What is the average of x and |y| ?

For those who want to solve this analytically, without plugging numbers.
average of x+|y| is (x+y)/2 or (x-y)/2

(1) gives (x+y)/2=10, but the we don't know if y is positve or negative. If y is negative then the average of x+|y| is not (x+y)/2. furthermore from statment (1) alone we can not find the value of x-y. therefore, (1) is insufficient.
(2) gives (x+y)/2=10 or (x+y)/2=-10. Similar to statement1, knowing x+y is not sufficient.

Since (1) and (2) are similar conditions, combined they are insufficient

Answer is E

We do not know sign of x and y.

We are looking for the value of \(\frac{x+|y|}{2}\) or just x+|y|.

(1) x + y = 20
If y is non negative, then y=|y| and x + y = x + |y| = 20...answer is 10
But if y is negative, then we require to know the value of x or y.
Insufficient

(2) |x + y| = 20
The information given becomes even more scanty.
Now x+y=20, and we have information as insufficient
If x+y=-20, then again we require to know the values of x and y.

Combined
The analysis of statement I still stands.

E

By definition of average, Average of x and |y| = x + |y| / 2. To answer this question, we need a unique value for x + |y|, which in turn depends on the values of x and y.

From statement I alone, x+y = 20.

If x = 20 and y = 0, x+y = 20. Average of x and |y| = 20 + |0| / 2 = 10
If x = 40 and y = -20, x+y = 20. Average of x and |y| = 40 + |-20| / 2 = 40 + 20 / 2 = 30
Statement I alone is insufficient. Answer options A and D can be eliminated.

From statement II alone, |x+y| = 20.

This means x+y = 20 or x+y = -20. While working with the information given in statement I, we saw how it was insufficient. Therefore, the information that we have here is hopelessly insufficient.
Statement II alone is insufficient. Answer option B can be eliminated.

Combining statements I and II, we can see that x+y = 20. This means that after combining the statements, we are back to square one i.e. to the data given in statement I, which is insufficient.
The combination of statements is insufficient. Answer option C can be eliminated.

The correct answer option is E.

Hope that helps!
Aravind BT

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