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Intern
Joined: 12 Feb 2006
Posts: 26

What is Sarah's annual income?
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20 Apr 2006, 19:02
Question Stats:
69% (00:54) correct 31% (01:00) wrong based on 416 sessions
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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. M0131
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GMAT Club Legend
Joined: 07 Jul 2004
Posts: 4906
Location: Singapore

1) Si/Mi = 4/3
Insufficient as Mi can be any value.
2) Se/Me = 3/2
Ss + Ms = 20,000
We do not know the breakdown of how they use their pay, we can't compute the annual income.
Insufficient.
Using 1) and 2),
Si = 4/3(Mi)
Si = Se + Ss
4/3(Mi) = 3/2(Se) + 20,000  Ms
4/3(Me + Ms) = 3/2(Se) + 20,000  Ms
1/6(Me) + 7/3(Ms) = 20,000
1/6(14Ms  Me) = 20,000
14Ms  Me = 120,000
If Ms = 10,000, then Me = 20,000 Mt = 30,000
If Ms can be 15,000 then Me = 90,000 Mt = 90,000
etc.
Ms can be of any value as long as it's below 20,000 since Ms + Ss = 20,000.
Insufficient as St can now vary.
Ans E



VP
Joined: 29 Apr 2003
Posts: 1374

I agree with E... Whats the OA?
Its says 'tricky' and that tricked me to look closely, unfortunately didnt find anything exciting!



Manager
Joined: 18 Jan 2007
Posts: 88

DS: Challenge Problem
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11 Sep 2007, 19:01
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?



Director
Joined: 08 Jun 2007
Posts: 557

Re: DS: Challenge Problem
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11 Sep 2007, 19:16
dr908 wrote: 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.



Director
Joined: 14 Jan 2007
Posts: 755

Re: DS: Challenge Problem
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11 Sep 2007, 19:22
dr908 wrote: 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?
Challenges are correct.
Answer should be 'E', as you can not get the Sarah's income with the given info.



Manager
Joined: 18 Jan 2007
Posts: 88

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.



Manager
Joined: 17 Aug 2007
Posts: 76

Re: DS: Challenge Problem
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11 Sep 2007, 21:30
dr908 wrote: 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?
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.



Intern
Joined: 09 Sep 2007
Posts: 5

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) + (Mx) = 20K
Two equations and 3 unknowns (S,M,x) so not solveable. E is the correct answer.



GMAT Club Legend
Joined: 07 Jul 2004
Posts: 4906
Location: Singapore

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



SVP
Joined: 06 Sep 2013
Posts: 1803
Concentration: Finance

Re: What is Sarah's annual income?
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22 Apr 2014, 06:35
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



Math Expert
Joined: 02 Sep 2009
Posts: 49350

Re: What is Sarah's annual income?
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22 Apr 2014, 10:20



Intern
Joined: 08 Jan 2014
Posts: 19
Location: United States
Concentration: General Management, Entrepreneurship
GMAT Date: 06302014
GPA: 3.99
WE: Analyst (Consulting)

Re: What is Sarah's annual income?
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10 May 2014, 11:01
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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Re: What is Sarah's annual income?
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19 Oct 2017, 08:06
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Re: What is Sarah's annual income? &nbs
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19 Oct 2017, 08:06






