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.