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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If 1/x-1/y=1/z, what is the value of y, in terms of x and z? tagged by: Max@Math Revolution ##### This topic has 4 expert replies and 1 member reply ### GMAT/MBA Expert ## If 1/x-1/y=1/z, what is the value of y, in terms of x and z? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [GMAT math practice question] If 1/x-1/y=1/z, what is the value of y, in terms of x and z? A. xz/(z-x) B. xz/(x-z) C. x/z(z-x) D. z/x(x-z) E. xz(z-x) _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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Max@Math Revolution wrote:
[GMAT math practice question]

If 1/x-1/y=1/z, what is the value of y, in terms of x and z?

A. xz/(z-x)
B. xz/(x-z)
C. x/z(z-x)
D. z/x(x-z)
E. xz(z-x)
Let x=1 and y=3/2, with the result that 1/z = 1 - 2/3 = 1/3, so z=3.

Since the question stem asks for the value of y, the correct answer must yield 3/2 when x=1 and z=3.
Since B and D include x-z and thus will yield a negative result, eliminate B and D.
Since E includes only multiplication and thus cannot yield 3/2, eliminate E.
Of A and C, only A yields 3/2:
xz/(z-x) = (1*3)/(3-1) = 3/2.

The correct answer is A.

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Max@Math Revolution wrote:
[GMAT math practice question]

If 1/x - 1/y = 1/z, what is the value of y, in terms of x and z?

A. xz/(z-x)
B. xz/(x-z)
C. x/z(z-x)
D. z/x(x-z)
E. xz(z-x)
We can also solve the question algebraically.

GIVEN: 1/x - 1/y = 1/z
Multiply both sides by x to get: 1 - x/y = x/z
Multiply both sides by y to get: y - x = xy/z
Multiply both sides by z to get: yz - xz = yx
Rearrange to get y terms on one side: yz - yx = xz
Factor left side: y(z - x) = xz
Divide both sides by (z - x) to get: y = xz/(z - x)

Cheers,
Brent

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We are expressing y in terms of x and z
$$\frac{1}{x}-\frac{1}{y}=\frac{1}{z}$$
$$\frac{1}{x}=\frac{1}{z}+\frac{1}{y}$$
$$\frac{1}{x}-\frac{1}{z}=\frac{1}{y}$$
$$\frac{z-x}{xz}=\frac{1}{y}$$
Cross multiply and divide both sides by (z-x)
$$\frac{y\left(z-x\right)}{\left(z-x\right)}=\frac{xz}{z-x}$$
$$y=\frac{xz}{z-x}$$

$$answer\ is\ Option\ A$$

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Max@Math Revolution wrote:
[GMAT math practice question]

If 1/x-1/y=1/z, what is the value of y, in terms of x and z?

A. xz/(z-x)
B. xz/(x-z)
C. x/z(z-x)
D. z/x(x-z)
E. xz(z-x)
First, letâ€™s isolate the term 1/y:

1/y = 1/x - 1/z = (z - x)/xz

Now, letâ€™s take the reciprocal of each side:

y = xz/(z - x)

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Making y the subject of the equation 1/x - 1/y = 1/z yields 1/y = 1/x - 1/z = (z-x)/xz, and y = xz/(z-x).

Therefore, the answer is A.

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