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The midpoints of 3 sides of the triangle ABC are respectivel

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by Max@Math Revolution » Mon May 02, 2016 10:40 pm
The midpoints of 3 sides of the triangle ABC are respectively D, E, F. What is the perimeter of triangle ABC?
1) The perimeter of the triangle DEF is 10
2) The length of the side AC is 4

* A solution will be posted in two days.
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Source: — Data Sufficiency |
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by Max@Math Revolution » Tue May 10, 2016 5:59 pm
Points D, E, and F are the midpoints for AB, AC and BC. Then, if DE=x, DF=y and EF=z, BC=2x, AC=2y and AB=2z. The question becomes 2(x+y+z)=?. Since the condition 1) essentially means x+y+z=10. The condition 1), thus, is sufficient, and the correct answer is A.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
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