On the number line above, p, q, r, s, and t…
If we have an evenly spaced set consisting of an odd number of numbers, then the middle number is the average. Since here we have 5 consecutive even integers (an evenly spaced set of an odd number of numbers) and r is the middle number, the average is r. Furthermore, not only is r is the average of the 5 numbers, but it’s also the average of the first and last number, i.e., p and t, and the average of the second and second-to-last number, i.e., q and s. We need to determine the value of r.
Note: If this is too difficult to see, let’s use 2, 4, 6, 8 and 10 as an example. We see that
1) 6 is the average of all 5 numbers since (2+4+6+8+10)/5 = 30/5 = 6,
2) 6 is the average of 2 and 10 since (2+10)/2 = 12/2 = 6, and
3) 6 is the average of 4 and 8 since (4+8)/2 = 12/2 = 6.
Statement One Alone:
q + s = 24
Since we know that r is the average of q and s, then r = (q + s)/2 = 24/2 = 12.
Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.
Statement Two Alone:
The average (arithmetic mean) of q and r is 11.
Using the information in statement two we know that (q + r)/2 = 11 or q + r = 22. Since q is the even integer before r on the given number line, q = r – 2. Thus we can substitute r – 2 for q in the equation q + r = 22, and we have:
(r – 2) + r = 22
2r – 2 = 22
2r = 24
r = 12
Statement two is also sufficient to answer the question.