NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 04:57 It is currently 25 Apr 2024, 04:57
Decision Tracker
My Rewards
New posts
New comers' posts

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

Is p^3 < p? (1) p < 1 (2) p is an integer

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92912
Own Kudos [?]: 618923 [1]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Is p^3 < p? (1) p < 1 (2) p is an integer [#permalink] New post   06 Apr 2018, 05:06
1
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

70% (01:13) correct 30% (00:54) wrong based on 80 sessions
Hide Show timer Statistics
Is p^3 < p?

(1) p < 1

(2) p is an integer
ShowHide Answer
Official Answer
E
User avatar
P
amanvermagmat
Retired Moderator
Joined: 22 Aug 2013
Posts: 1186
Own Kudos [?]: 2499 [0]
Given Kudos: 459
Location: India
Send PM
Is p^3 < p? (1) p < 1 (2) p is an integer [#permalink] New post   06 Apr 2018, 05:19
Bunuel wrote:
Is p^3 < p?

(1) p < 1

(2) p is an integer


Statement 1:
If p = 0, then both p and p^3 are equal so the answer is NO.
But if p = -2, then p^3 = -8 which is less than -2, so the answer is YES.
thus this statement in itself is not sufficient.

Statement 2:
If p=0 Or if p = 1, then both p and p^3 are equal so the answer is NO.
If p is a negative integer (except -1) than p^3 will be less than p so the answer will be YES.
If p is a positive integer > 1, then p^3 will be greater than p so the answer will be NO again.
thus this statement also is not sufficient.

Combining the statements, p is an integer < 1.
If p=0 or -1, then the answer is NO.
If p=-2 or -3, then the answer is YES. Again not sufficient. Hence E answer
User avatar
L
GMATBusters
GMAT Tutor
Joined: 27 Oct 2017
Posts: 1905
Own Kudos [?]: 5582 [1]
Given Kudos: 236
WE:General Management (Education)
Send PM
GMAT ToolKit User
Re: Is p^3 < p? (1) p < 1 (2) p is an integer [#permalink] New post   06 Apr 2018, 08:25
1
Kudos
Expert Reply
It can also be done by wavy curve method a s explained in the sketch attached.


See this
https://gmatclub.com/forum/inequalities ... l#p1582891
Attachments

Screenshot001.jpg
Screenshot001.jpg [ 64.41 KiB | Viewed 2813 times ]

User avatar
D
KSBGC
VP
VP
Joined: 31 Oct 2013
Posts: 1260
Own Kudos [?]: 1155 [0]
Given Kudos: 635
Concentration: Accounting, Finance
GPA: 3.68
WE:Analyst (Accounting)
Send PM
Re: Is p^3 < p? (1) p < 1 (2) p is an integer [#permalink] New post   06 Apr 2018, 10:04
Bunuel wrote:
Is p^3 < p?

(1) p < 1

(2) p is an integer


we are looking whetherp^3\(\) is less than p or not.

statement 1: it states that p<1. thus, p could be 0 , -2, - 100, -1/2. If we just consider p=0, p^3\(\) and p will be same. Thus, statement 1 is not sufficient.

statement 2: p is and integer.
o is also an integer. in that case p^3 and p will be same. Integer can be negative or positive. thus answer will vary.

statement 1+2: still not sufficient. statement 1 tells us the range and statement 2 tells us that p is an integer. because of 0, we won't get the perfect answer.

thus , the correct answer is E.
avatar
B
krish76
Intern
Intern
Joined: 16 Jan 2018
Posts: 48
Own Kudos [?]: 30 [0]
Given Kudos: 16
Concentration: Finance, Technology
GMAT 1: 600 Q40 V33
Send PM
Reviews Badge
Re: Is p^3 < p? (1) p < 1 (2) p is an integer [#permalink] New post   08 Apr 2018, 16:12
question becomes -

is P^3 -P <1

or is (p-0)(p-1)(p- (-1)) < 0

drawing number line says this is true only when P is b/n 0 and 1 (not inclusive) and P is <-1 (non inclusive)

1) P < 1 clearly NS ( as the equation is > 0 b/n -1 and 0 and -ve b/n 0 and 1)
2) P is an integer again NS

(1) + (2) -
equation doesn't hold true If P is -1 ( equation is > 0) .
equation holds true for integers to left of -1 i.e. P(p-1)(p+1) is < 0

Answer (E)
User avatar
L
Mo2men
RSM Erasmus Moderator
Joined: 26 Mar 2013
Posts: 2461
Own Kudos [?]: 1360 [0]
Given Kudos: 641
Concentration: Operations, Strategy
Schools: Erasmus (II)
Send PM
Reviews Badge
Re: Is p^3 < p? (1) p < 1 (2) p is an integer [#permalink] New post   08 Apr 2018, 17:31
Bunuel wrote:
Is p^3 < p?

(1) p < 1

(2) p is an integer



(1) p < 1

Let p = 0................Answer is No

Let p = -2...............Answer is Yes

Insufficient

(2) p is an integer

Let p = 0................Answer is No

Let p = -2...............Answer is Yes

Insufficient

Combine 1 & 2

Same examples lead to no clear cut

Answer: E
GMAT Club Bot
gmatclubot
Re: Is p^3 < p? (1) p < 1 (2) p is an integer [#permalink]
08 Apr 2018, 17:31
Moderator:
Bunuel
Math Expert
92912 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions