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# If 4/w + 4/x = 4/y and wx = y, then the average (arithmetic mean) of

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Math Expert
Joined: 02 Sep 2009
Posts: 46305
If 4/w + 4/x = 4/y and wx = y, then the average (arithmetic mean) of [#permalink]

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26 Feb 2015, 06:32
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Difficulty:

15% (low)

Question Stats:

76% (00:48) correct 24% (01:28) wrong based on 125 sessions

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If 4/w + 4/x = 4/y and wx = y, then the average (arithmetic mean) of w and x is

A. 1/2
B. 1
C. 2
D. 4
E. 8

Kudos for a correct solution.

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Math Expert
Joined: 02 Aug 2009
Posts: 5952
Re: If 4/w + 4/x = 4/y and wx = y, then the average (arithmetic mean) of [#permalink]

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26 Feb 2015, 06:37
1
Bunuel wrote:
If 4/w + 4/x = 4/y and wx = y, then the average (arithmetic mean) of w and x is

A. 1/2
B. 1
C. 2
D. 4
E. 8

Kudos for a correct solution.

ans A..1/2
4/w + 4/x = 4/y..
4/w + 4/x = 4/wx as wx=y..
simplifying (4x+4w)/wx=4/wx...
4x +4w=4..
x+w=1 or (x+w)/2=1/2...
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Re: If 4/w + 4/x = 4/y and wx = y, then the average (arithmetic mean) of [#permalink]

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26 Feb 2015, 16:24
1
Bunuel wrote:
If 4/w + 4/x = 4/y and wx = y, then the average (arithmetic mean) of w and x is

A. 1/2
B. 1
C. 2
D. 4
E. 8

Kudos for a correct solution.

Given: 4/w + 4/x = 4/y & wx=y
Find: (w+x)/2 = ?

4(1/w + 1/x) = 4(1/y) - divide both sides by 4
(1/w + 1/x) = 1/y
(x+w)/wx = 1/wx - sub'd in y=wx
x+w - 1 = 0
x+w = 1

Therefore (w+x)/2 = 1/2

Ans: A
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Re: If 4/w + 4/x = 4/y and wx = y, then the average (arithmetic mean) of [#permalink]

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26 Feb 2015, 18:42
2

$$\frac{4}{w} + \frac{4}{x} = \frac{4}{y}$$

$$\frac{w+x}{wx} = \frac{1}{y}$$

w+x = 1

$$\frac{w+x}{2} = \frac{1}{2}$$
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Re: If 4/w + 4/x = 4/y and wx = y, then the average (arithmetic mean) of [#permalink]

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28 Feb 2015, 04:41
Bunuel wrote:
If 4/w + 4/x = 4/y and wx = y, then the average (arithmetic mean) of w and x is

A. 1/2
B. 1
C. 2
D. 4
E. 8

Kudos for a correct solution.

Given that 4/w + 4/x = 4/y
Taking LCM,
[4x + 4w] / [wx] = 4/y
So, (w+x)/(wx) = 1/y
Put wx = y
So, (w+x)/(y) = 1/y
So, w+x = 1
We need (w+x)/2
Hence (w+x)/2 = 1/2

So option A.
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Math Expert
Joined: 02 Sep 2009
Posts: 46305
Re: If 4/w + 4/x = 4/y and wx = y, then the average (arithmetic mean) of [#permalink]

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02 Mar 2015, 06:03
Bunuel wrote:
If 4/w + 4/x = 4/y and wx = y, then the average (arithmetic mean) of w and x is

A. 1/2
B. 1
C. 2
D. 4
E. 8

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment:

averageofwandx_text.PNG [ 14.82 KiB | Viewed 2527 times ]

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Re: If 4/w + 4/x = 4/y and wx = y, then the average (arithmetic mean) of [#permalink]

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20 Mar 2017, 00:43
Bunuel wrote:
If 4/w + 4/x = 4/y and wx = y, then the average (arithmetic mean) of w and x is

A. 1/2
B. 1
C. 2
D. 4
E. 8

Kudos for a correct solution.

4/w + 4/x = 4/y
solving this we get
(w+x)/wx = 1/y
or w +x = wx/y

since wx = y, we can say that
w+x = 1
or (w+x)/2= 1/2

Option A
Re: If 4/w + 4/x = 4/y and wx = y, then the average (arithmetic mean) of   [#permalink] 20 Mar 2017, 00:43
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