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Multiple Variable Expression

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Source: — Problem Solving |

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by Brent@GMATPrepNow » Thu May 29, 2014 6:20 am
jsche229 wrote:Please help me solve the following expression for y: Thanks!

(1/x) + (1/5y) = (1/2z)
First, we can eliminate all of the fractions by multiplying both sides of the equation by the LOWEST COMMON MULTIPLE (LCM) of x, 5y and 2z. The LCM is 10xyz.

When we multiply both sides 10xyz, we get: 10yz + 2xz = 5xy
Rearrange to get the y-terms on one side: 10yz - 5xy = -2xz
Factor out the y to get: y(10z - 5x) = -2xz
Divide both sides by (10z - 5x) to get: y = -2xz/(10z - 5x)

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by GMATGuruNY » Thu May 29, 2014 6:42 am
jsche229 wrote:Please help me solve the following expression for y: Thanks!

(1/x)+(1/5Y)=(1/2z)
Below is an alternate approach.

Isolate the expression with y:
1/(5y) = 1/(2z) - 1/x

Put the right side over a common denominator:
1/(5y) = (x - 2z)/(2xz)

Take the reciprocal of both sides:
5y = 2xz/(x - 2z)

Divide each side by 5:
y = 2xz/(5x - 10z)
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by GMATGuruNY » Thu May 29, 2014 7:38 am
jsche229 wrote:Please help me solve the following expression for y: Thanks!

(1/x)+(1/5Y)=(1/2z)
Since the GMAT would provide answer choices, an alternate approach would be to plug in values for x and z and get a target value for y.

Let x=5 and z=2.
The equation becomes:
1/5 + 1/(5y) = 1/4
1/(5y) = 1/4 - 1/5
1/(5y) = 5/20 - 4/20
1/(5y) = 1/20
y = 4.

The target value is y=4.
Now plug x=5 and z=2 into the answer choices to see which yields our target value of 4.

Answer choice: 2xz/(5x - 10z)
(2*5*2)/(5*5 - 10*2) = 20/5 = 4.
Success!
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