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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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The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.
Since we have two quadrilaterals, we have 10 variables and 0 equations, E is most likely the answer. 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) together give us that:
Since we have BC = CD, EC = CF and ∠BCD = ∠DCF, triangles EBC and FDC are congruent according to the SAS property.
Since ∠EBC + ∠BED = 90° and ∠DEH = ∠BED, we have ∠DEH + ∠EDH = 90° and ∠DHE = 180° – 90° = 90°.
The answer is unique, so the condition is sufficient according to Common Mistake Type 2, which states that the number of answers must be only one.
Both conditions 1) & 2) together are sufficient.
Therefore, C is the correct 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.
