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

It is currently 22 Sep 2018, 00:46

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.

Close

Request Expert Reply

Confirm Cancel

If (x + 2)^2 = 9 and (y + 3)^2 = 25, then what is the maximum value of

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49300
If (x + 2)^2 = 9 and (y + 3)^2 = 25, then what is the maximum value of  [#permalink]

Show Tags

New post 11 Apr 2017, 23:46
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

61% (01:24) correct 39% (01:07) wrong based on 201 sessions

HideShow timer Statistics

Senior Manager
Senior Manager
User avatar
G
Joined: 19 Apr 2016
Posts: 274
Location: India
GMAT 1: 570 Q48 V22
GMAT 2: 640 Q49 V28
GPA: 3.5
WE: Web Development (Computer Software)
If (x + 2)^2 = 9 and (y + 3)^2 = 25, then what is the maximum value of  [#permalink]

Show Tags

New post 12 Apr 2017, 00:01
4
Bunuel wrote:
If (x + 2)^2 = 9 and (y + 3)^2 = 25, then what is the maximum value of x/y?

(A) 1/8
(B) 1/2
(C) 5/8
(D) 5/2
(E) 10/3


(x + 2)^2 = 9 ==> x can be 1 or -5
(y + 3)^2 = 25 ==> y can be 2 or -8

therefore the maximum value of x/y = -5/-8 = 5/8

Hence option C is correct
Hit Kudos if you liked it 8-)
CEO
CEO
User avatar
D
Joined: 12 Sep 2015
Posts: 2872
Location: Canada
Re: If (x + 2)^2 = 9 and (y + 3)^2 = 25, then what is the maximum value of  [#permalink]

Show Tags

New post 12 Apr 2017, 05:25
1
Top Contributor
Bunuel wrote:
If (x + 2)² = 9 and (y + 3)² = 25, then what is the maximum value of x/y?

(A) 1/8
(B) 1/2
(C) 5/8
(D) 5/2
(E) 10/3


(x + 2)² = 9
We have (something)² = 9
So, EITHER something = 3 OR something = -3
In other words, EITHER x + 2= 3 OR x + 2 = -3
If x + 2= 3. then x = 1
If x + 2= -3. then x = -5

(y + 3)² = 25
We have (something)² = 25
So, EITHER something = 5 OR something = -5
In other words, EITHER y + 3= 5 OR y + 3 = -5
If y + 3= 5, then y = 2
If y + 3= -5, then y = -8

We want to MAXIMIZE the value of x/y
If the x-value and y-value have OPPOSITE signs, x/y will be NEGATIVE
If the x-value and y-value have the SAME sign, x/y will be POSITIVE
So, need the x-value and y-value have the SAME sign

Try #1
x/y = 1/2

Try #2
x/y = (-5)/(-8) = 5/8

Since 5/8 is greater than 1/2, the correct answer is C

RELATED VIDEO

_________________

Brent Hanneson – GMATPrepNow.com
Image
Sign up for our free Question of the Day emails

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2835
Re: If (x + 2)^2 = 9 and (y + 3)^2 = 25, then what is the maximum value of  [#permalink]

Show Tags

New post 19 Apr 2017, 15:56
Bunuel wrote:
If (x + 2)^2 = 9 and (y + 3)^2 = 25, then what is the maximum value of x/y?

(A) 1/8
(B) 1/2
(C) 5/8
(D) 5/2
(E) 10/3


Let’s determine values for x and y.

(x + 2)^2 = 9

√(x + 2)^2 = √9

|x + 2| = 3

We need to determine the value of x when (x + 2) is positive and when (x + 2) is negative.

x + 2 = 3

x = 1

OR

-(x + 2) = 3

-x - 2 = 3

-x = 5

x = -5

So x = 1 or x = -5.

In a similar fashion, we determine the value of y.

(y + 3)^2 = 25

√(y + 3)^2 =√25

|y + 3| = 5

We need to determine the value of y when (y + 3) is positive and when (y + 3) is negative.

y + 3 = 5

y = 2

OR

-(y + 3) = 5

-y - 3 = 5

-y = 8

y = -8

y = 2 or y = -8

We can maximize the value of x/y if x and y are both positive or if x and y are both negative. If x and y are both positive, then x/y = 1/2. If x and y are both negative, then x/y = -5/-8 = 5/8. Since 5/8 > 1/2, the maximum value of x/y is 5/8.

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8136
Premium Member
Re: If (x + 2)^2 = 9 and (y + 3)^2 = 25, then what is the maximum value of  [#permalink]

Show Tags

New post 28 Jul 2018, 02:21
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: If (x + 2)^2 = 9 and (y + 3)^2 = 25, then what is the maximum value of &nbs [#permalink] 28 Jul 2018, 02:21
Display posts from previous: Sort by

If (x + 2)^2 = 9 and (y + 3)^2 = 25, then what is the maximum value of

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

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.