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

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by Max@Math Revolution » Mon Jun 27, 2016 5:41 pm
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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by 800_or_bust » Tue Jun 28, 2016 10:56 am
Max@Math Revolution 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.
Given: (1) xy = 4; and (2) x/y = 36

From (2), solve for x by multiplying both sides of the equation by y: x = 36y

Now substitute this into the first equation: (36y)y = 4

36y^2 = 4
y^2 = 1/9
y = +/- 1/3

But we're told from the prompt that y must be positive, so +1/3 is the only possible solution. Answer choice: C
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by Brent@GMATPrepNow » Tue Jun 28, 2016 11:41 am
Max@Math Revolution 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 alternate 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
Answer: C
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by Max@Math Revolution » Wed Jun 29, 2016 7:13 pm
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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