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What is the average (arithmetic mean) of a and b?

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Source: — Data Sufficiency |
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by deloitte247 » Thu Sep 27, 2018 11:06 am

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Question= What is average (arithmetic mean ) of a and b?
$$U\sin g\ \frac{Efx}{Ef}$$
$$Average\ arithmetic\ mean\ =\ \frac{\left(a\ +\ b\right)}{2},\ once\ we\ find\ the\ value\ of\ a\ and\ b\ OR\ a\ +\ b\ we've\ find\ the\ answer$$

Statement 1 = The average (arithmetic mean) of a + 2 and b + 7 = 12
$$\frac{\left(\left(a\ +\ 2\right)\ +\ \left(b\ +\ 7\right)\right)}{2}=\ 12$$
$$\frac{\left(a\ +\ b\ +\ 7\ +\ 2\right)}{2}=\ 12$$
$$\frac{\left(\left(a\ +\ b\ \right)\ +9\right)}{2}=\ 12$$
a + b = (12 * 2) - 9
a + b = 24 - 9
a + b = 15.
Hence, Statement 1 is SUFFICIENT.

Statement 2 = The average (arithmetic mean ) of a,b and 6 = 7
$$\frac{\left(a\ +\ b\ +6\right)}{3}=\ 7$$
a + b = (7 * 3 ) - 6
a + b = 21 - 6
a + b = 15.
Hence, Statement 2 is SUFFICIENT.
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by Scott@TargetTestPrep » Tue Oct 02, 2018 6:59 pm

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BTGmoderatorDC wrote:What is the average (arithmetic mean) of a and b?

(1) The average (arithmetic mean) of a + 2 and b + 7 is 12
(2) The average (arithmetic mean) of a, b and 6 is 7
We need to determine the average of a and b.

Statement One Alone:

The average (arithmetic mean) of a + 2 and b + 7 is 12.

We can create the equation:

(a + 2 + b + 7)/2 = 12

a + b + 9 = 24

a + b = 15

Thus, the average of a and b is 7.5. Statement one alone is sufficient.

Statement Two Alone:

The average (arithmetic mean) of a, b and 6 is 7

We can create the equation:

(a + b + 6)/3 = 7

a + b + 6 = 21

a + b = 15

Again, the average of a and b is 7.5. Statement two alone is sufficient.

Answer: D

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