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

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

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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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Manager
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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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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

Hope that helps

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Manager
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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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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

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Director
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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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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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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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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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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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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!).

[Reveal] Spoiler:
B

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# Rich Cohen

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Kudos [?]: 3530 [0], given: 173 Retired Moderator Joined: 12 Aug 2015 Posts: 2213 Kudos [?]: 876 [0], given: 602 Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink] ### Show Tags 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 _________________ Give me a hell yeah ...!!!!! Kudos [?]: 876 [0], given: 602 Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 1821 Kudos [?]: 940 [0], given: 3 Location: United States (CA) Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink] ### Show Tags 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 _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Kudos [?]: 940 [0], given: 3 Intern Joined: 08 Oct 2016 Posts: 12 Kudos [?]: 24 [0], given: 11 Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink] ### Show Tags 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? Kudos [?]: 24 [0], given: 11 EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 10158 Kudos [?]: 3530 [0], given: 173 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink] ### Show Tags 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. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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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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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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