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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
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Since we have 2 variables (AD and EC) in the original condition, C is most likely the answer. We can figure out where D and E are by AD and EC. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.
Conditions 1) & 2)
Since triangles AED and AEC are congruent, we have DE = CE and DB = 5 - 3 = 2.
The area of triangle ABC = (1/2)*4*3 = 6, which is also the sum of the areas of triangle ABE and triangle AEC.
Then we have (1/2)*5*DE + (1/2)*3*CE = (5/2)DE + (3/2)DE = (8/2)DE = 4DE = 6.
Thus, we have DE = 6/4, or DE = 3/2.
The area of triangle DBE is (1/2)*DB*DE = (1/2)*2*(3/2) = 3/2.
Since both conditions together yield a unique solution, they are sufficient.
Therefore, C is the answer.
Answer: C
In cases where 3 or more additional equations are required, such as for original conditions with "3 variables", or "4 variables and 1 equation", or "5 variables and 2 equations", conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2) when taken together. Obviously, there may be occasions on which the answer is A, B, C, or D.
