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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Is triangle ABC a right triangle? tagged by: Max@Math Revolution ##### This topic has 1 expert reply and 0 member replies ### GMAT/MBA Expert ## Is triangle ABC a right triangle? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [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 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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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,

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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