What is Sarah's annual income?

I disagree with answer.

What is Sarah's annual income?
(1) Sarah and Mary earn an annual income in the ratio of 4:3
(2) Sarah and Mary spend money in the in the ratio of 3:2 and together save $20,000 annually


I think answer is C. Challenges say E. Agree with me?

Clear E . I dont think these 2 stmnts are related to each other to solve the problem.

Challenges are correct.
Answer should be 'E', as you can not get the Sarah's income with the given info.

i see why now. because though i can find values that would add up to the 200 k, there are many different answers for mary's income. i could just vary the money they spent.

what you may have missed here is .. they together save 20,000 annually. Had they each saved 20,000 annually we could have got C.

Saras income = S
Mary's income = M
Let the money spent by Mary = x

First statement says:
S/M = 4/3

From second statement;
(S - 1.5x) + (M-x) = 20K

Two equations and 3 unknowns (S,M,x) so not solveable. E is the correct answer.

St1:
Insufficient. We don't have any concrete figures.

St2:
Insufficient. We don't know anything about their income and how much they spend.

Using st1 and st2:
We can't work out anything. We don't know the amount spent and the amount earnt.

Ans E

Please correct the question, it should say 'save' not 'spend' on the second statement otherwise the answer would be C not E

Thanks!
Cheers
J

The question is correct.

What is Sarah's annual income?

(1) The ratio of Sarah's and Mary's annual income is 4:3.

(2) The ratio of Sarah's and Mary's savings is 3:2, and combined they spend $20,000, annually.

Let s and m denote Sarah's and Mary's spending and S and M denote their incomes, then combining the two statements gives:

\(\frac{S}{M}=\frac{4}{3}\);

\(\frac{S-s}{M-m}=\frac{3}{2}\);

\(s+m=20000\).

We cannot solve the system of equations.

Answer: E.

Let S = Sarah's annual income
Let M = Mary's annual income
Let x = the amount Sarah spends each year
Let y = the amount Mary spends each year

Rephrased target question: What is the value of S?

Statement 1: Sarah and Mary earn an annual income in the ratio of 4:3
In other words: S/M = 4:3
Cross multiply to get 3S = 4M
Simplify: 3S - 4M = 0
We can't find the value of S, so statement 1 is NOT SUFFICIENT

Statement 2: Sarah and Mary spend money in the ratio of 3:2 and together save $20,000, annually.

Sarah and Mary spend money in the ratio of 3:2
We get x/y = 3/2
Simplify to get: 2x - 3y = 0

Together they save $20,000 annually
Sarah's savings + Mary's savings = 20,000
(S - x) + (M - y) = 20,000

We can't find the value of S, so statement w is NOT SUFFICIENT

Statements 1 and 2 combined:
We now know that:
3S - 4M = 0
2x - 3y = 0
(S - x) + (M - y) = 20,000

Since we have 3 equations and 4 unknowns, we cannot solve this system for S.
So, the combined statements are NOT SUFFICIENT

Hence Answer = E

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