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

[BTGmoderatorLU]

Source: Magoosh

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

1) The average (arithmetic mean) of x, y and k is 7.
2) The average (arithmetic mean) of x, y and 3k is 13.

The OA is C

[GMATGuruNY]

Source: Magoosh

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

1) The average (arithmetic mean) of x, y and k is 7.
2) The average (arithmetic mean) of x, y and 3k is 13.

SUM = (COUNT)(AVERAGE).

Statement 1:
x+y+k = (count)(average) = 3*7 = 21.
No way to determine the value of x+y.
INSUFFICIENT.

Statement 2:
x+y+3k = (count)(average) = 3*13 = 39.
No way to determine the value of x+y.
INSUFFICIENT.

Statements combined:
Subtracting x+y+k=21 from x+y+3k=39, we get:
(x+y+3k) - (x+y+k) = 39-21
2k = 18
k = 9.
Substituting k=9 into x+y+k=21, we get:
x+y+9 = 21
x+y = 12.
SUFFICIENT.

The correct answer is C.