ziyuenlau wrote:Is a+b > c?
1) a, b, and c represent three different lengths of the sides of a certain triangle
2) a² + b² = c²
Great question!
Target question: Is a+b > c?
Statement 1: a, b, and c represent three different lengths of the sides of a certain triangle
IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .
DIFFERENCE between sides A and B < third side < SUM of sides A and B
So, we can be certain that
a+b > c
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: a² + b² = c²
Statement 2 is what I love about this question!
Statement 1 got me thinking about triangles, then this equation (which looks exactly like the Pythagorean Theorem), got me thinking about right triangles. So, my initial reaction was to reapply the concept from statement 1 to conclude that statement 2 is also sufficient.
Then it dawned on me that, even though a² + b² = c² COULD apply to a right triangle (where the length of each side is a positive number), it could also apply to negative values of a, b, and c.
In fact, there are infinitely many values of a, b, and c that satisfy statement 2. Here are two:
Case a: a = 3, b = 4 and c = 5, in which case
a+b > c
Case b: a = -3, b = -4 and c = 5, in which case
a+b < c
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer:
A
Cheers,
Brent
