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

 It is currently 18 Oct 2018, 15:25

### 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

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

# What is the difference between the maximum and the minimum value of x/

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50000
What is the difference between the maximum and the minimum value of x/  [#permalink]

### Show Tags

03 Jul 2017, 03:49
2
1
1
00:00

Difficulty:

55% (hard)

Question Stats:

64% (01:45) correct 36% (02:11) wrong based on 142 sessions

### HideShow timer Statistics

What is the difference between the maximum and the minimum value of x/y for which (x − 2)^2 = 9 and (y − 3)^2 = 25?

(A) −15/8
(B) 3/4
(C) 9/8
(D) 19/8
(E) 25/8

_________________
Manager
Joined: 03 May 2017
Posts: 99
Re: What is the difference between the maximum and the minimum value of x/  [#permalink]

### Show Tags

03 Jul 2017, 04:04
x= -1, 5
y= -2, 8
Max x/y = 5/8 ; Min x/y = -5/2
Difference = 25/8
E.
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3187
Location: India
GPA: 3.12
What is the difference between the maximum and the minimum value of x/  [#permalink]

### Show Tags

03 Jul 2017, 04:07
1
Given data : $$(x − 2)^2 = 9$$ and $$(y − 3)^2 = 25$$

To find the difference between the maximum and minimum values of \frac{x}{y}

$$(x − 2)^2 = 9 -> (x-2) = 3$$ or $$(x-2) = -3$$
Maximum value of x : 5
Minimum value of x : -1

$$(y − 3)^2 = 25 -> (y-3) = 5$$ or $$(y-3) = -5$$
Maximum value of y : 8
Minimum value of y : -2

Maximum value of $$\frac{x}{y} = \frac{5}{8}$$, Minimum value of $$\frac{x}{y} = \frac{5}{-2}$$

Difference is $$\frac{5}{8} - (\frac{-5}{2}) = \frac{25}{8}$$(Option E)
_________________

You've got what it takes, but it will take everything you've got

Manager
Joined: 06 Sep 2016
Posts: 134
Location: Italy
Schools: EDHEC (A)
GMAT 1: 650 Q43 V37
GPA: 3.2
WE: General Management (Human Resources)
Re: What is the difference between the maximum and the minimum value of x/  [#permalink]

### Show Tags

03 Jul 2017, 06:43
1
pushpitkc wrote:
Given data : $$(x − 2)^2 = 9$$ and $$(y − 3)^2 = 25$$

To find the difference between the maximum and minimum values of \frac{x}{y}

$$(x − 2)^2 = 9 -> (x-2) = 3$$ or $$(x-2) = -3$$
Maximum value of x : 5
Minimum value of x : -1

$$(y − 3)^2 = 25 -> (y-3) = 5$$ or $$(y-3) = -5$$
Maximum value of y : 8
Minimum value of y : -2

Maximum value of $$\frac{x}{y} = \frac{5}{8}$$, Minimum value of $$\frac{x}{y} = \frac{5}{-2}$$

Difference is $$\frac{5}{8} - (\frac{-5}{2}) = \frac{25}{8}$$(Option D)

It's option E
I used the same method
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3187
Location: India
GPA: 3.12
Re: What is the difference between the maximum and the minimum value of x/  [#permalink]

### Show Tags

03 Jul 2017, 06:48
MvArrow wrote:
pushpitkc wrote:
Given data : $$(x − 2)^2 = 9$$ and $$(y − 3)^2 = 25$$

To find the difference between the maximum and minimum values of \frac{x}{y}

$$(x − 2)^2 = 9 -> (x-2) = 3$$ or $$(x-2) = -3$$
Maximum value of x : 5
Minimum value of x : -1

$$(y − 3)^2 = 25 -> (y-3) = 5$$ or $$(y-3) = -5$$
Maximum value of y : 8
Minimum value of y : -2

Maximum value of $$\frac{x}{y} = \frac{5}{8}$$, Minimum value of $$\frac{x}{y} = \frac{5}{-2}$$

Difference is $$\frac{5}{8} - (\frac{-5}{2}) = \frac{25}{8}$$(Option D)

It's option E
I used the same method

Damn, I have to proof read my solution.
Thanks a ton. Made the necessary change.
_________________

You've got what it takes, but it will take everything you've got

Intern
Joined: 01 May 2017
Posts: 31
Re: What is the difference between the maximum and the minimum value of x/  [#permalink]

### Show Tags

03 Jul 2017, 09:33
Taking square root on both sides and considering both positive and negative roots into consideration, x= -1, 5

Similarly, Taking square root on both sides and considering both positive and negative roots into consideration, y= -2, 8

Four values of x/y are possible : (1/2), (-1/8), (5/-2) & (5/8).

Of these, Max x/y = 5/8 ; Min x/y = -5/2

Difference = 25/8

Option E is the answer.

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
Intern
Joined: 26 Jun 2015
Posts: 37
Location: India
Concentration: Entrepreneurship, General Management
WE: Engineering (Energy and Utilities)
Re: What is the difference between the maximum and the minimum value of x/  [#permalink]

### Show Tags

03 Jul 2017, 10:15
If you solve respective equations for x and y, you will get as below.
X = 5 and -1
Y = 8 and -2
Just arrange all four combinations of x and y for our understanding of which is least and which is highest.

5/8, 5/-2, -1/8, -1/-2

Lowest (Most negative) is 5/-2 i.e. -2/5 and Highest is 5/8
So, 5/8 - ( -5/2) = 25/8
Hence answer is E.

Intern
Joined: 17 Feb 2016
Posts: 13
Re: What is the difference between the maximum and the minimum value of x/  [#permalink]

### Show Tags

12 Aug 2017, 22:44
pushpitkc wrote:
Given data : $$(x − 2)^2 = 9$$ and $$(y − 3)^2 = 25$$

To find the difference between the maximum and minimum values of \frac{x}{y}

$$(x − 2)^2 = 9 -> (x-2) = 3$$ or $$(x-2) = -3$$
Maximum value of x : 5
Minimum value of x : -1

$$(y − 3)^2 = 25 -> (y-3) = 5$$ or $$(y-3) = -5$$
Maximum value of y : 8
Minimum value of y : -2

Maximum value of $$\frac{x}{y} = \frac{5}{8}$$, Minimum value of $$\frac{x}{y} = \frac{5}{-2}$$

Difference is $$\frac{5}{8} - (\frac{-5}{2}) = \frac{25}{8}$$(Option E)

was thinking if we need to make x/y maximum, dont we have to divide x as max and y as min i.e 5/-2 and similarly for x/y to be min , x min. and y max i.e. -1/8 and then take the difference?
Director
Joined: 13 Mar 2017
Posts: 622
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: What is the difference between the maximum and the minimum value of x/  [#permalink]

### Show Tags

04 Oct 2018, 12:21
Bunuel wrote:
What is the difference between the maximum and the minimum value of x/y for which (x − 2)^2 = 9 and (y − 3)^2 = 25?

(A) −15/8
(B) 3/4
(C) 9/8
(D) 19/8
(E) 25/8

(x − 2)^2 = 9
x - 2 = +/- 3
x = 5, -1

and

(y − 3)^2 = 25
y - 3 = +/- 5
y = 8, -2

So, min. value of x/y = min. { -5/2, -1/8} = -5/2
max. value of x/y = max. {5/8, 1/2} = 5/8

Difference between the two values = 5/8 - (-5/2) = 5/8 + 5/2 = 5/8 (1+4) = 25/8

Answer : (E) 25/8
_________________

CAT 2017 99th percentiler : VA 97.27 | DI-LR 96.84 | QA 98.04 | OA 98.95
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".

Re: What is the difference between the maximum and the minimum value of x/ &nbs [#permalink] 04 Oct 2018, 12:21
Display posts from previous: Sort by

# What is the difference between the maximum and the minimum value of x/

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

 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®.