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# What is the average (arithmetic mean) of x, y, and z?

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Intern
Joined: 24 Nov 2018
Posts: 16
Location: India
What is the average (arithmetic mean) of x, y, and z?  [#permalink]

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14 Jan 2019, 21:08
6
00:00

Difficulty:

45% (medium)

Question Stats:

59% (01:18) correct 41% (01:37) wrong based on 75 sessions

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What is the average (arithmetic mean) of x, y, and z?

(1) —x − 4y + 3z = 14

(2) 5x + 8y + z = 26
Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: What is the average (arithmetic mean) of x, y, and z?  [#permalink]

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14 Jan 2019, 21:27
1
What is the average (arithmetic mean) of x, y, and z?

(1) —x − 4y + 3z = 14

(2) 5x + 8y + z = 26

We are looking for X+y+z..
Each statement gives us three variables,so each is not sufficient..

By looking at the two equations together we can see that the adding up will give us something in terms of what we are seeking..
5x+8y+z-x-4y+3z=26+14.....4x+4y+4z=40.....x+y+z=10..
Average is 10/3
Sufficient

C
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Joined: 18 Aug 2017
Posts: 1926
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Concentration: Sustainability, Marketing
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WE: Marketing (Energy and Utilities)
Re: What is the average (arithmetic mean) of x, y, and z?  [#permalink]

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15 Jan 2019, 05:48
What is the average (arithmetic mean) of x, y, and z?

(1) —x − 4y + 3z = 14

(2) 5x + 8y + z = 26

#1:
values of x,y,z not given
in sufficient
#2:
values of x,y,z not given
in sufficient

combining 1 & 2
we can determine x,y,z
sufficienet
IMO C
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VP
Joined: 09 Mar 2018
Posts: 1002
Location: India
Re: What is the average (arithmetic mean) of x, y, and z?  [#permalink]

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01 Feb 2019, 22:08
What is the average (arithmetic mean) of x, y, and z?

(1) —x − 4y + 3z = 14

(2) 5x + 8y + z = 26

To find: x+y+z / 3 -------(a)

from 1, When we substitute for x in (a), we cannot get a value for y and z

x = - (14+4y-3z)

-3y+4z/3

from 2, When we substitute for z in (a), we cannot get a value for x and y

26 - 4x -7y/3

But when we combine both the statements, we can get the value of

4x + 4y + 4z = 40

x+y+z as 10

Average becomes 10/3

C
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If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

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Re: What is the average (arithmetic mean) of x, y, and z?   [#permalink] 01 Feb 2019, 22:08
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