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

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Thu Feb 21, 2019 10:59 pm

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[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)

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Feb 22, 2019 4:28 am

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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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Feb 22, 2019 6:05 am

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)

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

by deloitte247 » Sun Feb 24, 2019 4:01 am

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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Scott@TargetTestPrep: GMAT Instructor; Posts: 8156; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sun Feb 24, 2019 5:32 am

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, let's isolate the term 1/y:

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

Now, let's take the reciprocal of each side:

y = xz/(z - x)

Answer: A

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Sun Feb 24, 2019 5:39 am

=>
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.
Answer: A

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