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As the figure below shows, line l is perpendicular to BD and

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As the figure below shows, line l is perpendicular to BD and

by Max@Math Revolution » Wed Jan 01, 2020 10:54 pm
[GMAT math practice question]

As the figure below shows, line l is perpendicular to BD and CE. What is the length of DE?

Image

$$\left(1\right)\ \triangle ABC\ is\ a\ right\ isosceles\ triangle\ with\ \angle BAC\ 90$$
$$\left(2\right)\ BD=3,\ and\ CE=4.$$
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Source: — Data Sufficiency |
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by Max@Math Revolution » Sat Jan 04, 2020 11:33 pm
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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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have 9 variables from 3 triangles and 2 equations from two right triangles, 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)

Since we have AB = AC from condition 1) and ∠DBA = ∠EAC, the triangles ADB and CEA are congruent.
Thus, DE = DA + AE = CE + BD = 3 + 4 = 7.

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.
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