What is the area of the above triangle?

Question

9.6.png What is the area of the above triangle? 1) y=z 2) y+z=10

Chethan92 · Answer

From statement 1:

The triangle can be an equilateral or isosceles triangle depending on the value of X.
Hence Insufficient.

From statement 2:

No info about the other side X.
Hence insufficient.

Combining both will not give any new info.

Hence E is the answer.

fskilnik · Answer

Let´s go straight to (1+2) . Reason: if we are able to (geometrically) BIFURCATE both statements together immediately, we save a significant amount of time!

The areas of both triangles presented are different, and both triangles satisfy both statements. We are done: the answer is (E).

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
fskilnik.

MathRevolution · Answer

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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 we have 3 variables (x, y and z) 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.

Conditions 1) & 2)

Attachment:

9.10.png [ 13.33 KiB | Viewed 1961 times ]

If \(x = y = z = 5\), then the triangle is equilateral, and its area is \((\frac{√3}{4})*52 = (\frac{25}{4}) √3\).
If \(x = 6\) and \(y = z = 5\), then the area of the triangle is \((\frac{1}{2})6*4 = 12.\)
Since the answer is not unique, conditions 1) & 2) are not sufficient, when taken together.

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. Obviously, there may be occasions on which the answer is A, B, C or D.

What is the area of the above triangle?

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What is the area of the above triangle?

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