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If the average (arithmetic mean) of x and y is 40, and z – x = 60, wha

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Bunuel
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If the average (arithmetic mean) of x and y is 40, and z – x = 60, wha [#permalink] New post   01 Sep 2016, 03:49
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If the average (arithmetic mean) of x and y is 40, and z – x = 60, what is the average of y and z?

A. 20
B. 50
C. 65
D. 70
E. 140
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D
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BrentGMATPrepNow
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Re: If the average (arithmetic mean) of x and y is 40, and z – x = 60, wha [#permalink] New post   06 Sep 2016, 14:13
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Bunuel wrote:
If the average (arithmetic mean) of x and y is 40, and z – x = 60, what is the average of y and z?

A. 20
B. 50
C. 65
D. 70
E. 140


Another approach is the assign values to x, y and z that satisfy the given conditions.

The average (arithmetic mean) of x and y is 40
Okay, two "nice" values are: x = 40 and y = 40

z – x = 60
Since we've let x = 40, then it must be the case that z = 100

What is the average of y and z?
If y = 40 and z = 100, then the average of y and z = (40+100)/2 = 70

Answer:
Show Spoiler
D


NOTE: there was nothing special about the values I chose for x, y and z, other than the fact that they satisfied the given conditions. ANY other set of numbers will also yield the same answer.
For example, we could have used x = 20, y = 60 and z = 80, and this would have led to the same answer.
Try your own values to confirm this.

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Re: If the average (arithmetic mean) of x and y is 40, and z – x = 60, wha [#permalink] New post   01 Sep 2016, 07:04
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Bunuel wrote:
If the average (arithmetic mean) of x and y is 40, and z – x = 60, what is the average of y and z?

A. 20
B. 50
C. 65
D. 70
E. 140


x+y/2 = 40
=> x+y = 80

x = z - 60...sub this value

z-60+y = 80
=>z+y = 140
=>z+y/2 = 70.

IMO option D.

OA please..will correct if I missed anything.
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Re: If the average (arithmetic mean) of x and y is 40, and z – x = 60, wha [#permalink] New post   12 Dec 2016, 11:26
Nice one.
Here mean(x,y)=40
Sum(x+y)=40*2=80
hence x+y=80
and z-x=60
Adding the two equations we get => z+y=140
Hence mean = 140/2 = 70

Hence D
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Re: If the average (arithmetic mean) of x and y is 40, and z – x = 60, wha [#permalink] New post   08 Oct 2019, 00:46
Bunuel wrote:
If the average (arithmetic mean) of x and y is 40, and z – x = 60, what is the average of y and z?

A. 20
B. 50
C. 65
D. 70
E. 140


Create 2 equations to solve this one

1) Mean of X& Y= 40

= (x+y)/2 = 40
X+Y =80
or Y =80- X

2) Second equation'

z= 60 +X

Target question is to find the avg of Y and Z

so (80-X + 60+X) /2 = 140/2 =70 ans choice D
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Re: If the average (arithmetic mean) of x and y is 40, and z – x = 60, wha [#permalink] New post   11 Oct 2019, 15:50
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Bunuel wrote:
If the average (arithmetic mean) of x and y is 40, and z – x = 60, what is the average of y and z?

A. 20
B. 50
C. 65
D. 70
E. 140



Since the average of x and y is 40, we have:

(x + y)/2 = 40

x + y = 80

We are also given that z - x = 60.

Adding together the two equations, we have:

y + z = 140

So the average of y and z is:

(y + z)/2 = 140/2 = 70

Answer: D
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Re: If the average (arithmetic mean) of x and y is 40, and z x = 60, wha [#permalink] New post   01 Aug 2022, 02:27
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Theory

    ➡ Average = Sum of all the Values / Total Number of Values
    ➡ Sum of All the values = Average * Total Number of Values

The average (arithmetic mean) of x and y is 40

Average of x and y = \(\frac{x + y}{2}\) = 40 (given)
=> x + y = 40*2 = 80 ...(1)

z – x = 60 (given) ...(2)

Adding (1) and (2) we get

x+ y + z - x = 80 + 60 = 140
=> y + z = 140

The average of y and z

Average of y and z = \(\frac{y + z}{2}\) = \(\frac{140}{2}\) = 70

So, Answer will be D.
Hope it helps!

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Re: If the average (arithmetic mean) of x and y is 40, and z x = 60, wha [#permalink]
01 Aug 2022, 02:27
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