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

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

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New post 03 Jul 2017, 03:49
2
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A
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D
E

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
Spoiler: OA

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Re: What is the difference between the maximum and the minimum value of x/ [#permalink]

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New post 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.
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What is the difference between the maximum and the minimum value of x/ [#permalink]

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New post 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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Re: What is the difference between the maximum and the minimum value of x/ [#permalink]

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New post 03 Jul 2017, 06:43
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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 :wink:
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Re: What is the difference between the maximum and the minimum value of x/ [#permalink]

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New post 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 :wink:


Damn, I have to proof read my solution.
Thanks a ton. Made the necessary change.
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Re: What is the difference between the maximum and the minimum value of x/ [#permalink]

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New post 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.

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Re: What is the difference between the maximum and the minimum value of x/ [#permalink]

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New post 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.

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Re: What is the difference between the maximum and the minimum value of x/ [#permalink]

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New post 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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