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

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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.

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

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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 av [#permalink]

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

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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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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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