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20 Apr 2006, 19:02
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E
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Difficulty:
25%
(medium)
Question Stats:
77% (01:22) correct
23%
(01:33)
wrong
based on 836
sessions
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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.
M01-31
(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.
M01-31
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22 Apr 2014, 10:20
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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
09 Aug 2025, 07:20
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Hi Brunel,
I think the answer should be C becauase combining 1 and 2 we find,
1) Salary = 4X + 3X
2) Let's say Sara spent y amount. Then, Mary spend 20,000 - y amount
3) Savings ratio is 3:2.
So, (4x - y)/{3x - (20,000 - y)} = 3/2
or, 2(4x - y) = 3{ 3x - (20,000 - y)}
Solving this, we find y = 10,000. Then, 20,000 - y = 10,000 too.
Putting value of y in the equation we find,
(4x - 10,000)/(3x - 10,000) = 3/2
Or, 8x - 20,000 = 9x - 30,000
Or, x = 10,000.
So, Sara's salary = 10,000. Mary's 30,000.
This also satisfies the savings ratio too.
What do you think?
I think the answer should be C becauase combining 1 and 2 we find,
1) Salary = 4X + 3X
2) Let's say Sara spent y amount. Then, Mary spend 20,000 - y amount
3) Savings ratio is 3:2.
So, (4x - y)/{3x - (20,000 - y)} = 3/2
or, 2(4x - y) = 3{ 3x - (20,000 - y)}
Solving this, we find y = 10,000. Then, 20,000 - y = 10,000 too.
Putting value of y in the equation we find,
(4x - 10,000)/(3x - 10,000) = 3/2
Or, 8x - 20,000 = 9x - 30,000
Or, x = 10,000.
So, Sara's salary = 10,000. Mary's 30,000.
This also satisfies the savings ratio too.
What do you think?
Bunuel
