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

Question

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.

run4run · Accepted Answer

(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

ywilfred · Answer

(x+y)/2 = 60
x+y = 120 --- 

(y+z)/2 = 80
y+z = 160 --- 

 - 
z-x = 40

qtip · Answer

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

mau5 · Answer

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.

stormbind · Answer

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

mau5 · Answer

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.

EMPOWERgmatRichC · Answer

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:  B

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

LogicGuru1 · Answer

\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

ScottTargetTestPrep · Answer

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

ScottTargetTestPrep · Answer

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

voccubd · Answer

What if I need to find the value of z-y. How to approach that?

EMPOWERgmatRichC · Answer

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

Abhishek009 · Answer

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

Snehaaaaa · Answer

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

ArnauG · Answer

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.

bumpbot · Answer

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

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