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

 It is currently 05 Dec 2019, 18:03

### 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

# Are positive numbers p, q and r equal?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 07 Oct 2011
Posts: 25
Are positive numbers p, q and r equal?  [#permalink]

### Show Tags

Updated on: 21 Jan 2018, 07:22
2
3
00:00

Difficulty:

35% (medium)

Question Stats:

57% (00:49) correct 43% (00:44) wrong based on 284 sessions

### HideShow timer Statistics

Are positive numbers p, q and r equal?

(1) p = q
(2) q^2 = r^2

What if p=2, q=2, r=sqroot4

then wouldn't it be E?

GMAT Club Tests m03q25

Originally posted by karthiksms on 31 May 2012, 19:45.
Last edited by Bunuel on 21 Jan 2018, 07:22, edited 3 times in total.
Edited the question
Intern
Joined: 28 Sep 2011
Posts: 22
Location: India
WE: Consulting (Computer Software)
Re: Are positive numbers p, q and r equal?  [#permalink]

### Show Tags

31 May 2012, 20:08
a) p = q Not Sufficient - as r can be any other positive number
b) Again Not Sufficient.It denotes that q= r as only positive numbers are to be considered
It cannot be 2^2 and (-2)^2

Combining , p=q=r , Hence sufficient

karthiksms wrote:
Are positive numbers p, q and r equal?

a) p = q
b) q^2 = r^2

What if p=2, q=2, r=sqroot4

then wouldn't it be E?

OA is C
Intern
Joined: 07 Oct 2011
Posts: 25
Re: Are positive numbers p, q and r equal?  [#permalink]

### Show Tags

31 May 2012, 20:11
Why can't sq root 4 be considered for r? It's a positive number. Then the ans would be E..
Intern
Joined: 28 Sep 2011
Posts: 22
Location: India
WE: Consulting (Computer Software)
Re: Are positive numbers p, q and r equal?  [#permalink]

### Show Tags

31 May 2012, 20:38
Karthik,
Lets stick our line of reasoning according to statements given.
Now, p,q,r are all positive nos.

Both individually can be eliminated. Now the case of combining the 2.
For Stmt - 1
p=2
q=2

For Stmt 2,
q^2 = 2^2 =4.
For r, r^2 should be 4. There can be 2 values for r.
2 or -2. But as r is positive no., hence r = 2. (r cannot be -2)

Please let me know if this helps.

karthiksms wrote:
Why can't sq root 4 be considered for r? It's a positive number. Then the ans would be E..
Intern
Joined: 24 Apr 2012
Posts: 5
Re: Are positive numbers p, q and r equal?  [#permalink]

### Show Tags

31 May 2012, 20:39
I got to answer (C).

(1) P=Q Not sufficient - you don't know what R is
(2) Q^2=R^2 Not sufficient - you don't know what P is

Together, you find that in statement (2) by square-rooting you get Q=R. From statement (1) you know P=Q thus by combining both statements you get P=Q=R.

*Note if the question did not state "positive numbers" the answer will be (E) as square-rooting it can either be + or - for statement (2).

Also I think you need to be aware that the statements given are "true". Do not plug-in numbers trying to dis-prove the statement as that can easily confuse you.
Intern
Joined: 07 Oct 2011
Posts: 25
Re: Are positive numbers p, q and r equal?  [#permalink]

### Show Tags

31 May 2012, 20:44
Makes sense now, cool. thanks !
Math Expert
Joined: 02 Sep 2009
Posts: 59561
Re: Are positive numbers p, q and r equal?  [#permalink]

### Show Tags

01 Jun 2012, 01:26
1
karthiksms wrote:
Are positive numbers p, q and r equal?

(1) p = q
(2) q^2 = r^2

What if p=2, q=2, r=sqroot4

then wouldn't it be E?

Are positive numbers $$p$$, $$q$$, and $$r$$ equal?

(1) $$p = q$$. Not sufficient, since no info about $$r$$
(2) $$q^2 = r^2$$ --> since given that $$p$$ and $$q$$ are positive numbers then $$q=r$$. Not sufficient since no info about $$p$$.

(1)+(2) As $$p = q$$ and $$q=r$$ then $$p=q=r$$. Sufficient.

Answer: C.

As for your question: if $$p=q=2$$ and $$r=\sqrt{4}$$ --> $$\sqrt{4}=2$$, so we have that $$p=q=r=2$$.

Hope it's clear.
Manager
Joined: 26 Feb 2013
Posts: 147
Re: Are positive numbers p, q and r equal?  [#permalink]

### Show Tags

18 Oct 2013, 04:41
I am getting confused at statement 2:

Since p^2=r^2, then we have |p|=|r|, whereas two of the possible solutions are
p = r
p = -r

Now, if p=q=2 and -r = -2, then p=q=r
But if p = -r and p = 2, then r = -2, then p=q=r doesn't hold, hence E.

What's wrong with my concept?
Math Expert
Joined: 02 Sep 2009
Posts: 59561
Re: Are positive numbers p, q and r equal?  [#permalink]

### Show Tags

18 Oct 2013, 05:00
Skag55 wrote:
I am getting confused at statement 2:

Since p^2=r^2, then we have |p|=|r|, whereas two of the possible solutions are
p = r
p = -r

Now, if p=q=2 and -r = -2, then p=q=r
But if p = -r and p = 2, then r = -2, then p=q=r doesn't hold, hence E.

What's wrong with my concept?

Notice that we are given that both p and r are positive numbers. Therefore from |p|=|r| we can write p=r.

Hope it's clear.
Manager
Joined: 26 Feb 2013
Posts: 147
Re: Are positive numbers p, q and r equal?  [#permalink]

### Show Tags

18 Oct 2013, 05:06
Bunuel wrote:
Skag55 wrote:
I am getting confused at statement 2:

Since p^2=r^2, then we have |p|=|r|, whereas two of the possible solutions are
p = r
p = -r

Now, if p=q=2 and -r = -2, then p=q=r
But if p = -r and p = 2, then r = -2, then p=q=r doesn't hold, hence E.

What's wrong with my concept?

Notice that we are given that both p and r are positive numbers. Therefore from |p|=|r| we can write p=r.

Hope it's clear.

Yes, but r will be a positive integer but it's value negative. I'm not sure if what I'm saying is valid.
Math Expert
Joined: 02 Sep 2009
Posts: 59561
Re: Are positive numbers p, q and r equal?  [#permalink]

### Show Tags

18 Oct 2013, 05:10
Skag55 wrote:
Bunuel wrote:
Skag55 wrote:
I am getting confused at statement 2:

Since p^2=r^2, then we have |p|=|r|, whereas two of the possible solutions are
p = r
p = -r

Now, if p=q=2 and -r = -2, then p=q=r
But if p = -r and p = 2, then r = -2, then p=q=r doesn't hold, hence E.

What's wrong with my concept?

Notice that we are given that both p and r are positive numbers. Therefore from |p|=|r| we can write p=r.

Hope it's clear.

Yes, but r will be a positive integer but it's value negative. I'm not sure if what I'm saying is valid.

I don't understand what you mean.
Manager
Joined: 26 Feb 2013
Posts: 147
Re: Are positive numbers p, q and r equal?  [#permalink]

### Show Tags

18 Oct 2013, 05:21
Bunuel wrote:

I don't understand what you mean.

I mean that a variable might be -ve or +ve so r might be -2 or 2.
And |r| might be +r or -r.
In case that r = 2 then -r = -2.
In case that r = -2 then -r = 2.

If we say that r is a positive number, that means that it's not -r. Though it's value might still be 2 or -2, we don't know. Hence p=q=2 and r might be -2.
Following my concept, it would be clearer if the question said that the values of the positive integers are also positive.
Math Expert
Joined: 02 Sep 2009
Posts: 59561
Re: Are positive numbers p, q and r equal?  [#permalink]

### Show Tags

18 Oct 2013, 05:23
Skag55 wrote:
Bunuel wrote:

I don't understand what you mean.

I mean that a variable might be -ve or +ve so r might be -2 or 2.
And |r| might be +r or -r.
In case that r = 2 then -r = -2.
In case that r = -2 then -r = 2.

If we say that r is a positive number, that means that it's not -r. Though it's value might still be 2 or -2, we don't know. Hence p=q=2 and r might be -2.
Following my concept, it would be clearer if the question said that the values of the positive integers are also positive.

Sorry, but this does not make sense.

r is positive, it cannot be -2, because -2 is negative.
Manager
Joined: 26 Feb 2013
Posts: 147
Re: Are positive numbers p, q and r equal?  [#permalink]

### Show Tags

18 Oct 2013, 05:25
Skag55 wrote:
Bunuel wrote:

I don't understand what you mean.

I mean that a variable might be -ve or +ve so r might be -2 or 2.
And |r| might be +r or -r.
In case that r = 2 then -r = -2.
In case that r = -2 then -r = 2.

If we say that r is a positive number, that means that it's not -r. Though it's value might still be 2 or -2, we don't know. Hence p=q=2 and r might be -2.
Following my concept, it would be clearer if the question said that the values of the positive integers are also positive.

On the other hand I'm overly thinking about it.
p,q and r are not variables, are numbers.
Software development failed me.
Current Student
Joined: 18 Oct 2014
Posts: 796
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
Re: Are positive numbers p, q and r equal?  [#permalink]

### Show Tags

21 Jun 2016, 10:41
karthiksms wrote:
Are positive numbers p, q and r equal?

(1) p = q
(2) q^2 = r^2

What if p=2, q=2, r=sqroot4

then wouldn't it be E?

GMAT Club Tests m03q25

(1) p = q

Nothing about r. Not sufficient.

(2) q^2 = r^2

Nothing about p. Not sufficient.

Combining both statement=

p^2=q^2 = r^2

So the numbers can either be +ve or -ve. But it is given in the question that numbers are +ve.

Hence Sufficient.

C is the answer
_________________
I welcome critical analysis of my post!! That will help me reach 700+
Non-Human User
Joined: 09 Sep 2013
Posts: 13710
Re: Are positive numbers p, q and r equal?  [#permalink]

### Show Tags

21 Jan 2018, 06:10
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Are positive numbers p, q and r equal?   [#permalink] 21 Jan 2018, 06:10
Display posts from previous: Sort by

# Are positive numbers p, q and r equal?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne