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3 different numbers x, y and z. What is average?

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by 4meonly » Sun Aug 17, 2008 3:53 am
A certain list consists of 3 different numbers x, y and z. The difference between x and y is twice the difference between x and z. If x is the largest, what is the average of the 3 numbers?

(1) y=10
(2) z=10

Answer is B

I've got stuck with it :(
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Source: — Data Sufficiency |
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Re: 3 different numbers x, y and z. What is average?

by sudhir3127 » Sun Aug 17, 2008 4:48 am
4meonly wrote:A certain list consists of 3 different numbers x, y and z. The difference between x and y is twice the difference between x and z. If x is the largest, what is the average of the 3 numbers?

(1) y=10
(2) z=10

Answer is B

I've got stuck with it :(
IMO B.

here it goes...

statement 1. Insufficient.

statement 2. Z=10

X-Y = 2( X-Z)

if u solve this equation as

X-Y = 2X- 2Z
X+Y = 2Z
X+Y = 2*10 = 20

hence the average is ( X+Y+Z)/3

thus avg is (20 + 10)/3 =10..

thus B is sufficient,
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by rishi235 » Sun Aug 17, 2008 8:42 am
Hi heres another method

We have X-Y = 2(X-Z)
=> X-Y=2X-2Z
=> X=2Z-Y

Now we need the average i.e. (X+Y+Z)/3
Substitute X=2Z-Y in the average equation
We have,
=> (2Z-Y+Y+Z)/3
=> 3Z/3
=> Z

Hence to find the average, we just need the value of Z which is given in statement (2).

We do not require stmt (1)

Hope this helps!!!
:)
Rishi
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