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16 Sep 2014, 00:16
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If Sarah and Mary had no savings at the beginning of last year and their only income last year was from their salary, what was Sarah's annual salary last year?
(1) The ratio of Sarah's and Mary's annual salaries last year was 4:3.
(2) The ratio of Sarah's and Mary's annual savings last year was 3:2, and their combined spending was $20,000.
(1) The ratio of Sarah's and Mary's annual salaries last year was 4:3.
(2) The ratio of Sarah's and Mary's annual savings last year was 3:2, and their combined spending was $20,000.
16 Sep 2014, 00:16
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Official Solution:
If Sarah and Mary had no savings at the beginning of last year and their only income last year was from their salary, what was Sarah's annual salary last year?
(1) The ratio of Sarah's and Mary's annual salaries last year was 4:3. Clearly insufficient.
(2) The ratio of Sarah's and Mary's annual savings last year was 3:2, and their combined spending was $20,000. Clearly insufficient.
(1)+(2) Let S and M denote Sarah's and Mary's salaries, and s and m denote their spending. We have the following equations:
\(\frac{S}{M} = \frac{4}{3}\), which gives \(3S=4M\);
\(\frac{S-s}{M-m} = \frac{3}{2}\), which gives \(2(S - s)=3(M-m)\)
\(s+m = 20000\)
We have three distinct linear equations and four unknowns, with no additional constraints on these unknown, therefore we cannot solve for the individual unknowns and get the value of \(S\). Not sufficient.
Answer: E
If Sarah and Mary had no savings at the beginning of last year and their only income last year was from their salary, what was Sarah's annual salary last year?
(1) The ratio of Sarah's and Mary's annual salaries last year was 4:3. Clearly insufficient.
(2) The ratio of Sarah's and Mary's annual savings last year was 3:2, and their combined spending was $20,000. Clearly insufficient.
(1)+(2) Let S and M denote Sarah's and Mary's salaries, and s and m denote their spending. We have the following equations:
\(\frac{S}{M} = \frac{4}{3}\), which gives \(3S=4M\);
\(\frac{S-s}{M-m} = \frac{3}{2}\), which gives \(2(S - s)=3(M-m)\)
\(s+m = 20000\)
We have three distinct linear equations and four unknowns, with no additional constraints on these unknown, therefore we cannot solve for the individual unknowns and get the value of \(S\). Not sufficient.
Answer: E
General Discussion
28 Feb 2023, 08:17
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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.
