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If xy=4, x/y=36, for positive numbers x and y, y=?

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If xy=4, x/y=36, for positive numbers x and y, y=?  [#permalink]

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New post 27 Jun 2016, 17:41
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A
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C
D
E

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Question Stats:

92% (01:21) correct 8% (01:38) wrong based on 150 sessions

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If xy=4, x/y=36, for positive numbers x and y, y=?
A. 1/2
B. 2
C. 1/3
D. 3
E. 1/6

*Answer will be posted in 2 days.

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Re: If xy=4, x/y=36, for positive numbers x and y, y=?  [#permalink]

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New post 27 Jun 2016, 20:51
Very easy question. 2 variables and 2 easy equations.

xy=4 ---> x=4/y - (i)
x/y=36 ---> replacing (i) here ---> 4/(y^2)=36 ---> y^2=4/36=1/9 ---> y=1/3 or -1/3

The question states that x and y are positive integers. Therefore, y=1/3 is the answer.

Answer C.


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Re: If xy=4, x/y=36, for positive numbers x and y, y=?  [#permalink]

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New post 28 Jun 2016, 10:08
MathRevolution wrote:
If xy=4, x/y=36, for positive numbers x and y, y=?
A. 1/2
B. 2
C. 1/3
D. 3
E. 1/6

*Answer will be posted in 2 days.


\(\frac{x}{y}\)=36

So, x = 36y

Now, It is given ; xy=4

Or, \((36y)y\) = 4

Or, \((y^2 )6^2\) = \(2^2\)

Or, 6y = 2

Or, y = \(\frac{1}{3}\)

Hence answer will be (C)

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Re: If xy=4, x/y=36, for positive numbers x and y, y=?  [#permalink]

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New post 28 Jun 2016, 11:43
Top Contributor
MathRevolution wrote:
If xy=4, x/y=36, for positive numbers x and y, y=?

A. 1/2
B. 2
C. 1/3
D. 3
E. 1/6


Another approach is to check the answer choices.

A) y = 1/2
Since xy = 4, we can conclude that x = 8
If y = 1/2 and x = 8, then x/y = (8)/(1/2) = 16.
NOT GOOD, x/y is SUPPOSED to equal 36
ELIMINATE A

B) y = 2
Since xy = 4, we can conclude that x = 2
If y = 2 and x = 2, then x/y = 2/2 = 1.
NOT GOOD, x/y is SUPPOSED to equal 36
ELIMINATE B

C) y = 1/3
Since xy = 4, we can conclude that x = 12
If y = 1/3 and x = 12, then x/y = (12)/(1/3) = 36.
GREAT! x/y is SUPPOSED to equal 36
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Re: If xy=4, x/y=36, for positive numbers x and y, y=?  [#permalink]

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New post 28 Jun 2016, 15:04
(x/y)/xy=36/4
y^2=1/9
y=1/3
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Re: If xy=4, x/y=36, for positive numbers x and y, y=?  [#permalink]

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New post 28 Jun 2016, 15:05
Top Contributor
gracie wrote:
(x/y)/xy=36/4
y^2=1/9
y=1/3


Nice!
I love the different ways these kinds of questions can be solved.
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Re: If xy=4, x/y=36, for positive numbers x and y, y=?  [#permalink]

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New post 29 Jun 2016, 19:13
If we substitute in x=4/y, from 4/y^2 =36, we get y^2=1/9. Hence, y=1/3. Thus, the correct answer is C.
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Re: If xy=4, x/y=36, for positive numbers x and y, y=?   [#permalink] 29 Jun 2016, 19:13

If xy=4, x/y=36, for positive numbers x and y, y=?

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