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16 Sep 2014, 00:15
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If Jim saved a total of $90 in 3 weeks, how much did he save in week 2?
(1) Jim's average (arithmetic mean) savings per week for the first two weeks was $22.5.
(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.
(1) Jim's average (arithmetic mean) savings per week for the first two weeks was $22.5.
(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.
16 Sep 2014, 00:15
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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 per week for the first two 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
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 per week for the first two 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
General Discussion
18 Oct 2023, 09:01
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
