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If the average (arithmetic mean) of x and y is 60 and the average (ari

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If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink]

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New post 01 Feb 2010, 17:51
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If the average (arithmetic mean) of x and y is 60 and the average (arithmetic mean) of y and z is 80, what is the value of \(z - x\)?

(a) 70
(b) 40
(c) 20
(d) 10
(e) It cannot be determined from the information given.
[Reveal] Spoiler: OA
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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink]

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New post 01 Feb 2010, 17:55
(X + Y)/2=60 (Z + Y)/2=80


So Z + Y=160
X+Y = 120
Subtract the equations

and we get Z - X (the Y's cancel) = 40

so answer choice B.

Hope that helps
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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink]

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New post 01 Feb 2010, 18:03
Write out the equations:

x + y = 120
y + z = 160

Get y alone:

y = 160 - z
y = 120 - x

Set them equal to one another and (z - x) appears:

160 - z = 120 - x
40 = z - x

Answer is B.
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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink]

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New post 01 Feb 2010, 21:45
roceeet wrote:
If the average (arithmetic mean) of x and y is 60 and the average (arithmetic mean) of y and z is 80, what is the value of \(z - x\)?

(a) 70
(b) 40
(c) 20
(d) 10
(e) It cannot be determined from the information given.


x+y= 120 & y+z = 160


z-x = 160-120 = 40

Therefore "B"
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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink]

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New post 02 Feb 2010, 10:22
Yes B ,

quite an easy question.
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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink]

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New post 02 Feb 2010, 15:50
thanks for the replies.
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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink]

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New post 18 Sep 2015, 21:30
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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink]

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New post 19 Sep 2015, 17:17
Hi All,

While most Test Takers would use an algebra approach to answer this question (which is fine), this prompt can also be solved by TESTing VALUES....

We're told that (X+Y)/2 = 60 and (Y+Z)/2 = 80. With a little algebra, we can rewrite these equations as...

X+Y = 120
Y+Z = 160

We're asked for the value of Z-X....

IF....
X = 60
Y = 60
Z = 100

So, Z-X = 100-60 = 40

No matter what values you TEST for X, Y and Z, the answer will always be the same (go ahead and try it and you'll see!).

Final Answer:
[Reveal] Spoiler:
B


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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink]

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New post 15 Dec 2016, 05:33
Here is my solution to this one

x+y=120
y+z=160

Hence z-x=160-120=40
Hence B

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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink]

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New post 19 Dec 2016, 10:56
roceeet wrote:
If the average (arithmetic mean) of x and y is 60 and the average (arithmetic mean) of y and z is 80, what is the value of \(z - x\)?

(a) 70
(b) 40
(c) 20
(d) 10
(e) It cannot be determined from the information given.


We are given that the average of x and y is 60. Thus:

(x + y)/2 = 60

x + y = 120

x = 120 - y

We are also given that the average of y and z is 80. Thus:

(y + z)/2 = 80

z = 160 - y

Since x = 120 - y and z = 160 - y:

z - x = 160 - y - (120 - y) = 160 - 120 = 40

Answer: B
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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink]

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New post 29 Dec 2016, 09:31
EMPOWERgmatRichC wrote:
Hi All,

While most Test Takers would use an algebra approach to answer this question (which is fine), this prompt can also be solved by TESTing VALUES....

We're told that (X+Y)/2 = 60 and (Y+Z)/2 = 80. With a little algebra, we can rewrite these equations as...

X+Y = 120
Y+Z = 160

We're asked for the value of Z-X....

IF....
X = 60
Y = 60
Z = 100

So, Z-X = 100-60 = 40

No matter what values you TEST for X, Y and Z, the answer will always be the same (go ahead and try it and you'll see!).

Final Answer:
[Reveal] Spoiler:
B


GMAT assassins aren't born, they're made,
Rich

What if I need to find the value of z-y. How to approach that?
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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink]

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New post 29 Dec 2016, 11:03
Hi voccubd,

Unfortunately, the 'design' of this question does NOT given you the necessary information to answer THAT question. You have to remember that NOTHING about a GMAT question is ever 'random' - the information that you're given is specific, the wording is specific and the numbers involved were specifically chosen by whoever wrote the prompt... to help you answer the specific question that is asked. The prompt would have to be rewritten for you to properly answer the question that you're asking about.

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Rich
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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink]

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New post 29 Dec 2016, 11:13
roceeet wrote:
If the average (arithmetic mean) of x and y is 60 and the average (arithmetic mean) of y and z is 80, what is the value of \(z - x\)?

(a) 70
(b) 40
(c) 20
(d) 10
(e) It cannot be determined from the information given.


x + y = 120
y + z = 160

So, z = 160 - y and y = 120 - x

Or, z = 160 - ( 120 - x )

Or, z = 160 - 120 + x

Or, z - x = 40

Hence, correct answer will be (B) 40

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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari   [#permalink] 29 Dec 2016, 11:13
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