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

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tinman1412
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If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink] New post  23 Jul 2007, 19:33
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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.
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run4run
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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink] New post  01 Feb 2010, 17:55
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(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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ywilfred
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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink] New post  23 Jul 2007, 19:37
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(x+y)/2 = 60
x+y = 120 ---[1]

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

[2]-[1]
z-x = 40
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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink] New post  24 Jul 2007, 07:48
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
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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink] New post  16 Jun 2013, 01:13
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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.


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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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink] New post  16 Jun 2013, 02:04
That's brilliant Mau5. Do you know of a guide with general speed tips?
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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink] New post  16 Jun 2013, 02:26
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] New post  19 Sep 2015, 17:17
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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!).

Final Answer:
Show Spoiler
B


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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink] New post  23 Jul 2016, 07:43
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)

\(Z-X=40\)

ANSWER IS B
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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink] New post  16 Oct 2016, 18:20
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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.


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

Answer: B
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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink] New post  19 Dec 2016, 10:56
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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

Answer: B
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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink] 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:
Show 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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EMPOWERgmatRichC
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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink] New post  29 Dec 2016, 11:03
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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.

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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink] 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] New post  18 Jan 2022, 21:58
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.


Explanation-

(x+y)/2 = 60
(y+z)/2 = 80
Value of z-x = ?

Solving,
x+y =120 ==> y= 120-x

y+z =160
Substituting y= 120-x,
120-x+z =160
z-x =40
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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink] New post  29 May 2023, 00:23
To find the value of z - x, we need to determine the values of both z and x.

Given that the average of x and y is 60, we can write the equation:
(x + y) / 2 = 60

Similarly, the average of y and z is 80:
(y + z) / 2 = 80

We can rearrange the first equation to solve for y:
x + y = 120
y = 120 - x

Substituting this value of y into the second equation, we get:
(120 - x + z) / 2 = 80
120 - x + z = 160
z - x = 40

Therefore, the value of z - x is 40.
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Re: If the average (arithmetic mean) of x and y is 60 and the average (ari [#permalink]
29 May 2023, 00:23
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