GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Jul 2018, 19:19

### 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

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

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47157
Is p^3 < p? (1) p < 1 (2) p is an integer  [#permalink]

### Show Tags

06 Apr 2018, 05:06
00:00

Difficulty:

35% (medium)

Question Stats:

70% (00:48) correct 30% (00:35) wrong based on 52 sessions

### HideShow timer Statistics

Is p^3 < p?

(1) p < 1

(2) p is an integer

_________________
DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1288
Location: India
Is p^3 < p? (1) p < 1 (2) p is an integer  [#permalink]

### Show Tags

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
DS Forum Moderator
Joined: 27 Oct 2017
Posts: 623
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: Is p^3 < p? (1) p < 1 (2) p is an integer  [#permalink]

### Show Tags

06 Apr 2018, 08:25
1
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 [ 64.41 KiB | Viewed 572 times ]

_________________
Senior Manager
Joined: 31 Oct 2013
Posts: 376
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: Is p^3 < p? (1) p < 1 (2) p is an integer  [#permalink]

### Show Tags

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.
Manager
Joined: 16 Jan 2018
Posts: 51
GMAT 1: 600 Q40 V33
Re: Is p^3 < p? (1) p < 1 (2) p is an integer  [#permalink]

### Show Tags

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

SVP
Joined: 26 Mar 2013
Posts: 1726
Re: Is p^3 < p? (1) p < 1 (2) p is an integer  [#permalink]

### Show Tags

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

Re: Is p^3 < p? (1) p < 1 (2) p is an integer &nbs [#permalink] 08 Apr 2018, 17:31
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.