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Math Expert V
Joined: 02 Sep 2009
Posts: 56307
Let x/y + w/z = 2. Then the value of y/x + z/w is  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 80% (01:29) correct 20% (01:25) wrong based on 67 sessions

### HideShow timer Statistics Let $$\frac{x}{y} + \frac{w}{z} = 2$$. Then the value of $$\frac{y}{x} + \frac{z}{w}$$ is

(A) 1/2
(B) 3/4
(C) 1
(D) 5
(E) It cannot be determined from the information given.

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CEO  V
Joined: 12 Sep 2015
Posts: 3857
Re: Let x/y + w/z = 2. Then the value of y/x + z/w is  [#permalink]

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Top Contributor
Bunuel wrote:
Let $$\frac{x}{y} + \frac{w}{z} = 2$$. Then the value of $$\frac{y}{x} + \frac{z}{w}$$ is

(A) 1/2
(B) 3/4
(C) 1
(D) 5
(E) It cannot be determined from the information given.

A fast approach is to identify values for w, x, y and z that satisfy the given equation, $$\frac{x}{y} + \frac{w}{z} = 2$$
One set of values is w = 1, x = 1, y = 1 and z = 1

Now plug these values into the target expression.
We get: $$\frac{y}{x} + \frac{z}{w} = \frac{1}{1} + \frac{1}{1}$$

$$= 1 + 1$$

$$= 2$$

Since 2 is not among the first four answer choices, the correct answer must be ....

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Joined: 24 Aug 2016
Posts: 804
Concentration: Entrepreneurship, Operations
GMAT 1: 630 Q48 V28 GMAT 2: 540 Q49 V16 Re: Let x/y + w/y = 2. Then the value of y/x + z/w is  [#permalink]

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Xin Cho wrote:
Let $$\frac{x}{y}$$ + $$\frac{w}{z}$$ = 2. Then the value of $$\frac{y}{x}$$ + $$\frac{z}{w}$$ is

A. 1/2
B. 3/4
C. 1z
D. 5
E. It cannot be determined from the information given.

Source: Nova's GMAT Prep Course (Chapter - Equations)

$$\frac{x}{y}$$ + $$\frac{w}{z}$$ = 2
or $$\frac{xz +yw}{yz}$$ = 2
or $${xz +yw}$$ = 2yz

Now, $$\frac{y}{x}$$ + $$\frac{z}{w}$$=$$\frac{yw+xz}{xw}$$ = $$\frac{2yz}{xw}$$..... Thus cannot be determined with given info......Option E
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MBA Section Director V
Affiliations: GMATClub
Joined: 22 May 2017
Posts: 2561
GPA: 4
WE: Engineering (Computer Software)
Re: Let x/y + w/y = 2. Then the value of y/x + z/w is  [#permalink]

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Let $$\frac{x}{y} = a$$ and $$\frac{w}{z} = b$$

=> a + b = 2

We need to find the value of $$\frac{1}{a} + \frac{1}{b}$$ = $$\frac{a+b}{ab}$$

We know the value of a + b but we don't know the value of a*b

Hence option E
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Joined: 29 May 2016
Posts: 9
Re: Let x/y + w/y = 2. Then the value of y/x + z/w is  [#permalink]

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Is the answer not A.1/2 because $$\frac{x}{y}$$ + $$\frac{w}{z}$$ is not reciprocal of $$\frac{y}{x}$$ + $$\frac{z}{w}$$?
MBA Section Director V
Affiliations: GMATClub
Joined: 22 May 2017
Posts: 2561
GPA: 4
WE: Engineering (Computer Software)
Re: Let x/y + w/y = 2. Then the value of y/x + z/w is  [#permalink]

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1
Xin Cho wrote:
Is the answer not A.1/2 because $$\frac{x}{y}$$ + $$\frac{w}{z}$$ is not reciprocal of $$\frac{y}{x}$$ + $$\frac{z}{w}$$?

$$\frac{x}{y}$$ + $$\frac{w}{z}$$ is NOT reciprocal of $$\frac{y}{x}$$ + $$\frac{z}{w}$$

$$\frac{x}{y}$$ + $$\frac{w}{z}$$ = $$\frac{xz+wy}{yz}$$ ------- 1

$$\frac{y}{x}$$ + $$\frac{z}{w}$$ = $$\frac{wy+xz}{xw}$$ -------- 2

1 and 2 are not reciprocal to each other.
_________________ Re: Let x/y + w/y = 2. Then the value of y/x + z/w is   [#permalink] 21 Jul 2018, 00:14
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# Let x/y + w/z = 2. Then the value of y/x + z/w is  