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

tagged by: M7MBA

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

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

(1) The average of x + 3 and y + 5 is 14.
(2) The average of x, y, and 16 is 12.

The OA is the option D .

I know that the statement (2) is sufficient. But, how can I prove that the statement (1) is sufficient?

### GMAT/MBA Expert

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M7MBA wrote:
What is the average (arithmetic mean) of x and y?

(1) The average of x + 3 and y + 5 is 14.
(2) The average of x, y, and 16 is 12.

The OA is the option D .

I know that the statement (2) is sufficient. But, how can I prove that the statement (1) is sufficient?
Avg = (x + y)/2 --> we need to be able to find x + y

(1) SUFFICIENT

(x + 3 + y + 5)/2 = 14
x + y + 8 = 28
x + y = 20
(x + y)/2 = 10

(2) SUFFICIENT

(x + y + 16)/3 = 12
x + y + 16 = 36
x + y = 20
(x + y)/2 = 10

### Top Member

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M7MBA wrote:
What is the average (arithmetic mean) of x and y?

(1) The average of x + 3 and y + 5 is 14.
(2) The average of x, y, and 16 is 12.

The OA is the option D .

I know that the statement (2) is sufficient. But, how can I prove that the statement (1) is sufficient?
Question : Average of a and b = ?

i.e. Question : x+y = ?

Statement 1: The average of x + 3 and y + 5 is 14.

(x+3)+(y+5) = 2*14
i.e. x + y = 20
SUFFICIENT

Statement 2: The average of x, y, and 16 is 12

i.e. x+y+16 = 12*3
i.e. x + y = 20
SUFFICIENT

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