MBA Spotlight – The Biggest MBA Fair is June 13-14
close
It is currently 29 May 2023, 02:50
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
New comers' posts

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

M06-08

7 posts Go to First Unread Post
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 88712
CAT Tests Forum Quiz Mode Top Member of the Month
M06-08 [#permalink] New post  16 Sep 2014, 00:27
7
Kudos
88
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

95% (hard)

Question Stats:

45% (02:42) correct 55% (02:44) wrong based on 638 sessions

Hide Show timer Statistics

If \(q^2 + pr = 10\) and \(r^2 + pq = 10\), and \(r \ne q\), what is the value of \(p^2 + q^2 + r^2?\)

A. 10
B. 15
C. 20
D. 25
E. 30
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.

_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
Most Helpful Expert Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 88712
CAT Tests Forum Quiz Mode Top Member of the Month
Re M06-08 [#permalink] New post  16 Sep 2014, 00:27
11
Kudos
12
Bookmarks
Expert Reply
Official Solution:

If \(q^2 + pr = 10\) and \(r^2 + pq = 10\), and \(r \ne q\), what is the value of \(p^2 + q^2 + r^2?\)

A. 10
B. 15
C. 20
D. 25
E. 30


Given:

(1): \(q^2 + pr = 10\);

(2): \(r^2 + pq = 10\)

Subtract (2) from (1):

\(q^2 + pr - r^2 - pq= 0\)

\(q^2 - r^2 + pr - pq= 0\)

\((q - r)(q + r) - p(q - r)= 0\)

\((q-r)(q+ r - p)= 0\)

Since it is given that \(q - r \ne 0\), we can safely divide the equation by it to obtain: \(q+r - p = 0\), which can be rewritten as \(p = q+r\)

Now, sum (1) and (2):

\(q^2 + pr + r^2 + pq= 20\)

\(q^2 + r^2 + p(r + q) = 20\)

Since we found that \(p = q+ r\), then:

\(r^2 + q^2 + p(r + q) = 20\)

\(r^2 + q^2 + p^2= 20\)


Answer: C
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
General Discussion
User avatar
Senthil7
Senior Manager
Senior Manager
Joined: 31 Mar 2016
Posts: 330
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE:Operations (Commercial Banking)
GMAT ToolKit User
Re: M06-08 [#permalink] New post  05 Aug 2016, 03:48
I think this is a high-quality question and I agree with explanation. Brilliant Algebraic manipulation question!
avatar
anuragpokhariyal
Intern
Intern
Joined: 30 Dec 2016
Posts: 1
Re: M06-08 [#permalink] New post  31 Dec 2016, 00:07
1
Bookmarks
I think this is a high-quality question and I agree with explanation. real good question
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 88712
CAT Tests Forum Quiz Mode Top Member of the Month
Re: M06-08 [#permalink] New post  09 May 2023, 03:04
Expert Reply
I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
avatar
B
saby1410
Manager
Manager
Joined: 06 Feb 2017
Posts: 173
Location: India
CAT Tests
Re: M06-08 [#permalink] New post  21 May 2023, 01:35
Bunuel wrote:
I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

Bunuel

i wasn't able to figure out this question under time limit.is there any type of standard process to deal this type of question or has to go with manipulation.if not any tips to solve this type of problems.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 88712
CAT Tests Forum Quiz Mode Top Member of the Month
Re: M06-08 [#permalink] New post  21 May 2023, 03:16
Expert Reply
saby1410 wrote:
Bunuel wrote:
I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

Bunuel

i wasn't able to figure out this question under time limit.is there any type of standard process to deal this type of question or has to go with manipulation.if not any tips to solve this type of problems.


7. Algebra



For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
GMAT Club Bot
gmatclubot
Re: M06-08 [#permalink]
21 May 2023, 03:16
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderator:
Bunuel
Math Expert
88712 posts

cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions