It is currently 20 Oct 2017, 17:17
Search
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
Unanswered

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 Workbook Learn more
Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar
CLICK HERE TO HIDE/SHOW EVENTS

If x and y are numbers such that (x+9)(y-9)=0, what is the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
  Sort by Date Sort by Kudos  
Search for:
 
Print view
First unread post
Author Message
TAGS:

Hide Tags
1 KUDOS received
Intern
Intern
avatar
Joined: 10 Sep 2013
Posts: 6

Kudos [?]: 13 [1], given: 1

If x and y are numbers such that (x+9)(y-9)=0, what is the [#permalink]

Show Tags

New post 15 Sep 2013, 12:35
1
This post received
KUDOS
6
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

70% (00:50) correct 30% (02:06) wrong based on 228 sessions

HideShow timer Statistics

If x and y are numbers such that (x+9)(y-9)=0, what is the smallest possible value of x^2 + y^2

A. 0
B. 9
C. 18
D. 81
E. 162

I understand its a basic question, but I fail to understand the concept. I simply put x+9=0, so x=-9. in the same way, y-9=0, so y=9
so x^2 + y^2 = 81+81=162
what am I doing wrong?
[Reveal] Spoiler: OA

Last edited by Bunuel on 15 Sep 2013, 12:37, edited 1 time in total.
Edited the question.

Kudos [?]: 13 [1], given: 1

Expert Post
4 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129035 [4], given: 12187

Premium Member CAT Tests
Top Member of the Month
Re: If x and y are numbers such that (x+9)(y-9)=0, what is the [#permalink]

Show Tags

New post 15 Sep 2013, 12:41
4
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
sandra123 wrote:
If x and y are numbers such that (x+9)(y-9)=0, what is the smallest possible value of x^2 + y^2

A. 0
B. 9
C. 18
D. 81
E. 162

I understand its a basic question, but I fail to understand the concept. I simply put x+9=0, so x=-9. in the same way, y-9=0, so y=9
so x^2 + y^2 = 81+81=162
what am I doing wrong?


From (x+9)(y-9)=0 it follows that either x=-9 or y=9. Thus either x^2=81 or y^2=81.

Now, if x^2=81, then the least value of y^2 is 0, so the least value of x^2 + y^2 = 81 + 0 = 81.
Similarly if y^2=81, then the least value of x^2 is 0, so the least value of x^2 + y^2 = 0 + 81 = 81.

Answer: D.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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. ,11 Mixed Questions, 12 Fresh Meat

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., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 129035 [4], given: 12187

1 KUDOS received
Intern
Intern
avatar
Joined: 07 Sep 2013
Posts: 25

Kudos [?]: 13 [1], given: 0

Concentration: Entrepreneurship
GPA: 3.52
Re: If x and y are numbers such that (x+9)(y-9)=0, what is the [#permalink]

Show Tags

New post 15 Sep 2013, 17:49
1
This post received
KUDOS
In the given equation, if x = -9 then y could = ANYTHING

If y = 9, then x could = ANYTHING

They DON'T BOTH have to be true at the same time.

9^2 + 0^2 = 81

Choose
[Reveal] Spoiler:
D


t1000

Kudos [?]: 13 [1], given: 0

Intern
Intern
avatar
Joined: 04 Dec 2012
Posts: 8

Kudos [?]: [0], given: 7

Schools: ISB '15
Re: If x and y are numbers such that (x+9)(y-9)=0, what is the [#permalink]

Show Tags

New post 22 Sep 2013, 05:26
sandra123 wrote:
If x and y are numbers such that (x+9)(y-9)=0, what is the smallest possible value of x^2 + y^2

A. 0
B. 9
C. 18
D. 81
E. 162

I understand its a basic question, but I fail to understand the concept. I simply put x+9=0, so x=-9. in the same way, y-9=0, so y=9
so x^2 + y^2 = 81+81=162
what am I doing wrong?


This question could me solved in this way.

(x+9)(x-9) = 0
=> xy - 81 = 9(x-y)
=> (x-y) = (xy/9) - 9
=> Squaring on both sides and cancelling equal terms
=> x^2 + y^2 = (xy)^2/81 + 81

Notice that 81 is added to (xy)^2/81, so the absolute minimum value of the above expression will be equal to 81 when x=9 and y=9 => x^2 + y^2 = 162.

Kudos [?]: [0], given: 7

Manager
Manager
User avatar
S
Joined: 22 May 2015
Posts: 74

Kudos [?]: 15 [0], given: 22

Re: If x and y are numbers such that (x+9)(y-9)=0, what is the [#permalink]

Show Tags

New post 04 Sep 2017, 08:54
Since (x+9)(y-9) = 0 => x= -9 OR y=9

If x= -9 => X^2 = 81
The smallest value y can now take is y =0
Hence x^2+y^2 = 81

Same is the case with Y=9
_________________

Consistency is the Key

Kudos [?]: 15 [0], given: 22

Re: If x and y are numbers such that (x+9)(y-9)=0, what is the   [#permalink] 04 Sep 2017, 08:54
Print view
First unread post
Display posts from previous: Sort by

If x and y are numbers such that (x+9)(y-9)=0, what is the

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

Moderators: Engr2012, mikemcgarry, Abhishek009, VeritasPrepKarishma, Skywalker18, msk0657, abhimahna, Bunuel, Vyshak

Search for:


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions