Is p a negative number? (1) p3(1 – p2) < 0 (2) p2 – 1

Is p a negative number? (1) p3(1 – p2) < 0 (2) p2 – 1 < 0

Oldest

Best Reply

Author

Message

TAGS:

Manager

Joined: 09 Feb 2010

Posts: 72

Followers: 0

Kudos [?]: 4 [0], given: 4

Is p a negative number? (1) p3(1 – p2) < 0 (2) p2 – 1 < 0 [#permalink]

14 Jul 2010, 07:52

00:00

Question Stats:

18% (01:58) correct

81% (01:17) wrong

based on 1 sessions

Can someone explain how to solve this quickly

Is p a negative number?

(1) p3(1 – p2) < 0

(2) p2 – 1 < 0

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11516

Followers: 1792

Kudos [?]: 9537 [0], given: 826

Re: DS - inequality problem [#permalink]

14 Jul 2010, 08:12

zest4mba wrote:

Can someone explain how to solve this quickly

Is p a negative number?

(1) p3(1 – p2) < 0

(2) p2 – 1 < 0

Is p<0?

(1) p^3(1-p^2)<0, or which is the same p(1-p^2)<0 --> p<p^3 --> either p is more than 1, p>1 OR p is negative fraction -1<p<0.

So we have two ranges for p: p>1 or -1<p<0. Not sufficient.

(2) p^2-1<0 --> -1<p<1. Not sufficient.

(1)+(2) Intersection of the ranges from (1) and (2) is the range -1<p<0, so the answer to the question "is p<0" is YES. Sufficient.

Answer: C.

Hope it's clear.
_________________

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!

What are GMAT Club Tests?
25 extra-hard Quant Tests

Find out what's new at GMAT Club - latest features and updates

Status: The last round

Joined: 18 Jun 2009

Posts: 1327

Concentration: Strategy, General Management

Schools: Stanford '14 (D), Booth '14 (D), Johnson '14 (D)

GMAT 1: 680 Q48 V34

Followers: 43

Kudos [?]: 383 [0], given: 156

Re: DS - inequality problem [#permalink]

14 Jul 2010, 08:18

I assume that stmt 1 is p^2-1<0 & stmt 2 is p^3(1-p^2)

Stmt 1.
p^3(1-p^2)<0
Either p^3<0 or 1-p^2<0
p<0 or p^2>1
p<0 or p>1 or p<-1 so not sufficient

Stmt 2
p^2-1<0
(p-1)(p+1)<0
either p<1 or p<-1 Not sufficient again

Combing the two, again multiple answers. So "E" for me. I think Bunuel can clarify better, I can be wrong
_________________

[ From 470 to 680-My Story ] [ My Last Month Before Test ]
[ GMAT Prep Analysis Tool ] [ US. Business School Dashboard ] [ Int. Business School Dashboard ]

I Can, I Will

Find out what's new at GMAT Club - latest features and updates

Status: The last round

Joined: 18 Jun 2009

Posts: 1327

Concentration: Strategy, General Management

Schools: Stanford '14 (D), Booth '14 (D), Johnson '14 (D)

GMAT 1: 680 Q48 V34

Followers: 43

Kudos [?]: 383 [0], given: 156

Re: DS - inequality problem [#permalink]

14 Jul 2010, 08:21

Bunuel, If I put 2 in Stmt 1 then it comes true. So stmt 1 also shows p>1.

Where am I wrong?
_________________

Current Student

Joined: 31 Mar 2010

Posts: 167

Schools: Tuck Class of 2013

Followers: 2

Kudos [?]: 12 [0], given: 4

Re: DS - inequality problem [#permalink]

14 Jul 2010, 08:28

The fastest way to solve this problem is to plot a graph. I would love to help but I lack right now the resources to post a picture. :oops:

I believe that Bunuel will soon show up and help us.

I will try to explain anyway:

(1) Consider three parallel number lines (p) , one for p^3, one for 1-p^2 and a third one to represent the product of the these two functions. The "+" and "-" represents the sign (Y) of the functions.

A: p^3:-------(-1)---0+++(+1)++++
B: 1-p^2:----(-1)+++0+++(+1)-----
A*B:++++++++(-1)---0+++(+1)----- --> So p can be either positive or negative = Insuff.

(2) p^2 - 1 ++++(-1)---(0)---(+1)++++++ Same as in (1), p can be either positive or negative = Insuff.

(1) and (2) together shows a clear intersection when p < 0, so Suff.

Current Student

Joined: 31 Mar 2010

Posts: 167

Schools: Tuck Class of 2013

Followers: 2

Kudos [?]: 12 [0], given: 4

Re: DS - inequality problem [#permalink]

14 Jul 2010, 08:32

Wow, I was writting my reply and in the mean time you guys had already posted !

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11516

Followers: 1792

Kudos [?]: 9537 [0], given: 826

Re: DS - inequality problem [#permalink]

14 Jul 2010, 08:46

Hussain15 wrote:

Bunuel, If I put 2 in Stmt 1 then it comes true. So stmt 1 also shows p>1.

Where am I wrong?

Statement (1) is true for: p>1 (1.5, 2, 7, 12.5, ...) AND -1<p<0 (-1/2, -3/4, ...).
Statement (2) is true for: -1<p<1 (-5/6, -2/9, 0, 1/2, 3/4, 7/8, ...).

----(-1)----(0)----(1)----
----(-1)----(0)----(1)----

Combined:

----(-1)----(0)----(1)----
_________________

Intern

Joined: 11 Jul 2009

Posts: 22

Followers: 0

Kudos [?]: 0 [0], given: 0

Re: DS - inequality problem [#permalink]

14 Jul 2010, 11:50

shouldn't the question be

is p negative??

in the above solution we considered "p" in the range -1<p<0

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11516

Followers: 1792

Kudos [?]: 9537 [0], given: 826

Re: DS - inequality problem [#permalink]

14 Jul 2010, 12:23

FedX wrote:

shouldn't the question be

is p negative??

in the above solution we considered "p" in the range -1<p<0

Question: is p negative? Is p<0?

When we considered statements together we've got that -1<p<0: every p from this range is negative (every p from this range is <0). Hence taken together statements are sufficient.

Answer: C.

Hope it's clear.
_________________

Intern

Joined: 11 Jul 2009

Posts: 22

Followers: 0

Kudos [?]: 0 [0], given: 0

Re: DS - inequality problem [#permalink]

14 Jul 2010, 13:08

Bunuel wrote:

FedX wrote:

shouldn't the question be

is p negative??

in the above solution we considered "p" in the range -1<p<0

This is fine..but the original poster has put it as "Is p a negative number"?
Do they both mean the same??

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11516

Followers: 1792

Kudos [?]: 9537 [0], given: 826

Re: DS - inequality problem [#permalink]

14 Jul 2010, 13:20

FedX wrote:

Bunuel wrote:

FedX wrote:

shouldn't the question be

is p negative??

in the above solution we considered "p" in the range -1<p<0

This is fine..but the original poster has put it as "Is p a negative number"?
Do they both mean the same??

The questions "is p negative" and "is p a negative number" are the same. Maybe you confused "number" with "integer"?
_________________

Intern

Joined: 11 Jul 2009

Posts: 22

Followers: 0

Kudos [?]: 0 [0], given: 0

Re: DS - inequality problem [#permalink]

14 Jul 2010, 13:34

Thanks for the clarification Bunuel !!.

Intern

Joined: 03 Mar 2010

Posts: 41

Followers: 1

Kudos [?]: 6 [0], given: 1

Re: DS - inequality problem [#permalink]

22 Jul 2010, 00:41

C should be the correct answer, just see the following counterexamples:
statement 1: p=2
statement 2: p=-0.1

Considering both statements, p3 must be negative then p negative
_________________

Hardworkingly, you like my post, so kudos me.

Re: DS - inequality problem [#permalink] 22 Jul 2010, 00:41

	Similar topics	Author	Replies	Last post
Similar Topics:	IS p < 0? 1) p + 6 < \|p\| 2) p^2 - p > p^2 Thanks	subrac	2	27 Sep 2004, 19:41
	If mv<pv<0 , is v > 0 ? (1) m < p (2) m < 0	copper_waters	1	16 Feb 2006, 06:38
	If mv < pv < 0, is v>0? 1) m < p 2) m < 0	lfox2	4	20 Dec 2006, 06:14
	if mv<pv<0> 0 ? (1) m<p (2) m<0	tlntd42	2	30 Sep 2007, 09:19
	Is p a negative number? (1) p3(1 p2) < 0 (2) p2 1 < 0	hariharakarthi	12	18 Aug 2009, 22:02

Is p a negative number? (1) p3(1 – p2) < 0 (2) p2 – 1 < 0

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.

GMAT Courses

Admissions Consulting

Is p a negative number? (1) p3(1 – p2) < 0 (2) p2 – 1 < 0

Is p a negative number? (1) p3(1 – p2) < 0 (2) p2 – 1 < 0

Main navigation

GMAT Resources

Partners

MBA Resources