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# What is Sarah's annual income?

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Intern
Joined: 12 Feb 2006
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What is Sarah's annual income? [#permalink]  20 Apr 2006, 18:02
00:00

Difficulty:

35% (medium)

Question Stats:

63% (02:09) correct 37% (01:07) wrong based on 114 sessions
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. M01-31 [Reveal] Spoiler: OA GMAT Club Legend Joined: 07 Jul 2004 Posts: 5095 Location: Singapore Followers: 19 Kudos [?]: 153 [0], given: 0 [#permalink] 20 Apr 2006, 18:42 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: 1408 Followers: 2 Kudos [?]: 16 [0], given: 0 [#permalink] 20 Apr 2006, 21:44 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: 97 Followers: 1 Kudos [?]: 3 [0], given: 0 DS: Challenge Problem [#permalink] 11 Sep 2007, 18:01 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
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Re: DS: Challenge Problem [#permalink]  11 Sep 2007, 18:16
dr908 wrote:

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: 782 Followers: 2 Kudos [?]: 56 [0], given: 0 Re: DS: Challenge Problem [#permalink] 11 Sep 2007, 18:22 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
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yup [#permalink]  11 Sep 2007, 18:23
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
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Re: DS: Challenge Problem [#permalink]  11 Sep 2007, 20:30
dr908 wrote:

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 Followers: 0 Kudos [?]: 0 [0], given: 0 [#permalink] 11 Sep 2007, 21:15 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. GMAT Club Legend Joined: 07 Jul 2004 Posts: 5095 Location: Singapore Followers: 19 Kudos [?]: 153 [0], given: 0 [#permalink] 11 Sep 2007, 22:04 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: 1728 Location: United States Concentration: Finance GMAT 1: 710 Q48 V39 WE: Corporate Finance (Investment Banking) Followers: 14 Kudos [?]: 189 [0], given: 293 Re: What is Sarah's annual income? [#permalink] 22 Apr 2014, 05:35 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: 23351 Followers: 3602 Kudos [?]: 28695 [0], given: 2809 Re: What is Sarah's annual income? [#permalink] 22 Apr 2014, 09:20 Expert's post jlgdr wrote: 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.

_________________
Intern
Joined: 08 Jan 2014
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Location: United States
Concentration: General Management, Entrepreneurship
GMAT Date: 06-30-2014
GPA: 3.99
WE: Analyst (Consulting)
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Kudos [?]: 14 [0], given: 4

Re: What is Sarah's annual income? [#permalink]  10 May 2014, 10:01
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

Re: What is Sarah's annual income?   [#permalink] 10 May 2014, 10:01
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