Bunuel wrote:
If Mark saved an average (arithmetic mean) of $80 per week for 3 consecutive weeks, how much did he save the second week?
(1) The average amount that Mark saved per week for the first 2 weeks was $60.
(2) The amount that Mark saved the first week was 1/2 the amount he saved the second week and 1/3 the amount he saved the third week.
We are given that Mark saved an average (arithmetic mean) of $80 per week for 3 consecutive weeks. Thus, we can say:
The sum of money saved for 3 weeks = 80 x 3 = 240
We need to determine how much he saved in the second week.
Statement One Alone:
The average amount that Mark saved per week for the first 2 weeks was $60.
Statement one tells us that Mark saved a total of $60 x 2 = $120 in the first two weeks. This means that he saved $120 in the third week. However, we cannot determine the amount of money he saved in the second week. We can eliminate answer choices A and D.
Statement Two Alone:
The amount that Mark saved the first week was 1/2 the amount he saved the second week and 1/3 the amount he saved the third week.
We can let the amount saved in the 1st week = w. Since this was 1/2 the amount he saved in the 2nd week, the amount he saved in the 2nd week was twice that in the 1st week. Therefore, the amount saved in the 2nd week = 2w. Likewise, since the amount saved in the 1st week is 1/3 the amount he saved in the 3rd week, the amount he saved in the 3rd week was three times that in the 1st week, therefore, the amount saved in the 3rd week = 3w. So we can create the following equation:
w + 2x + 3w = 240
6w = 240
w = 40
Since the amount he saved in the 2nd week is 2w, the amount saved is 2(40) = $80. Statement two alone is sufficient to answer the question.
Answer: B