M01-20

Official Solution:


If Jim saved a total of $90 in 3 weeks, how much did he save in week 2?

Let \(s_1\), \(s_2\), and \(s_3\) represent the amounts Jim saved in the first, second, and third weeks, respectively.

(1) Jim's average (arithmetic mean) savings for the first 2 weeks was $22.5.

From this, we infer: \(s_1 + s_2 = 2*22.5 = 45\). However, this does not provide the specific value of \(s_2\). Hence, not sufficient.

(2) In the first week, Jim saved half of what he saved in week 2 and one-third of what he saved in week 3.

The above implies that \(2 *s_1 = s_2\) and \(3*s_1 = s_3\). Given that \(s_1 + s_2 + s_3 = 90\), we get \(s_1 + 2 *s_1 + 3*s_1 = 90\). Solving this, gives \(s_1 = 15\), and therefore, \(s_2 = 2*s_1 = 30\). This is sufficient.


Answer: B