This data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in a leap year or the meaning of the word counterclockwise), you must indicate whether –
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Question
Is triangle ABC obtuse angled?
I) a^2 + b^2 > c^2
II) The center of the circle circumscribing the triangle does not lie inside the triangle
The correct answer is Choice E. Data is insufficient.
Explanatory Answer
In an obtuse angled triangle, if ‘c’ is the longest side, then c^2 > a^2 + b^2
Statement 1
a^2 + b^2 > c^2.
We have no information about whether c is the longest side in the triangle. Hence, we cannot answer the question. Statement 1 is INSUFFICIENT.
Statement 2
The center of the circle circumscribing the triangle does not lie inside the triangle.
> For an acute angled triangle, the center of the circle circumscribing the triangle lies inside the triangle.
> For a right triangle, the center of the circle circumscribing the triangle lies at the mid point of the hypotenuse.
> For an obtuse angled triangle, the center of the circle circumscribing the triangle lies outside the triangle.
From statement 2, we can deduce that the triangle is not an acute angled triangle. It may be a right angled triangle or an obtuse angled triangle. Hence, statement 2 is also INSUFFICIENT.
Combining the two statements, we cannot deduce anything more than what we could deduce using the information from the two statements independently.
Hence, Choice E is the correct answer.
You could get additional GMAT Data Sufficiency Practice questions here.