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Is triangle ABC a right triangle?

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Is triangle ABC a right triangle?

by Max@Math Revolution » Fri May 10, 2019 12:02 am

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[GMAT math practice question]

Is triangle ABC a right triangle?

1) The perimeter of triangle ABC is 12
2) The length of the shortest side of triangle ABC is 3
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Source: — Data Sufficiency |
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by Max@Math Revolution » Sun May 12, 2019 5:31 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.

Since questions about triangles require 3 variables, E is most likely to be 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.

Let x, y and z be the side-lengths of triangle ABC, and suppose x ≤ y ≤ z.
Then x = 3 and x + y + z = 12.
If y = 4 and z = 5, triangle ABC has side lengths 3, 4 and 5. Thus it is a right triangle, and the answer is 'yes'.
If y = 4.5 and z = 4.5, triangle ABC has side lengths 3, 4.5 and 4.5. It is not a right triangle, and the answer is 'no'.
Since the two conditions don't yield a unique answer when applied together, they are not sufficient,

Therefore, E is the answer.
Answer: E

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. Ob
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