In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding

[BTGmoderatorDC]

In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 360 points, how many points is the third question worth?
A. 18
B. 24
C. 26
D. 32
E. 44


OA C

Source: GMAT Prep

[Scott@TargetTestPrep]

In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 360 points, how many points is the third question worth?
A. 18
B. 24
C. 26
D. 32
E. 44


OA C

Source: GMAT Prep

The first question is worth x, the 2nd worth x + 4, the 3rd worth x + 2(4) = x + 8, ..., the 10th is worth x + 9(4) = x + 36.

Since we have a set of evenly-spaced numbers, the average is (x + x + 36)/2 = (2x + 36)/2 = x + 18.

Since sum = average * quantity we have:

360 = (x + 18) * 10

36 = x + 18

18 = x

The first question is worth x = 18 points. So the third question is worth x + 8 = 18 + 8 = 26 points.

Answer: C