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The figure below shows the dimensions of triangle ABC. What is ∠BIC?

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The figure below shows the dimensions of triangle ABC. What is ∠BIC?

by Max@Math Revolution » Tue Feb 04, 2020 1:21 am
[GMAT math practice question]

The figure below shows the dimensions of triangle ABC. What is ∠BIC?
2.4DS.png
1) Point I is the incenter of △ABC.
2) Line DE is parallel to line BC.
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Source: — Data Sufficiency |
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Re: The figure below shows the dimensions of triangle ABC. What is ∠BIC?

by Max@Math Revolution » Wed Feb 05, 2020 11:38 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.

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)

Since we can find an incenter of a triangle by the intersection of lines bisecting interior angles, ∠DBI is equal to ∠IBC, and ∠ECI is equal to ∠ICB.
2.4DS(A).png
Then we have ∠IBC = 22° and ∠ICB = 30°.
Thus, we have ∠BIC = 180° - ∠IBC - ∠ICB = 180° – 22° – 30° = 128°.

Since condition 1) yields a unique solution, it is sufficient.

Condition 2)

Since we don’t know the position of I on segment DE, condition 2) does not yield a unique solution, and it is not sufficient.

Therefore, A is the answer.
Answer: A
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