RBBmba@2014 wrote:Thanks Mitch. I missed the catch "the total number of associates = d*a".
The approach I followed (obviously after getting the above missing link right, from your solution) is plugging in values ,although it took a lot of time to reach to answer. Whereas, your equation based approach is a faster one BUT I guess, it's a bit tricky to understand during test environment that this 'equation based approach' could be used in such a way.
The purpose of algebra is to show how the values in a problem are CONSTRAINED.
When we evaluate statement 1, we have the following information:
Each director sold 10 cars.
Each associate sold 20 cars.
The total number of cars sold was 270.
This information clearly implies an equation:
(number of cars sold by the directors) + (number of cars sold by the associates) = 270.
Since this equation is clearly implied, we should check how it constrains the unknowns in the problem.
Most critical part would be I think, to quickly understand this -
d(1 + 2a) = 27.
Thus, d is a factor of 27: 1, 3, 9, or 27.
So, my question is whether there is any other smarter approach to this 700+ level (I presume it's so) problem?
Equation implied by statement 1:
10d + 20ad = 270.
When given an equation, SIMPLIFY.
Here, we can simplify by dividing by 10 and by factoring out d:
d + 2ad = 27.
d(1 + 2a) = 27.
Now we can see how the values of a and d are constrained.
d and (1 + 2a) must both be factors of 27.
Please note that there is no such thing as a "smarter" approach.
Whenever it is suggested that a particular solution is the "best," be skeptical:
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The best approach for one test-taker might not be the best approach for another.
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