GMATinsight wrote:

Is the area of the circle circumscribing triangle ABC less than 25π?

1) Triangle ABC is a right angle triangle with sides length integers

2) Two of the Sides of Triangle ABC are 6 and 8

Source:

http://www.GMATinsight.comForget 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 we have 3 variables for sides of the triangles and 0 equations, 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.

We can determine the circle from the triangle, which means if we have a specific triangle, we can determine the circumscribing circle.

Condition 1) & 2):

\(a^2 + b^2 = c^2\) from the condition 1) where \(c\) is a hypotenuse of the triangle.

\(a = 6\) and \(b = 8\) from the condition 2) and we have \(c = 10\).

The diameter of the circumscribing circle is the length of the right triangle's hypotenuse.

Thus both conditions together are sufficient.

Therefore, the answer is 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 on which the answer is A, B, C or D.

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