Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 24 Oct 2016, 18:45

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

M01, #31

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
Manager
Joined: 26 Jan 2008
Posts: 210
Followers: 3

Kudos [?]: 25 [0], given: 36

Show Tags

28 Jun 2010, 15:36
Quote:
What is Sarah's annual income?

The ratio of Sarah's and Mary's annual income is 4:3.
The ratio of Sarah's and Mary's savings is 3:2, and combined they spend \$20,000, annually.

This linear system has 3 equations and 4 unknowns. Consequently, we cannot solve the system of equations.

Is it correct to assume that if there are more variables than number of expressions, the problem cannot be solved?
CEO
Joined: 15 Aug 2003
Posts: 3460
Followers: 68

Kudos [?]: 847 [1] , given: 781

Re: M01, #31 [#permalink]

Show Tags

29 Jun 2010, 01:28
1
KUDOS
Apologies, we should explain that in more detail.

It is not an assumption.

To visualize the idea, think of a system of linear equations as straight lines on a graph. The solution to any system of equations is one and only one point where these lines intersect. With more unknowns than equations, you will find many such solutions.

Try and work with a smaller example: 3 unknowns and 2 equations.
Intern
Joined: 29 Sep 2010
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: M01, #31 [#permalink]

Show Tags

29 Sep 2010, 02:22
hi,

I thought about the question and since 20,000 is given as the amount they together spend annually, then it seems that 20,000 must be the difference in the ratios of 4:3 and 3:2. All of the ratios are met if the below is true:

40,000 = Sarah's annual income
30,000 = Mary's annual income

30,000 = Sarah's savings
20,000 = Mary's savings

Then the 20,000 spending is split equally (10,000 each)

Why would this not work?

Thanks!
Manager
Joined: 21 Feb 2012
Posts: 70
Location: United States
Concentration: Finance
Schools: Anderson '15 (M)
GMAT 1: 730 Q49 V40
GPA: 3.5
WE: Consulting (Health Care)
Followers: 1

Kudos [?]: 10 [0], given: 9

Re: M01, #31 [#permalink]

Show Tags

12 Mar 2012, 20:18
michaeldavis,

I was wondering the same thing. I believe the correct answer should be C.

since we get a concrete number for the amount of spending between the two people, we can set up 4x+3x-20000=5x... and we get the unknown multiplier of 10000 and figure out the annual income of both people.

Can anyone confirm that the answer should be C?
Intern
Joined: 31 Dec 2010
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: M01, #31 [#permalink]

Show Tags

19 Mar 2012, 14:54
I'd say:
Income ratio: 4x/3x ::: total income 7x
Saving ratio: 3x/2x ::: total savings 5x
Total expenditure is 20,000

Total income - total savings = total expenditure
7x - 5x = 20,000 :::: x=10,000
Sara's income: 10,000x4= 40,000
Intern
Joined: 21 Feb 2012
Posts: 12
Location: Chile
Followers: 0

Kudos [?]: 6 [0], given: 3

Re: M01, #31 [#permalink]

Show Tags

23 Mar 2012, 12:24
Hi yoonsiklim1, nicasc

The problem is that you are both assuming that the quantity by which each part of the ratio is "scaled" is the same. That is not correct. In doing so, you are using an additional constraint not described in the original problem. Look at the following example.

Sara's income (S) could be 40000, but could also be 20000. If S = 20000, according to the first statement, Mary's income (M) = 3*S/4. Then, if S = 20000, M = 15000.

$$\frac{S}{M} = \frac{20000}{15000} = \frac{4}{3}*\frac{5000}{5000}$$

where that 5000 is the number you called x.

In this case, the spending of Sara (z) is 11000 and the spending of Mary (y) is 9000 (you can get these numbers using all the information given by the statements). Therefore,

$$\frac{(S - z)}{(M - y)} = \frac{(20000 - 11000)}{(15000 - 9000)} = \frac{9000}{6000} = \frac{3}{2} * \frac{3000}{3000}$$

where that 3000 is ALSO the number you called x.

The red numbers are the quantities by which each part of the ratio is multiplied in order to obtain the actual incomes, spendings, and savings (Manhattan GMAT defines this quantity as the "Unknown Multiplier"). You can see that they are different. It happens, however, that in the case of S = 40000 and M = 30000 (the one you described) these quantities (your x´s) are both equal to 10000.
_________________

Francisco

Re: M01, #31   [#permalink] 23 Mar 2012, 12:24
Similar topics Replies Last post
Similar
Topics:
m01 1 27 May 2009, 11:20
17 M01 #11 26 25 Sep 2008, 14:24
19 m01 Q17 18 18 Sep 2008, 03:14
5 M01 27 11 21 Aug 2008, 10:29
19 M01-Q15 20 16 Jul 2008, 21:25
Display posts from previous: Sort by

M01, #31

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

Moderator: Bunuel

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.