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# If w-z/w = 3-5 2/5 , and neither w nor z is equal to zero,

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If w-z/w = 3-5 2/5 , and neither w nor z is equal to zero, [#permalink]  21 May 2019, 11:31
Expert's post
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Question Stats:

38% (01:14) correct 61% (01:04) wrong based on 18 sessions
If $$\frac{w-z}{w} = 3-5 \frac{2}{5}$$ , and neither w nor z is equal to zero, then $$\frac{w}{z} =$$

A. $$- \frac{5}{12}$$

B. $$- \frac{5}{17}$$

C. $$\frac{5}{17}$$

D. $$\frac{5}{12}$$

E. $$\frac{12}{17}$$
[Reveal] Spoiler: OA

_________________
GRE Instructor
Joined: 10 Apr 2015
Posts: 2387
Followers: 78

Kudos [?]: 2358 [0], given: 33

Re: If w-z/w = 3-5 2/5 , and neither w nor z is equal to zero, [#permalink]  11 Jun 2019, 06:45
Expert's post
Carcass wrote:
If $$\frac{w-z}{w} = 3-5 \frac{2}{5}$$ , and neither w nor z is equal to zero, then $$\frac{w}{z} =$$

A. $$- \frac{5}{12}$$

B. $$- \frac{5}{17}$$

C. $$\frac{5}{17}$$

D. $$\frac{5}{12}$$

E. $$\frac{12}{17}$$

Useful property: $$\frac{x-y}{z}=\frac{x}{z}-\frac{y}{z}$$

GIVEN: $$\frac{w-z}{w} = 3-5 \frac{2}{5}$$

Apply above property to rewrite left side: $$\frac{w}{w}-\frac{z}{w} = 3-5 \frac{2}{5}$$

Simplify both sides: $$1-\frac{z}{w} = \frac{15}{5}-\frac{27}{5}$$

Simplify right side: $$\frac{5}{5}-\frac{z}{w} = \frac{-12}{5}$$

Subtract $$\frac{5}{5}$$ from both sides: $$-\frac{z}{w} = \frac{-17}{5}$$

Multiply both sides by -1 to get: $$\frac{z}{w} = \frac{17}{5}$$

If $$\frac{z}{w} = \frac{17}{5}$$, then $$\frac{w}{z} = \frac{5}{17}$$

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Re: If w-z/w = 3-5 2/5 , and neither w nor z is equal to zero,   [#permalink] 11 Jun 2019, 06:45
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