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As the figure below shows, ABC is a right triangle. Wha

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As the figure below shows, ABC is a right triangle. Wha

by Max@Math Revolution » Mon Jan 06, 2020 12:36 am
[GMAT math practice question]

As the figure below shows, ABC is a right triangle. What is the measure of ∠ B?

1) DM is a perpendicular bisector of segment AB.
2) ∠ MAD = ∠ CAD

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Source: — Data Sufficiency |
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by Max@Math Revolution » Tue Jan 07, 2020 11:35 pm
=>

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.

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.

Condition 1) tells us that triangle ABD is isosceles with BD = AC and ∠ B = ∠ MBD = ∠ MAD. Condition 2) tells us that ∠ MAD = ∠ CAD.
Since ∠ C = 90, we have ∠ MBD + ∠ MAD + ∠ CAD + ∠ C = 180, ∠ MBD + ∠ MAD + ∠ CAD + 90 = 180, or ∠ MBD + ∠ MAD + ∠ CAD = 90 and ∠ MBD = ∠ MAD = ∠ CAD. As each angle is the same and all three add up to 90, each angle must be 30.
Thus we have ∠ B = ∠ MBD = 30.

Since both conditions together yield a unique solution, they are sufficient.

Therefore, C is the answer.
Answer: C
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