Last visit was: 23 Apr 2026, 21:37 It is currently 23 Apr 2026, 21:37
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
User avatar
Zarrolou
User avatar
Joined: 02 Sep 2012
Last visit: 11 Dec 2013
Posts: 842
Own Kudos:
5,187
 [22]
Given Kudos: 219
Status:Far, far away!
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Posts: 842
Kudos: 5,187
 [22]
Is |p|^2<|p| ? (1) p^2 <= 1 (2) p^2 - 1 not 0 Updated on: 17 Jul 2024, 00:06
Originally posted by Zarrolou on 18 Apr 2013, 13:32.
Last edited by Bunuel on 17 Jul 2024, 00:06, edited 3 times in total.
11
Kudos
Add Kudos
11
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

38% (01:36) correct 62% (01:34) wrong based on 398 sessions

History

Date
Time
Result
Not Attempted Yet
Is \(|p|^2<|p|\) ?

(1) \(p^2\leq{1}\)

(2) \(p^2-1\neq{0}\)

Show Spoiler
Hi guys! I created this DS, if you want give it a try!

This is my first creation, I appreciate any feedback
Scroll down for OE.­
­
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
Zarrolou
User avatar
Joined: 02 Sep 2012
Last visit: 11 Dec 2013
Posts: 842
Own Kudos:
5,187
 [7]
Given Kudos: 219
Status:Far, far away!
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Posts: 842
Kudos: 5,187
 [7]
Is |p|^2<|p| ? (1) p^2 <= 1 (2) p^2 - 1 not 0 18 Apr 2013, 15:48
6
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Official Explanation

Is \(|p|^2<|p|\) ?

Splitting the equation into two scenarios \(p>0\) and \(p<0\)

I)\(p>0\)
\(p^2-p>0\)
\(0<p<1\)
II)\(p<{}0\)
\((-p)^2+p<0\)
\(-1<p<0\)

We can rewrite the question as: is \(-1<p<1\) and \(p\neq{0}\)?

1.\(p^2\leq{1}\)
\(-1\leq{}p\leq{}1\)
We cannot say if given this interval p will have one of those values: \(-1<p<1\) and \(p\neq{0}\)
Not Sufficient

2.\(p^2-1\neq{0}\)
\(p\neq{}+,-1\)
Clearly not Sufficient

1+2. Using both 1 and 2 we can conclude that \(-1<p<1\) but p could equal 0. Not Sufficient

OA:
Show SpoilerOA
E
General Discussion
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]
Is |p|^2<|p| ? (1) p^2 <= 1 (2) p^2 - 1 not 0 Updated on: 18 Apr 2013, 16:31
Originally posted by yezz on 18 Apr 2013, 14:29.
Last edited by yezz on 18 Apr 2013, 16:31, edited 1 time in total.
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Zarrolou
Is \(|p|^2<|p|\) ?

1.\(p^2\leq{1}\)
2.\(p^2-1\neq{0}\)

Hi guys! I created this DS, if you want give it a try!

I'll post the solution after some discussion
This is my first creation, I appreciate any feedback
Show more


E it is ... my bad :)
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]
Is |p|^2<|p| ? (1) p^2 <= 1 (2) p^2 - 1 not 0 18 Apr 2013, 15:34
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Zarrolou
Is \(|p|^2<|p|\) ?

1.\(p^2\leq{1}\)
2.\(p^2-1\neq{0}\)

Hi guys! I created this DS, if you want give it a try!

I'll post the solution after some discussion
This is my first creation, I appreciate any feedback
Show more

From F.S 1, for p=0, we have a NO. For p=-1/2, we have a YES. Insufficient.

From F.S 2, Just as above. Insufficient.

Both together, for p=0, a NO. For p=-1/2, a YES. Insufficient.

E.
avatar
geotheox90
avatar
Joined: 16 Dec 2012
Last visit: 26 Apr 2013
Posts: 1
Own Kudos:
1
 [1]
Given Kudos: 1
Posts: 1
Kudos: 1
 [1]
Is |p|^2<|p| ? (1) p^2 <= 1 (2) p^2 - 1 not 0 18 Apr 2013, 15:52
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
/p/(/p/-1)<0 we cannot divide the inequality with /p/ since we don't know if /p/=0.
from statement 1 ,we have that -1<=p<=1 insuff
from statement 2, p<>+-1. insuff

combined p lies in(-1 U +1). p=0.5 ,we have YES,p=0 we have NO. insuff
IMO E
User avatar
manishuol
User avatar
Joined: 30 Sep 2012
Last visit: 15 Jun 2014
Posts: 43
Own Kudos:
236
 [1]
Given Kudos: 11
Status:Pushing Hard
Affiliations: GNGO2, SSCRB
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.33
WE:Analyst (Healthcare/Pharmaceuticals)
Products:
My Reviews
Posts: 43
Kudos: 236
 [1]
Is |p|^2<|p| ? (1) p^2 <= 1 (2) p^2 - 1 not 0 19 Apr 2013, 11:36
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Zarrolou
Official Explanation

Is \(|p|^2<|p|\) ?

Splitting the equation into two scenarios \(p>0\) and \(p<0\)

I)\(p>0\)
\(p^2-p>0\)
\(0<p<1\)
II)\(p<{}0\)
\((-p)^2+p<0\)
\(-1<p<0\)

We can rewrite the question as: is \(-1<p<1\) and \(p\neq{0}\)?

1.\(p^2\leq{1}\)
\(-1\leq{}p\leq{}1\)
We cannot say if given this interval p will have one of those values: \(-1<p<1\) and \(p\neq{0}\)
Not Sufficient

2.\(p^2-1\neq{0}\)
\(p\neq{}+,-1\)
Clearly not Sufficient

1+2. Using both 1 and 2 we can conclude that \(-1<p<1\) but p could equal 0. Not Sufficient

OA:
Show SpoilerOA
E
Show more
----------------------------------------------------------------

Hey, Good Q ..... I'm bit confused ... Correct me if I'm wrong ....

The Question asks....

Is |p|^2<|p| ? , one must always keep in mind that Is |p| is always positive, no matter the sign of P ..Okay & second thing that p^2 will always remain +ve. Now, |p|^2<|p| will only be possible if |p| must be a proper fraction okay. So, we have to find if |p|
is a proper fraction or not. okay.

now statement 1 says .......... p^2 =<1 ...... this means that P can be equal to +1, -1 or p can be equal to any proper fraction as P^2 must always be less than 1 only if P is a proper fraction. so from this we have three values of P... 1, -1 & any proper fraction... however this is insufficient because of multiple possibilities.

Now statement 2 says ....... p^2-1 is not equal to Zero. that means that p is not equal to +,-1 , therefore it is clearly insufficient. .....

Now, 1+2 ........ as statement 1 says that p can be 1 or -1 or any proper fraction & statement 2 says that P is not equal to +,-1 , therefore we can conclude that p = Proper fraction & if P is a Proper fraction whether +ve Proper fraction or -ve Proper fraction, ..... |p|^2<|p| will always remain true. Hence , C.

Please correct me if I'm wrong. Pls......
User avatar
Zarrolou
User avatar
Joined: 02 Sep 2012
Last visit: 11 Dec 2013
Posts: 842
Own Kudos:
5,187
 [2]
Given Kudos: 219
Status:Far, far away!
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Posts: 842
Kudos: 5,187
 [2]
Is |p|^2<|p| ? (1) p^2 <= 1 (2) p^2 - 1 not 0 19 Apr 2013, 11:54
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi manishuol,

lets see if I can remove your doubts. The graph will help a lot, scroll down it's \(|p|^2-|p|<0\) we have to look where it is negative!

\(|p|^2<|p|\), remember that both |p| and |p|^2 don't have to be positive, they can also equal 0.

"So, we have to find if |p| is a proper fraction or not. okay." Not correct, we must find out if p is in the interval \(-1<p<1\) AND \(\neq{0}\).

"this means that P can be equal to +1, -1 or p can be equal to any proper fraction" AND 0 I would add, p ranges in the interval \(-1\leq{p}\leq{1}\)
"however this is insufficient because of multiple possibilities." Correct

"Now statement 2 is clearly insufficient" Correct

Question: is p \(-1<p<1\) AND \(\neq{0}\)?
Statement 1: \(-1\leq{p}\leq{1}\)
Statement 2 \(p\neq{-,+1}\)

1+2 \(-1<p<1\) But no one says anything about \(p=0\)

The point is all here: p could still equal 0, and both statement don't give us info about this possibility.
Attachments

mia.png
mia.png [ 8.74 KiB | Viewed 7601 times ]

User avatar
manishuol
User avatar
Joined: 30 Sep 2012
Last visit: 15 Jun 2014
Posts: 43
Own Kudos:
236
Given Kudos: 11
Status:Pushing Hard
Affiliations: GNGO2, SSCRB
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.33
WE:Analyst (Healthcare/Pharmaceuticals)
Products:
My Reviews
Posts: 43
Kudos: 236
Is |p|^2<|p| ? (1) p^2 <= 1 (2) p^2 - 1 not 0 19 Apr 2013, 12:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Zarrolou
Hi manishuol,

lets see if I can remove your doubts. The graph will help a lot, scroll down it's \(|p|^2-|p|<0\) we have to look where it is negative!

\(|p|^2<|p|\), remember that both |p| and |p|^2 don't have to be positive, they can also equal 0.

"So, we have to find if |p| is a proper fraction or not. okay." Not correct, we must find out if p is in the interval \(-1<p<1\) AND \(\neq{0}\).

"this means that P can be equal to +1, -1 or p can be equal to any proper fraction" AND 0 I would add, p ranges in the interval \(-1\leq{p}\leq{1}\)
"however this is insufficient because of multiple possibilities." Correct

"Now statement 2 is clearly insufficient" Correct

Question: is p \(-1<p<1\) AND \(\neq{0}\)?
Statement 1: \(-1\leq{p}\leq{1}\)
Statement 2 \(p\neq{-,+1}\)

1+2 \(-1<p<1\) But no one says anything about \(p=0\)

The point is all here: p could still equal 0, and both statement don't give us info about this possibility.
Show more

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

Yeah You're certainly right. I missed out 0 as one of the possibility. .......I really appreciate your quick help.Thanks !! Brother !!
User avatar
WholeLottaLove
User avatar
Joined: 13 May 2013
Last visit: 13 Jan 2014
Posts: 301
Own Kudos:
640
 [1]
Given Kudos: 134
Posts: 301
Kudos: 640
 [1]
Is |p|^2<|p| ? (1) p^2 <= 1 (2) p^2 - 1 not 0 25 Jun 2013, 16:59
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Is |p|^2<|p| ?

1.p^2≤1

2.p^2-1≠0

Is |p|^2<|p|? ==> is -1<p<1

1.) insufficient as p could be 1 or -1 meaning p|^2 could equal |p| or p|^2 could be less than |p| Insufficient.

2.) p^2-1≠0 insufficient. p could = 1/2 which when squared = 1/4 which doesn't = 0 and p^2 would be less than P. On the other hand P could = 10 and 10^2-1 > 10.

1+2) we know that -1<p<1 and that p^2-1≠0 so the range of values to test is between -1 and 1. Fine. For ALL values of p except -1, 0 and 1 is |p|^2<|p|. However, while -1^2 - 1 and 1^2 - 1 = 0 (which rules out p being -1 or 1) p could be 0 In which case p^2 = p or it could be a fraction in which p^2 is less than p!

Answer = E.

Great question Zarrolou!
avatar
akhan126
avatar
Joined: 31 Jul 2017
Last visit: 27 Jan 2018
Posts: 5
Own Kudos:
1
Posts: 5
Kudos: 1
Is |p|^2<|p| ? (1) p^2 <= 1 (2) p^2 - 1 not 0 17 Sep 2017, 20:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If this question stated that P didn't equal 0, would the answer be B?
When I worked this problem out, I forgot to take into account for the number 0.

Zarrolou
Official Explanation

Is \(|p|^2<|p|\) ?

Splitting the equation into two scenarios \(p>0\) and \(p<0\)

I)\(p>0\)
\(p^2-p>0\)
\(0<p<1\)
II)\(p<{}0\)
\((-p)^2+p<0\)
\(-1<p<0\)

We can rewrite the question as: is \(-1<p<1\) and \(p\neq{0}\)?

1.\(p^2\leq{1}\)
\(-1\leq{}p\leq{}1\)
We cannot say if given this interval p will have one of those values: \(-1<p<1\) and \(p\neq{0}\)
Not Sufficient

2.\(p^2-1\neq{0}\)
\(p\neq{}+,-1\)
Clearly not Sufficient

1+2. Using both 1 and 2 we can conclude that \(-1<p<1\) but p could equal 0. Not Sufficient

OA:
Show SpoilerOA
E
Show more
User avatar
energetics
User avatar
Joined: 05 Feb 2018
Last visit: 09 Oct 2020
Posts: 294
Own Kudos:
970
Given Kudos: 325
Posts: 294
Kudos: 970
Is |p|^2<|p| ? (1) p^2 <= 1 (2) p^2 - 1 not 0 01 Mar 2019, 09:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
For equation |p|² < |p|, testing values:


1) p² ≤ 1
If p = 1/2 then 1/4 < 1/2 (negative fractions will be the same), YES
If p = 1 then 1 < 1 (-1 and any value above 1 will do the same), NO
This is the trick, if p = 0 it satisfies our constraint and it is also NO in the original equation
Insufficient.

2) p² - 1 ≠ 0
(p-1)(p+1) ≠ 0 so p can't be -1 or 1, same as above and we can get even more values that work.

1&2) Even taking both constraints into account we still can't eliminate p = 0 so it is E
avatar
avikroy
avatar
Joined: 04 Jun 2010
Last visit: 26 Mar 2020
Posts: 94
Own Kudos:
34
Given Kudos: 264
Location: India
GMAT 1: 660 Q49 V31
GPA: 3.22
GMAT 1: 660 Q49 V31
Posts: 94
Kudos: 34
Is |p|^2<|p| ? (1) p^2 <= 1 (2) p^2 - 1 not 0 16 May 2019, 05:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Zarrolou
Official Explanation

Is \(|p|^2<|p|\) ?

Splitting the equation into two scenarios \(p>0\) and \(p<0\)

I)\(p>0\)
\(p^2-p>0\)
\(0<p<1\)
II)\(p<{}0\)
\((-p)^2+p<0\)
\(-1<p<0\)

We can rewrite the question as: is \(-1<p<1\) and \(p\neq{0}\)?


Good question..........obviously missed the p could be zero part

1.\(p^2\leq{1}\)
\(-1\leq{}p\leq{}1\)
We cannot say if given this interval p will have one of those values: \(-1<p<1\) and \(p\neq{0}\)
Not Sufficient

2.\(p^2-1\neq{0}\)
\(p\neq{}+,-1\)
Clearly not Sufficient

1+2. Using both 1 and 2 we can conclude that \(-1<p<1\) but p could equal 0. Not Sufficient

OA:
Show SpoilerOA
E
Show more
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 23 Apr 2026
Posts: 8,628
Own Kudos:
5,190
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GMAT Focus 2: 645 Q83 V82 DI81
GPA: 4
WE:Marketing (Energy)
Products:
GMAT Club Tests Forum Quiz
GMAT Focus 2: 645 Q83 V82 DI81
Posts: 8,628
Kudos: 5,190
Is |p|^2<|p| ? (1) p^2 <= 1 (2) p^2 - 1 not 0 06 Jan 2022, 09:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
we know that
lxl= √x^2
so
\(|p|^2<|p|\)
(√p^2)^2 <√p^2
p^2<p
need to determine whether p^2-p<0

1.\(p^2\leq{1}\)

possible when p = 1/4 or 0
we get yes & no to target
insufficient

2.\(p^2-1\neq{0}\)

p = 0 or 1/4
insufficient
from 1 &2
nothing can be determined
OPTION E is correct


Zarrolou
Is \(|p|^2<|p|\) ?

1.\(p^2\leq{1}\)

2.\(p^2-1\neq{0}\)

Hi guys! I created this DS, if you want give it a try!

This is my first creation, I appreciate any feedback
Scroll down for OE.
Show more
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,963
Own Kudos:
1,117
Posts: 38,963
Kudos: 1,117
Is |p|^2<|p| ? (1) p^2 <= 1 (2) p^2 - 1 not 0 16 Jul 2024, 18:29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109784 posts
kingbucky
498 posts
Gmat860sanskar
212 posts