
Own Kudos:
24
 [2]
Given Kudos: 38
Posts: 12
Kudos: 24
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Is x a negative number?

(1) x^2 is a positive number.

(2) x⋅|y| is not a positive number.

Solution:-

There is no information in the question stem to process so we move to the statements directly.

(1) x^2 is a positive number.

Square of any number is positive, be it a negative or a positive number.
So, X can be a negative number or a positive number as well. Hence, INSUFFICIENT

(2) x⋅|y| is not a positive number.

Now, We need to read this statement very carefully. It says x⋅|y| is NOT A POSITIVE number. It does not say that x⋅|y| is A NEGATIVE number. So, There are 2 possibilities now, x⋅|y| can either be a Negative number or it can be ZERO. (Because Zero is neither positive nor negative)
Lets say x⋅|y|=0
So, if |y|=0, X can either be positive or negative.
Lets say x⋅|y|= Negative
So, here X can only be negative.

Since, This statement is also not providing us a clear answer, Its INSUFFICIENT

Taking both statements together will do us no good because both statements suggest the same thing that X can either be positive or negative.

So the answer is E.


Please give kudos if you found my posts helpful!
User avatar
GMATwithAK
Joined: 15 Feb 2021
Last visit: 18 Apr 2022
Posts: 15
Own Kudos:
Given Kudos: 24
Posts: 15
Kudos: 5
Kudos
Add Kudos
Bookmarks
Bookmark this Post
hogann
Is x a negative number?

(1) x^2 is a positive number.

(2) x*|y| is not a positive number.


Answer (E)

x^2 will be positive or zero (if x=0)

x*|y| may be positive, negative or zero depending on whether x is postive/negative/zero or y is zero

Therefore, no conclusions can be drawn

Regards

Arun Krishnan
GMAT with AK
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,788
Own Kudos:
12,504
 [2]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,788
Kudos: 12,504
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GMATwithAK
hogann
Is x a negative number?

(1) x^2 is a positive number.

(2) x*|y| is not a positive number.


Answer (E)

x^2 will be positive or zero (if x=0)

x*|y| may be positive, negative or zero depending on whether x is postive/negative/zero or y is zero

Therefore, no conclusions can be drawn

Regards

Arun Krishnan
GMAT with AK

Hi Arun,

In Fact 1, we're told that X^2 is a POSITIVE number, so X itself could be positive OR negative (but NOT 0).

GMAT assassins aren't born, they're made,
Rich
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,450
Own Kudos:
Posts: 37,450
Kudos: 1,013
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.
Moderators:
Math Expert
102625 posts
455 posts