Last visit was: 24 Apr 2026, 01:20 It is currently 24 Apr 2026, 01:20
Home
Messages
Tests
Schools
Events
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
Back to Forum
Create Topic
Sub 505 (Easy)|   Algebra|      
User avatar
faifai0714
User avatar
Joined: 02 Sep 2006
Last visit: 11 Apr 2007
Posts: 175
Own Kudos:
626
 [14]
Posts: 175
Kudos: 626
 [14]
If p&q = p^2 + q^2 – 2pq, for what value of q is p&q equal Updated on: 30 Jan 2014, 22:54
Originally posted by faifai0714 on 19 Mar 2007, 21:39.
Last edited by Bunuel on 30 Jan 2014, 22:54, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
2
Kudos
Add Kudos
12
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

5% (low)

Question Stats:

85% (01:17) correct 15% (01:54) wrong based on 515 sessions

History

Date
Time
Result
Not Attempted Yet
If p&q = p^2 + q^2 – 2pq, for what value of q is p&q equal to p^2 for all values of p?

A. -2
B. -1
C. 0
D. 1
E. 2
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 23 Apr 2026
Posts: 16,442
Own Kudos:
79,399
 [6]
Given Kudos: 485
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,442
Kudos: 79,399
 [6]
If p&q = p^2 + q^2 – 2pq, for what value of q is p&q equal 30 Jan 2014, 21:08
3
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
joshlevin90
techjanson
faifai0714
If p&q = p2 + q2 – 2pq, for what value of q is p&q equal to p2 for all values of p?

a)-2
b)-1
c)0
d)1
e)2

(p2=p to the power 2)

C

p2 + q2 – 2pq = p2
=> q2 - 2pq = 0
=> q (q - 2p) = 0
=> q = 0 or q = 2p

im not following the logic you used here.. how did you replace p&q with 0 could someone help explain it in MORE DETAIL
Show more

Given \(p&q = p^2 + q^2 - 2pq\) (I am assuming the sign before 2pq is '-')

We want the value of q such that \(p&q = p^2\)
i.e. \(p^2 + q^2 - 2pq = p^2\)
This means that \(q^2 - 2pq\) should be 0 so that left side becomes equal to right side.
If q = 0, both q^2 and 2pq will become 0.
or you can do it algebraically too: \(q^2 - 2pq = 0\)
\(q(q - 2p) = 0\)
So if q = 0 or if q = 2p, p&q will be equal to \(p^2\).

We have q = 0 in the options hence answer (C)
General Discussion
User avatar
ricokevin
User avatar
Joined: 11 Feb 2007
Last visit: 09 Jan 2009
Posts: 193
Own Kudos:
1,115
 [1]
Posts: 193
Kudos: 1,115
 [1]
If p&q = p^2 + q^2 – 2pq, for what value of q is p&q equal 20 Mar 2007, 00:49
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
p&q = p^2 + q^2 – 2pq = (p-q)^2
Therefore, if q = 0, p&q = p^2.

The answer is C.

:)
User avatar
claytont
User avatar
Joined: 18 Oct 2006
Last visit: 28 Feb 2010
Posts: 13
Own Kudos:
8
Posts: 13
Kudos: 8
If p&q = p^2 + q^2 – 2pq, for what value of q is p&q equal 20 Mar 2007, 18:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
C for me...

though I saw it could be factored, I just plugged 0 in for q to see what happened... lucky guess...

but yes, the approach above is what you would normally do
User avatar
techjanson
User avatar
Joined: 28 Feb 2007
Last visit: 18 May 2010
Posts: 103
Own Kudos:
55
Location: California
Posts: 103
Kudos: 55
If p&q = p^2 + q^2 – 2pq, for what value of q is p&q equal 21 Mar 2007, 16:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
faifai0714
If p&q = p2 + q2 – 2pq, for what value of q is p&q equal to p2 for all values of p?

a)-2
b)-1
c)0
d)1
e)2

(p2=p to the power 2)
Show more


C

p2 + q2 – 2pq = p2
=> q2 - 2pq = 0
=> q (q - 2p) = 0
=> q = 0 or q = 2p
avatar
joshlevin90
avatar
Joined: 22 Oct 2013
Last visit: 11 Dec 2014
Posts: 4
Given Kudos: 4
Posts: 4
Kudos: 0
If p&q = p^2 + q^2 – 2pq, for what value of q is p&q equal 30 Jan 2014, 18:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
techjanson
faifai0714
If p&q = p2 + q2 – 2pq, for what value of q is p&q equal to p2 for all values of p?

a)-2
b)-1
c)0
d)1
e)2

(p2=p to the power 2)

C

p2 + q2 – 2pq = p2
=> q2 - 2pq = 0
=> q (q - 2p) = 0
=> q = 0 or q = 2p
Show more

im not following the logic you used here.. how did you replace p&q with 0 could someone help explain it in MORE DETAIL
User avatar
lalania1
User avatar
Joined: 17 Nov 2013
Last visit: 04 May 2017
Posts: 63
Own Kudos:
297
Given Kudos: 19
Posts: 63
Kudos: 297
If p&q = p^2 + q^2 – 2pq, for what value of q is p&q equal 22 Nov 2016, 17:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I have a question, can i convert p^2 + 2pq + q^2 => (p + q)^2

If I use (p + q)^2, the I can solve the question much easier because at the end I see the below:

(square root(14) + square root(13) + square root(14) - square root(13))^2 => (square root(14) + square root(14))^2 =>
=> 14 + 2square root(14)square root(14) + 14 => 28 + 28 = 56

What are your thoughts?
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 23 Apr 2026
Posts: 16,442
Own Kudos:
79,399
Given Kudos: 485
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,442
Kudos: 79,399
If p&q = p^2 + q^2 – 2pq, for what value of q is p&q equal 23 Nov 2016, 03:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
lalania1
I have a question, can i convert p^2 + 2pq + q^2 => (p + q)^2

If I use (p + q)^2, the I can solve the question much easier because at the end I see the below:

(square root(14) + square root(13) + square root(14) - square root(13))^2 => (square root(14) + square root(14))^2 =>
=> 14 + 2square root(14)square root(14) + 14 => 28 + 28 = 56

What are your thoughts?
Show more

I don't understand your logic at all.

You are given that:
p&q = p^2 + q^2 - 2pq = p^2

So q^2 = 2pq
So q is either 0 or 2p.
User avatar
lalania1
User avatar
Joined: 17 Nov 2013
Last visit: 04 May 2017
Posts: 63
Own Kudos:
297
Given Kudos: 19
Posts: 63
Kudos: 297
If p&q = p^2 + q^2 – 2pq, for what value of q is p&q equal 24 Nov 2016, 07:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
thank you for your response. My apologies for the confusion.

in essence, my question is... is p^2 + 2pq + q^2 = (p + q)^2. if so, how would it work in making this question easier
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 2,974
Own Kudos:
8,710
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 2,974
Kudos: 8,710
If p&q = p^2 + q^2 – 2pq, for what value of q is p&q equal 13 Jun 2018, 16:26
Kudos
Add Kudos
Bookmarks
Bookmark this Post
faifai0714
If p&q = p^2 + q^2 – 2pq, for what value of q is p&q equal to p^2 for all values of p?

A. -2
B. -1
C. 0
D. 1
E. 2
Show more

We see that if q = 0, then p&0 = p^2 - 0^2 - 2p(0) = p^2. So q must be 0.

Alternate solution:

Notice that p^2 + q^2 - 2pq = (p - q)^2, so p&q = (p - q)^2. We see that if q = 0, then (p - q)^2 = p^2.

Answer: C
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,965
Own Kudos:
1,117
Posts: 38,965
Kudos: 1,117
If p&q = p^2 + q^2 – 2pq, for what value of q is p&q equal 12 Nov 2024, 02:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109802 posts
Krunaal
Tuck School Moderator
853 posts