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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If x and y are positive, and 1/x percent of y equals 9y percent
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24 Jun 2022, 06:16
24 Jun 2022, 06:16
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If \(x\) and \(y\) are positive, and \(\frac{1}{x}\) percent of \(y\) equals \(9y\) percent of \(x\), what is the value of \(\)x?
(A) \(\frac{1}{81}\)
(B) \(\frac{1}{3}\)
(C) \(3\)
(D) \(9\)
(E) \(81\)
(A) \(\frac{1}{81}\)
(B) \(\frac{1}{3}\)
(C) \(3\)
(D) \(9\)
(E) \(81\)
Re: If x and y are positive, and 1/x percent of y equals 9y percent
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24 Jun 2022, 16:40
24 Jun 2022, 16:40
GreenlightTestPrep, can you please post an explanation for this question?
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If x and y are positive, and 1/x percent of y equals 9y percent
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25 Jun 2022, 06:49
25 Jun 2022, 06:49
1
GreenlightTestPrep wrote:
If \(x\) and \(y\) are positive, and \(\frac{1}{x}\) percent of \(y\) equals \(9y\) percent of \(x\), what is the value of \(\)x?
(A) \(\frac{1}{81}\)
(B) \(\frac{1}{3}\)
(C) \(3\)
(D) \(9\)
(E) \(81\)
(A) \(\frac{1}{81}\)
(B) \(\frac{1}{3}\)
(C) \(3\)
(D) \(9\)
(E) \(81\)
Important concept: k% = \(\frac{k}{100}\)
So we can take our given information and write the following equation: \(\frac{\frac{1}{x}}{100}y = \frac{9y}{100}x\)
Simplify: \(\frac{y}{100x }= \frac{9xy}{100}\)
Cross multiply: \(900x^2y = 100y\)
Divide both sides by \(100y\) to get: \(9x^2 = 1\)
Divide both sides by \(9\) to get: \(x^2 = \frac{1}{9}\), which means \(x = \frac{1}{3}\) or \(x = -\frac{1}{3}\)
Since we're told \(x\) is positive, we know that \(x = \frac{1}{3}\)
Answer: B
