If Q = {x, y, 2z, x, y, 2z}, then what is the average (arithmetic mean

Question

If Q = {x, y, 2z, x, y, 2z}, then what is the average (arithmetic mean) of set Q ?

(1) x + y + z = 8
(2) x + y = 10

Showmeyaa · Answer

Asked:
 \frac{{x+y+2z+x+y+2z}}{6} ?
 \frac{{2x + 2y + 4z}}{6} ?
 \frac{2{x + y + 2z}}{6} ?
 \frac{{x + y + 2z}}{3} ?

1) x + y + z = 8, we need the value of 2z - Not Sufficient!
2) x + y = 10, we need the value of z - Not sufficient!
Combining (1) (2)
z = -2, So, 2z = -4, x + y = 10
 \frac{10 - 4}{3} = 2 , IMO (C)!

pressy1828 · Answer

i taught it was E

...since both are insufficient i didn't have the idea to combine

chetan2u · Answer

The average =  \frac{x+ y+ 2z+ x+ y+ 2z}{6}=\frac{2(x+ y+ 2z)}{6}

So we require to know the value of x+y+2z.

(1) x + y + z = 8
So x+y+2z=8+z.
We do not know the value of z.
Insufficient

(2) x + y = 10
So x+y+2z=10+2z.
We do not know the value of z.
Insufficient

Combined
8+z=10+2z.......z=-2
So x+y+2z=8+z=8+(-2)=6
Average = \frac{2(x+ y+ 2z)}{6}=\frac{2*6}{6}=2 
Sufficient

C

CrackverbalGMAT · Answer

Arithmetic mean = Sum of terms / Number of terms

Sum of all terms of set Q = 2x + 2y + 4z
Number of terms in set Q = 6

Therefore, arithmetic mean of terms in set Q =  \frac{2x + 2y + 4z }{ 6} .

Factoring out 2 in the numerator, we have Arithmetic mean =  \frac{2(x+y+2z) }{ 6}  =  \frac{x+y+2z }{ 3}

To find the value of the arithmetic mean, we need the value of x+y+2z.

From statement I alone, x + y + z = 8. This is not sufficient to find the value of x + y + 2z.
Statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.

From statement II alone, x + y = 8. This is not sufficient to find the value of x + y + 2z since we do not have the value of z.
Statement II alone is insufficient. Answer option B can be eliminated. Possible answer options are C or E.

Combining statements I and II, we have the following:

From statement I alone, x + y + z = 8
From statement II alone, x + y = 10. 
Therefore, z = -2 and x + y + 2z = 10 – 4 = 6

Arithmetic mean =  \frac{6 }{3}  = 2.

The combination of statements is sufficient to find the arithmetic mean. Answer option E can be eliminated.
The correct answer option is C.

Hope that helps!
Aravind B T

Hariharan1 · Answer

Average= (2x+2y+4z)/6
1. Option 1- x+y+z=8,
Average= (16+2z)/6, NS
2. Z not provided. NS
3. X+y=10
So z =-2
Average= (16-4)/8=2,S
Option C

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If Q = {x, y, 2z, x, y, 2z}, then what is the average (arithmetic mean

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If Q = {x, y, 2z, x, y, 2z}, then what is the average (arithmetic mean

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