Bunuel
What is the area of the triangle ABC?
(1) The edge AB of the triangle is 8 inches.
(2) Triangle ABC is equilateral
Target question: What is the area of the triangle ABC? Statement 1: The edge AB of the triangle is 8 inches. Knowing the length of ONE side is not enough information to determine the area of the triangle, since there are infinitely many triangles (with infinitely many areas) in which one side length is 8 inches,
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: Triangle ABC is equilateralWe still don't know how LARGE this equilateral triangle is.
For example, an equilateral triangle with side lengths 10 will have a much bigger area than an equilateral triangle with side lengths 1.
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 2 tells us that we have an equilateral triangle, which means all three sides are the same length.
Statement 1 tells us one side has length 8, which means ALL three sides have lengths 8, which means we COULD determine the area of this triangle (although we would never waste valuable time on test day doing so). We need only determine that we COULD answer the target question.
Since we COULD answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent