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GRE Math Challenge #123-If (1/4x)+1/y = 1/3(1/x + 1/y)
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15 May 2015, 12:04
15 May 2015, 12:04
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Question Stats:
79% (01:46) correct
20% (02:32) wrong based on 73 sessions
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If \(\frac{1}{4x} + \frac{1}{y}\)= \(\frac{1}{3}\) \(*\) \((\frac{1}{x} + \frac{1}{y})\), what is the ratio of x to y?
(A) 3 to 4
(B) 2 to 3
(C) 1 to 2
(D) 1 to 8
(E) 1 to 9
(A) 3 to 4
(B) 2 to 3
(C) 1 to 2
(D) 1 to 8
(E) 1 to 9
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
GRE Math Challenge #123-If (1/4x)+1/y = 1/3(1/x + 1/y)
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16 May 2015, 07:57
16 May 2015, 07:57
3
sandy wrote:
If \(\frac{1}{4x} + \frac{1}{y}\)= \(\frac{1}{3}\) \(*\) \((\frac{1}{x} + \frac{1}{y})\), what is the ratio of x to y?
(A) 3 to 4
(B) 2 to 3
(C) 1 to 2
(D) 1 to 8
(E) 1 to 9
(A) 3 to 4
(B) 2 to 3
(C) 1 to 2
(D) 1 to 8
(E) 1 to 9
GOAL: find the value of \(\frac{x}{y}\)
Given: \(\frac{1}{4x} + \frac{1}{y}\)= \(\frac{1}{3}\) \(*\) \((\frac{1}{x} + \frac{1}{y})\)
First expand right side to get: \(\frac{1}{4x}+\frac{1}{y} = \frac{1}{3x} + \frac{1}{3y}\)
Next, eliminate the fractions.
To do so, we'll examine the denominators - the least common multiple of \(4x\), \(y\), \(3x\) and \(3y\) is \(12xy\).
So, we'll multiply both sides of the equation by \(12xy\) to get: \(3y + 12x = 4y + 4x\)
Rearrange and simplify to get: \(8x = y\)
Divide both sides by \(y\) to get: \(\frac{8x}{y} = 1\)
Divide both sides by \(8\) to get: \(\frac{x}{y} = \frac{1}{8}\)
So, \(x : y = 1 : 8\)
Answer: D
Cheers,
Brent
Re: GRE Math Challenge #123-If (1/4x)+1/y = 1/3(1/x + 1/y)
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02 Dec 2021, 10:13
02 Dec 2021, 10:13
Expert Reply
Bumping for discussion. Try this one and get Kudos for a correct solution!!!!
