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

1. Jim's average savings for the first 2 weeks were $20

2. Jim's first week's savings were half of his savings in week 2 and a third of his savings in week 3

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient

* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient

* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient

* EACH statement ALONE is sufficient

* Statements (1) and (2) TOGETHER are NOT sufficient

OA is given as B. However, I think it St. 2 contradicts the information given in St.1.

The explanation given is:

**Quote:**

Suppose \(S_1\) , \(S_2\) , and \(S_3\) are the amounts Jim saved for the first, second, and third week, respectively.

Statement (1) by itself is not sufficient. \(S_1+S_2=\$40\) . Although \(S_3\) can be calculated, the value of \(S_2\) cannot be calculated. Consider \(S_1=\$20\) and \(S_2=\$20\) or \(S_1=\$5\) and \(S_2=\$35\) .

Statement (2) by itself is sufficient. From Statement (2): \(S_2 =2 * S_1\) and \(S_3 = 3 * S_1\)

\(S_1 + 2 * S_1 + 3 * S_1 = \$90\)

\(6 * S_1 = \$90\)

\(S_1 = \$15\)

Solving for \(S_2\) gives a value of \(S_2 = 2 * S_1 = 2 * 15 =\$30\) .

The problem is with St.2, \(S_1 + S_2 = 15 + 30 = 45\). This is not 40, as per St. 1