## If x and y are positive, and 1/x percent of y equals 9y percent

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### If x and y are positive, and 1/x percent of y equals 9y percent

by [email protected] » Fri Jun 24, 2022 6:17 am

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## Global Stats

If x and y are positive, and 1/x percent of y equals 9y percent of x, what is the value of x?

(A) 1/81
(B) 1/3
(C) 3
(D) 9
(E) 81
Source: gmatprepnow.com

### GMAT/MBA Expert

GMAT Instructor
Posts: 16177
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### Re: If x and y are positive, and 1/x percent of y equals 9y percent

by [email protected] » Sat Jun 25, 2022 6:45 am
[email protected] wrote:
Fri Jun 24, 2022 6:17 am
If x and y are positive, and 1/x percent of y equals 9y percent of x, what is the value of x?

(A) 1/81
(B) 1/3
(C) 3
(D) 9
(E) 81
Source: gmatprepnow.com
Important concept: k% = k/100

So we can take our given information and write the following equation: [(1/x)/100](y) = (9y/100)(x)

Simplify: y/100x = 9xy/100

Multiply both sides of the equation by 100 to get: y/x = 9xy

Multiply both sides of the equation by x to get: y = 9x²y

Divide both sides by y to get: 1 = 9x²

Divide both sides by 9 to get: 1/9 = x², which means x = 1/3 or x = -1/3

Since we're told x is positive, we know that x = 1/3