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Bunuel
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Bunuel
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


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
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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
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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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