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Question Stats:
71% (01:16) correct 29% (01:14) wrong based on 231 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.
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Official Solution: Statement (1) by itself is not sufficient. Statement (2) by itself is not sufficient. Statements (1) and (2) combined are not sufficient. If \(s\) and \(m\) denote Sarah's and Mary's spending and \(S\) and \(M\) denote their incomes, then combining the two statements gives: \(\frac{S}{M} = \frac{4}{3}\)
\(\frac{Ss}{Mm} = \frac{3}{2}\)
\(s+m = 20000\) This linear system has 3 equations and 4 unknowns. Consequently, we cannot solve the system of equations. Answer: E
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Re: M0131
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24 Sep 2014, 16:29
Hi Bunuel, Thanks for the Solution. I framed teh equations but spent lot of time to figure whether it could be solved or not. can you please help me with the theory or logic behind it? How do we decide that there are 3 equations and 4 unknowwns hence not solvable.
Please provide any linke for this theory if you have any
Thanks



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22 Nov 2014, 15:06
shankar245 wrote: Hi Bunuel, Thanks for the Solution. I framed teh equations but spent lot of time to figure whether it could be solved or not. can you please help me with the theory or logic behind it? How do we decide that there are 3 equations and 4 unknowwns hence not solvable.
Please provide any linke for this theory if you have any
Thanks Typically, if you have x number of variables, you will only be able to solve for each variable if you have x number of equations. This is because you need to substitute. for instance if asked to solve for x, and given x+y=4 alone, we cannot solve. But if we are also told that y+3=4, we can use this eq. to find y=1, then replace y with 1 in the first eq. and we'll have 1+x=4. now we can solve for x, x=3. Just the rule. Question: should S/M = 3/4 be S/M = (4x)/(3x), since this is just a proportion and the numbers can take various values, so long as they remain proportionate?



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Re: M0131
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23 Nov 2014, 07:10
JackSparr0w wrote: shankar245 wrote: Hi Bunuel, Thanks for the Solution. I framed teh equations but spent lot of time to figure whether it could be solved or not. can you please help me with the theory or logic behind it? How do we decide that there are 3 equations and 4 unknowwns hence not solvable.
Please provide any linke for this theory if you have any
Thanks Question: should S/M = 3/4 be S/M = (4x)/(3x), since this is just a proportion and the numbers can take various values, so long as they remain proportionate? Does not 3x/4x = 3/4 ?
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26 Nov 2014, 09:51
True



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31 Jul 2015, 11:49
i solve it like Income 4x and 3x Savings 4y and 3y Expenditure total for both = 20000 Income = saving + expenditure so 7x=7y + 20000 Hence 1 and 2 toghether insufficient Is this correct way of solving ?
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Re: M0131
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11 Nov 2015, 03:17
Hi Could you please tell me.. where did I go wrong (1) S & M Income in the ratio of 4:3; I equated it to a constant K; 7K ..(Insufficient) (2) s & m saving in the ratio of 3:2; I equated it to a constant K; total saving 5K Now total income = 5K + Total expenses Total Income = 5K + 20000 Combining (1) & (2) 7K=5K + 20000 K = 10000; S = 40000, M=30000 So where did I go wrong. I presume equating both the equations to same constant is where I went wrong. Is it so, could you please clarify



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Re: M0131
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10 Mar 2016, 16:28
Why is the answer not C?
ratio of incomes is 4:3, using an unknown multiplier it is 4x:3x, therefore total income is 7x ratio of savings is 3:2, using an unknown multiplier it is 3x:2x, therefore total savings is 5x combining the statements we have total income  total savings = total spending, 7x5x=20,000 x=10,000 Sarah's annual income is 4*10,000 = $40,000



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20 Jul 2016, 10:16
Can someone explain what's wrong with below approach. ratio of incomes is 4:3, 4x:3x, therefore total income is 7x ratio of savings is 3:2, 3x:2x, therefore total savings is 5x combining the statements we have total income  total savings = total spending, 7x5x=20,000 x=10,000 Sarah's annual income is 4*10,000 = $40,000
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Re: M0131
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20 Jul 2016, 11:26
smartguy595 wrote: Can someone explain what's wrong with below approach.
ratio of incomes is 4:3, 4x:3x, therefore total income is 7x ratio of savings is 3:2, 3x:2x, therefore total savings is 5x combining the statements we have total income  total savings = total spending, 7x5x=20,000 x=10,000 Sarah's annual income is 4*10,000 = $40,000 You cannot use same multiplier x for both income and savings.
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Re: M0131
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20 Jul 2016, 20:48
Bunuel wrote: smartguy595 wrote: Can someone explain what's wrong with below approach.
ratio of incomes is 4:3, 4x:3x, therefore total income is 7x ratio of savings is 3:2, 3x:2x, therefore total savings is 5x combining the statements we have total income  total savings = total spending, 7x5x=20,000 x=10,000 Sarah's annual income is 4*10,000 = $40,000 You cannot use same multiplier x for both income and savings. Thanks Bunuel. I realized my mistake!
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23 Oct 2016, 19:46
I think this is a highquality question and I don't agree with the explanation. i Think these eqation can be solved Let salary be 4x and 3x Let Saving be 3y and 2y Expenditure = 4x3y +3x2y=7x5y 20,000=7x5y
therefore only Values of X and Y which satisfies these equation are X=5000 and Y=3000



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Re: M0131
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23 Oct 2016, 23:01
Ayush Mishra wrote: I think this is a highquality question and I don't agree with the explanation. i Think these eqation can be solved Let salary be 4x and 3x Let Saving be 3y and 2y Expenditure = 4x3y +3x2y=7x5y 20,000=7x5y
therefore only Values of X and Y which satisfies these equation are X=5000 and Y=3000 20,000=7x5y has infinitely many solutions. You cannot solve two variable linear equation to get only one solution (assuming you don't have any other constraints).
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Yes, I agree with explanation, as their total income and the expenditures of Sarah and Mary respectively are unknown. INCOME  EXPENDITURE =SAVINGS



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Re: M0131
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01 Apr 2019, 05:13
arunmandapaka wrote: Hi Could you please tell me.. where did I go wrong (1) S & M Income in the ratio of 4:3; I equated it to a constant K; 7K ..(Insufficient) (2) s & m saving in the ratio of 3:2; I equated it to a constant K; total saving 5K Now total income = 5K + Total expenses Total Income = 5K + 20000 Combining (1) & (2) 7K=5K + 20000 K = 10000; S = 40000, M=30000 So where did I go wrong. I presume equating both the equations to same constant is where I went wrong. Is it so, could you please clarify u cannot use constant 'k' for both income and savings. both are two different entities
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