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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If the average (arithmetic mean) of x and y is 60 and the average (ari

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Intern  Joined: 08 Sep 2006
Posts: 39
If the average (arithmetic mean) of x and y is 60 and the average (ari  [#permalink]

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4
5 00:00

Difficulty:   5% (low)

Question Stats: 85% (00:55) correct 15% (01:05) wrong based on 490 sessions

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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.
CEO  Joined: 07 Jul 2004
Posts: 2917
Location: Singapore
Re: If the average (arithmetic mean) of x and y is 60 and the average (ari  [#permalink]

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1
(x+y)/2 = 60
x+y = 120 ---

(y+z)/2 = 80
y+z = 160 ---

-
z-x = 40
Intern  Joined: 08 Sep 2006
Posts: 31
Re: If the average (arithmetic mean) of x and y is 60 and the average (ari  [#permalink]

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tinman1412 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.

This question is from the OG 10, but I do not understand their explanation. Hopefully someone can give me their approach.

Thanks,

I did this problem a couple of ways but it is essential the same as other posters.

(x+y)/2 = 60 (from avg formula)
(y+z)/2 = 80 (from avg formula)

set both equal to each other but we need to subtract 20 from 2nd equation to ensure they are equal (60):

(x+y)/2 = (y+z)/2 - 20 ->
x+y = y+z - 40 ->
z - x = 40
Manager  Joined: 02 Aug 2009
Posts: 93
Re: If the average (arithmetic mean) of x and y is 60 and the average (ari  [#permalink]

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1
(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
Verbal Forum Moderator B
Joined: 10 Oct 2012
Posts: 563
Re: If the average (arithmetic mean) of x and y is 60 and the average (ari  [#permalink]

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2
tinman1412 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.

10 second approach :

Mean of x and y is 60. We can assume both x = y = 60. Again, mean of y and z is 80; We can keep the value of y = 60 and assume the value of z = 100. Thus, z-x = 100-60 = 40.

B.
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Intern  Joined: 08 Jan 2013
Posts: 29
Re: If the average (arithmetic mean) of x and y is 60 and the average (ari  [#permalink]

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That's brilliant Mau5. Do you know of a guide with general speed tips?
Verbal Forum Moderator B
Joined: 10 Oct 2012
Posts: 563
Re: If the average (arithmetic mean) of x and y is 60 and the average (ari  [#permalink]

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stormbind wrote:
That's brilliant Mau5. Do you know of a guide with general speed tips?

As for general speed tips, as it is with everyone on gmatclub, I have learnt a lot by just observing Bunuel's solutions! In this case particularly, what I did is just one of the many ways of interpreting averages,i.e. if average of 2 things is X, then each of them can be assumed to be X.
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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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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!).

GMAT assassins aren't born, they're made,
Rich
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Director  B
Joined: 04 Jun 2016
Posts: 532
GMAT 1: 750 Q49 V43
Re: If the average (arithmetic mean) of x and y is 60 and the average (ari  [#permalink]

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tinman1412 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.

$$\frac{X+Y}{2}=60 ; X+Y=120$$

$$\frac{Y+Z}{2}=80 ; Y+Z=160$$

$$(Y+Z)-(X+Y)= 160-120$$

$$Y+Z-X-Y=40$$ (+Y AND -Y CANCELS EACH OTHER)

$$Z-X=40$$

_________________
Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
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Target Test Prep Representative V
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Posts: 10594
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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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1
tinman1412 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.

We are given that the average (arithmetic mean) of x and y is 60 and the average (arithmetic mean) of y and z is 80. We can create the following equations:

Equation 1:

(x + y)/2 = 60

x + y = 120

y = 120 - x

Equation 2:

(y + z)/2 = 80

y + z = 160

y = 160 - z

Since y = 120 - x and y = 160 - z, we can equate the two expressions.

120 - x = 160 - z

z - x = 40

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# Scott Woodbury-Stewart

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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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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

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern  Joined: 08 Oct 2016
Posts: 12
Re: If the average (arithmetic mean) of x and y is 60 and the average (ari  [#permalink]

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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!).

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

What if I need to find the value of z-y. How to approach that?
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
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Posts: 16746
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If the average (arithmetic mean) of x and y is 60 and the average (ari  [#permalink]

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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
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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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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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Abhishek....

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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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_________________ Re: If the average (arithmetic mean) of x and y is 60 and the average (ari   [#permalink] 06 Nov 2018, 02:20

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