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

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

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03 Jul 2017, 03:49
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Difficulty:

65% (hard)

Question Stats:

62% (01:24) correct 38% (02:10) wrong based on 121 sessions

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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

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Joined: 03 May 2017
Posts: 108
Re: What is the difference between the maximum and the minimum value of x/ [#permalink]

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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.
BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2839
Location: India
GPA: 3.12
What is the difference between the maximum and the minimum value of x/ [#permalink]

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03 Jul 2017, 04:07
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)
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Manager
Joined: 06 Sep 2016
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Location: Italy
Schools: EDHEC (A)
GMAT 1: 650 Q43 V37
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Re: What is the difference between the maximum and the minimum value of x/ [#permalink]

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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
BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2839
Location: India
GPA: 3.12
Re: What is the difference between the maximum and the minimum value of x/ [#permalink]

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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.
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Intern
Joined: 01 May 2017
Posts: 32
Re: What is the difference between the maximum and the minimum value of x/ [#permalink]

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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

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Intern
Joined: 26 Jun 2015
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Concentration: Entrepreneurship, General Management
WE: Engineering (Energy and Utilities)
Re: What is the difference between the maximum and the minimum value of x/ [#permalink]

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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

Intern
Joined: 17 Feb 2016
Posts: 14
Re: What is the difference between the maximum and the minimum value of x/ [#permalink]

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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?
Re: What is the difference between the maximum and the minimum value of x/   [#permalink] 12 Aug 2017, 22:44
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