Explanation

In this question, to obtain the average of a and b, it would certainly be sufficient to learn their individual values. But since the average of a and b is half their sum, it would also be sufficient to learn the sum of a and b, even if we don't learn their individual values. Let's turn to the statements, separately first.

Statement (1) tells us the average of these two related numbers. We think algebra is on our side in this case, so let's use the average formula. The statement tells us that







We have the sum of a and b, so we know what their average will be (it's 11). Therefore, Statement (1) gives us sufficient information to answer the question definitively.

Statement (2) gives us a similar statement. Using the same approach, we have







Again, we have found the sum of a and b. This statement is also sufficient. The correct answer is (D).

Both statements can also be evaluated purely conceptually. Statement (2) is simpler. If the average of three numbers is 11, and one of them is 11, the number 11, as a member of the set, does nothing to adjust the average of the numbers in the set. It doesn't tug one way or another away from the average; it just adds weight to the average already established by the other two numbers. It follows that the average of the other two numbers, a and b, is 11. Statement (1) allows a similar type of analysis. If one number is increased by 5 and the other is increased by 3, the sum of them is increased by 8, or an average of 4. So the resultant average, 15, is 4 more than the average of the unaffected numbers, and that latter average must therefore be 11.

Again, the correct answer is (D).