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

 It is currently 15 Dec 2018, 01:15

### 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

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Free GMAT Strategy Webinar

December 15, 2018

December 15, 2018

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# If p = 3q, is p^2 > q^2

Author Message
TAGS:

### Hide Tags

Manager
Joined: 18 Oct 2013
Posts: 72
Location: India
Concentration: Technology, Finance
GMAT 1: 580 Q48 V21
GMAT 2: 530 Q49 V13
GMAT 3: 590 Q49 V21
WE: Information Technology (Computer Software)
If p = 3q, is p^2 > q^2  [#permalink]

### Show Tags

Updated on: 03 Jan 2014, 07:01
3
9
00:00

Difficulty:

95% (hard)

Question Stats:

47% (01:49) correct 53% (02:01) wrong based on 220 sessions

### HideShow timer Statistics

If p = 3q, is p^2 > q^2

(1) q + p < q - p

(2) p^2 = 9q^2

Originally posted by vikrantgulia on 03 Jan 2014, 06:57.
Last edited by Bunuel on 03 Jan 2014, 07:01, edited 1 time in total.
Renamed the topic and edited the question.
Manager
Joined: 18 Oct 2013
Posts: 72
Location: India
Concentration: Technology, Finance
GMAT 1: 580 Q48 V21
GMAT 2: 530 Q49 V13
GMAT 3: 590 Q49 V21
WE: Information Technology (Computer Software)
Re: if p=3q, is p^2 > q^2  [#permalink]

### Show Tags

03 Jan 2014, 07:02
I wouldn't find a suitable way to solve this problem.Moreover, can we simplify the algebra problem as we do in Word problems or arithmetic problems.
If i simplify it by putting the p=3q then question become 9q^2>q^2 and further simplifying it as q^2 is always positive so we divide it which destroy the complete question.

Math Expert
Joined: 02 Sep 2009
Posts: 51215
If p = 3q, is p^2 > q^2  [#permalink]

### Show Tags

03 Jan 2014, 07:10
1
If p = 3q, is p^2 > q^2

Substitute $$p = 3q$$ into the question: is $$9q^2>q^2$$? --> is $$8q^2>0$$? --> is $$q\neq{0}$$?

(1) q + p < q - p --> $$p<0$$. Since $$p = 3q$$, then q is less than 0, so not equal to 0. Therefore we have an YES answer to the question. Sufficient.

(2) p^2 = 9q^2. We already know this from the stem: $$p = 3q$$ --> $$p^2 = 9q^2$$. Therefore this statement is useless. Not sufficient.

Hope it's clear.
_________________
Senior Manager
Joined: 06 Aug 2011
Posts: 339
Re: If p = 3q, is p^2 > q^2  [#permalink]

### Show Tags

03 Jan 2014, 10:28
vikrantgulia wrote:
If p = 3q, is p^2 > q^2

(1) q + p < q - p

(2) p^2 = 9q^2

p2>q2?

statement A: q+p<q-p ======> that means p<0.

If p is less than 0 means p is negative..

p=3q...that means q will be negative too. if q will be negative that means p will less than q?

square of large negative number will be greater in value than less negative number.

so p2 will be greater than q2.

Statement B is insufficient.(same as bunuel's explantion)

I took more than 3 mints. After luking at bunuel's solution i think thats much easy to do.
_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Manager
Status: GMAT Coach
Joined: 05 Nov 2012
Posts: 130
Location: Peru
GPA: 3.98
If p = 3q, is p^2 > q^2  [#permalink]

### Show Tags

18 Jun 2015, 11:43
Bunuel wrote:
If p = 3q, is p^2 > q^2

Substitute $$p = 3q$$ into the question: is $$9q^2>q^2$$? --> is $$8q^2>0$$? --> is $$q>0$$?

(1) q + p < q - p --> $$p<0$$. As $$p = 3q$$, then q is also less than 0, therefore we have a NO answer to the question. Sufficient.

(2) p^2 = 9q^2. We already know this from the stem: $$p = 3q$$ --> $$p^2 = 9q^2$$. Therefore this statement is useless. Not sufficient.

Hope it's clear.

I agree that A is the answer; however, the answer to the question is "yes". You divided both sides of the inequality by q, which is negative, without flipping the inequality sign.
p < q (both negative) but P^2 > q^2

As a matter of fact, the question, as you said, is $$9q^2>q^2$$? if you divide both sides by q^2 (positive, no flipping sign) you get 3>1? and the answer is yes. We only need statement 1 in order to eliminate zero as an answer.
_________________

Clipper Ledgard
GMAT Coach

Intern
Joined: 11 Apr 2015
Posts: 5
Location: Singapore
Concentration: Human Resources, Strategy
Schools: HKU'16 (S)
GMAT 1: 690 Q48 V36
Re: If p = 3q, is p^2 > q^2  [#permalink]

### Show Tags

18 Jun 2015, 21:14
I have a confusion. Even if q is less than 0, 8q^2 will be greater than 0. So the condition 8q^2 >0 hold true always.. Isn't it?
Retired Moderator
Joined: 06 Jul 2014
Posts: 1235
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
If p = 3q, is p^2 > q^2  [#permalink]

### Show Tags

18 Jun 2015, 22:32
cledgard wrote:
Bunuel wrote:
If p = 3q, is p^2 > q^2

Substitute $$p = 3q$$ into the question: is $$9q^2>q^2$$? --> is $$8q^2>0$$? --> is $$q>0$$?

(1) q + p < q - p --> $$p<0$$. As $$p = 3q$$, then q is also less than 0, therefore we have a NO answer to the question. Sufficient.

(2) p^2 = 9q^2. We already know this from the stem: $$p = 3q$$ --> $$p^2 = 9q^2$$. Therefore this statement is useless. Not sufficient.

Hope it's clear.

I agree that A is the answer; however, the answer to the question is "yes". You divided both sides of the inequality by q, which is negative, without flipping the inequality sign.
p < q (both negative) but P^2 > q^2

As a matter of fact, the question, as you said, is $$9q^2>q^2$$? if you divide both sides by q^2 (positive, no flipping sign) you get 3>1? and the answer is yes. We only need statement 1 in order to eliminate zero as an answer.

Hello cledgard
When $$9q^2>q^2$$ transform to $$8q^2>0$$ it's not dividing but subtracting $$q^2$$ from both sides. During subtracting we shouldn't change sign of inequality.
But I think you are right about answer because I too see that answer is "yes" $$p^2 > q^2$$
_________________
Retired Moderator
Joined: 06 Jul 2014
Posts: 1235
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
Re: If p = 3q, is p^2 > q^2  [#permalink]

### Show Tags

18 Jun 2015, 22:41
1
NehaBhargava wrote:
I have a confusion. Even if q is less than 0, 8q^2 will be greater than 0. So the condition 8q^2 >0 hold true always.. Isn't it?

Hello NehaBhargava
You are right but not in the case when q = 0
So this part $$8q2>0$$? --> is $$q>0$$ should looks like $$8q2>0$$? --> is $$q<>0$$
_________________
Manager
Status: GMAT Coach
Joined: 05 Nov 2012
Posts: 130
Location: Peru
GPA: 3.98
Re: If p = 3q, is p^2 > q^2  [#permalink]

### Show Tags

19 Jun 2015, 11:44
Harley1980 wrote:
cledgard wrote:
Bunuel wrote:
If p = 3q, is p^2 > q^2

Substitute $$p = 3q$$ into the question: is $$9q^2>q^2$$? --> is $$8q^2>0$$? --> is $$q>0$$?

(1) q + p < q - p --> $$p<0$$. As $$p = 3q$$, then q is also less than 0, therefore we have a NO answer to the question. Sufficient.

(2) p^2 = 9q^2. We already know this from the stem: $$p = 3q$$ --> $$p^2 = 9q^2$$. Therefore this statement is useless. Not sufficient.

Hope it's clear.

I agree that A is the answer; however, the answer to the question is "yes". You divided both sides of the inequality by q, which is negative, without flipping the inequality sign.
p < q (both negative) but P^2 > q^2

As a matter of fact, the question, as you said, is $$9q^2>q^2$$? if you divide both sides by q^2 (positive, no flipping sign) you get 3>1? and the answer is yes. We only need statement 1 in order to eliminate zero as an answer.

Hello cledgard
When $$9q^2>q^2$$ transform to $$8q^2>0$$ it's not dividing but subtracting $$q^2$$ from both sides. During subtracting we shouldn't change sign of inequality.
But I think you are right about answer because I too see that answer is "yes" $$p^2 > q^2$$

The question was simplified: is $$9q^2>q^2$$? --> is $$8q^2>0$$? --> is $$q>0$$?
I was referring to the last step $$q>0$$?
To get from $$8q^2>0$$ to $$q>0$$? you must either divide by 8q or take the square root from both sides, and then the question would be is |q|>0? This answer must be yes, unless q is 0. It is because the possibility of q being 0 that we need statement 1.
_________________

Clipper Ledgard
GMAT Coach

Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Re: If p = 3q, is p^2 > q^2?  [#permalink]

### Show Tags

01 Sep 2018, 19:02
Mo2men wrote:
If p = 3q, is p^2 > q^2?

(1) q + p < q - p

(2) p^2 = 9q^2

kudos for the explanation of the answer

Given, p=3q.

Question stem:- Is $$p^2 > q^2?$$
Or, Is $$(3q)^2> q^2$$
Or, Is $$9q^2>q^2$$
Or, Is $$q^2>0$$
Does 'q' lie in the interval (-inf,0) or (0,+inf)?

St1:- q + p < q - p
Or, 4q<(-3q)
Or, q<0
Answer to question stem is Yes.
Sufficient.

St2:- $$p^2 = 9q^2$$
Or, $$9q^2=9q^2$$
This is true for all values of q.
Hence insufficient.

Ans. (A)
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Director
Joined: 31 Jul 2017
Posts: 505
Location: Malaysia
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: If p = 3q, is p^2 > q^2  [#permalink]

### Show Tags

01 Sep 2018, 21:34
vikrantgulia wrote:
If p = 3q, is p^2 > q^2

(1) q + p < q - p

(2) p^2 = 9q^2

From Statement I: p < 0, q < 0.
As $$p = 3q$$ and both are of same sign, $$p^2 > q^2$$.

From Statement II:

When, $$p =0, q = 0$$.. Its Insufficient.

Hence, $$A$$.
_________________

If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!

Intern
Joined: 21 May 2017
Posts: 16
Re: If p = 3q, is p^2 > q^2  [#permalink]

### Show Tags

16 Nov 2018, 03:14
Given : p = 3q

From 1: q+p<q-p
Solving Statement 1 , 2p<0 therefore, p<0 which means that q<0.
Hence, 1 is sufficient.

From 2: p^2= 9q^2
Solving Statement 2, p^2-9q^2=0 or (p-3q)(p+3q)=0 or p=3q or p=-3q.
We are not sure of the value p holds and hence cannot conclude about p^2>q^2.
Therefore, 2 is not sufficient.

Re: If p = 3q, is p^2 > q^2 &nbs [#permalink] 16 Nov 2018, 03:14
Display posts from previous: Sort by