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# M01-31

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Math Expert
Joined: 02 Sep 2009
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Math Expert
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General Discussion
Math Expert
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Concentration: Operations, Sustainability
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I have an issue related to this question. I solved this question by a different method. it is clear that both statements are insufficient individually. To solve these statements together, I took the salary of Sarah and Mary as 4x and 3x and saving as 3y and 2y respectively. As combined spending is $20,000, it will be spending of Sarah + spending of Mary= 20,000 (4x-3y) + (3x-2y)= 20,000 7x-5y=20000 When I reached this equation. I got confused as I am not sure whether the unique values of x and y are possible from this equation or not. coz if unique values are possible then the answer will be C and if not then the answer will be E. How to deal with this kind of situation as it is hard sometime to guess numbers that fit in equations? Math Expert Joined: 02 Sep 2009 Posts: 94580 Own Kudos [?]: 643204 [0] Given Kudos: 86728 Re: M01-31 [#permalink] Expert Reply gauravsirohi93 wrote: I have an issue related to this question. I solved this question by a different method. it is clear that both statements are insufficient individually. To solve these statements together, I took the salary of Sarah and Mary as 4x and 3x and saving as 3y and 2y respectively. As combined spending is$20,000, it will be

spending of Sarah + spending of Mary= 20,000
(4x-3y) + (3x-2y)= 20,000
7x-5y=20000
When I reached this equation. I got confused as I am not sure whether the unique values of x and y are possible from this equation or not. coz if unique values are possible then the answer will be C and if not then the answer will be E. How to deal with this kind of situation as it is hard sometime to guess numbers that fit in equations?

7x-5y=20000

y = 7x/5 - 4000

Whenever x is large enough multiple of 5, y will turn out to be a positive integer. So, the above equation has more than one set of solutions.

Generally, even though there are some advanced techniques that allow to find whether a linear Diophantine equation of the form ax + by = c has a unique solution, for GMAT purposes it's better to test numbers.
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I think this is a high-quality question and I agree with explanation.
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I think this is a high-quality question and I agree with explanation. Minor issue: Please erase the extra period in statement 2 ".."

The ratio of Sarah's and Mary's annual savings last year was 3:2, and their combined spending was \$20,000..
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