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What is the length of CD in the figure?

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What is the length of CD in the figure?

by Max@Math Revolution » Tue Jan 28, 2020 11:50 pm
[GMAT math practice question]

What is the length of CD in the figure?
1.29ds.png
1) Point I is the incenter of triangle ABC, and D, E, and F are the tangential points.
2) The length of BC is 11, and BE is 8.
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Source: — Data Sufficiency |
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Re: What is the length of CD in the figure?

by Max@Math Revolution » Fri Jan 31, 2020 1:42 am
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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 a triangle, we have 3 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)
Since point I is the incenter of the triangle ABC, AD, AE, BE, BF, CD, and CE are tangent to the same circle, and we have AD = AE, BE = BF and CD = CF.
Then we have CD = FC = BC – BF = BC – BE = 11 – 8 = 3.

Since both conditions together yield a unique solution, they are sufficient.
1.29DS(A).png
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 in which the answer is A, B, C, or D.
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