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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42 GPA: 3.82
If 1/x-1/y=1/z, what is the value of y, in terms of x and z?  [#permalink]

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Difficulty:   15% (low)

Question Stats: 78% (01:12) correct 23% (02:24) wrong based on 40 sessions

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[GMAT math practice question]

If $$\frac{1}{x}-\frac{1}{y}=\frac{1}{z}$$, what is the value of $$y$$, in terms of $$x$$ and $$z$$?

$$A. \frac{xz}{(z-x)}$$
$$B. \frac{xz}{(x-z)}$$
$$C. \frac{x}{z(z-x)}$$
$$D. \frac{z}{x(x-z)}$$
$$E. xz(z-x)$$

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

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MathRevolution wrote:
[GMAT math practice question]

If $$\frac{1}{x}-\frac{1}{y}=\frac{1}{z}$$, what is the value of $$y$$, in terms of $$x$$ and $$z$$?

$$A. \frac{xz}{(z-x)}$$
$$B. \frac{xz}{(x-z)}$$
$$C. \frac{x}{z(z-x)}$$
$$D. \frac{z}{x(x-z)}$$
$$E. xz(z-x)$$

$$\frac{1}{x}-\frac{1}{y}=\frac{1}{z}$$

$$\frac{1}{x}-\frac{1}{z}=\frac{1}{y}$$

$$\frac{(z-x)}{zx}=\frac{1}{y}$$

Taking reciprocal at both sides.

$$\frac{zx}{(z-x)}=y$$

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Re: If 1/x-1/y=1/z, what is the value of y, in terms of x and z?  [#permalink]

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Asked y interms of x and z ,Therefore answer should be y= blah blah x blah blah z
1/x-1/y=1/z
Now let’s eliminate the denominators with the LCM (xyz)
( xyz)•1/(x) - (xyz)•1/y= (xyz)•1/z
yz - xz = xy
yz -xy = xz
y(z - x) = xz
y = xz/(z - x)

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Re: If 1/x-1/y=1/z, what is the value of y, in terms of x and z?  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

If $$\frac{1}{x}-\frac{1}{y}=\frac{1}{z}$$, what is the value of $$y$$, in terms of $$x$$ and $$z$$?

$$A. \frac{xz}{(z-x)}$$
$$B. \frac{xz}{(x-z)}$$
$$C. \frac{x}{z(z-x)}$$
$$D. \frac{z}{x(x-z)}$$
$$E. xz(z-x)$$

Let $$x=1$$ and $$y=\frac{3}{2}$$, with the result that $$\frac{1}{z} = 1 - \frac{2}{3} = \frac{1}{3}$$, so $$z=3$$.

Since the question stem asks for the value of y, the correct answer must yield $$\frac{3}{2}$$ 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 $$\frac{3}{2}$$, eliminate E.
Between A and C, only A yields $$\frac{3}{2}$$:
$$\frac{xz}{z-x} = \frac{1*3}{3-1} = \frac{3}{2}$$

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If 1/x-1/y=1/z, what is the value of y, in terms of x and z?  [#permalink]

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=>
Making $$y$$ the subject of the equation $$\frac{1}{x} – \frac{1}{y} = \frac{1}{z}$$ yields $$\frac{1}{y} = \frac{1}{x} – \frac{1}{z} = \frac{(z-x)}{xz}$$, and $$y = \frac{xz}{(z-x)}.$$

Therefore, the answer is A.
_________________ Re: If 1/x-1/y=1/z, what is the value of y, in terms of x and z?   [#permalink] 24 Feb 2019, 07:00
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