CrackVerbalGMAT wrote:
Bunuel wrote:
If a semicircle and triangle are pieced together to form the figure shown above, what is the total unit area of the figure?
(1) The length of AB is 2 units.
(2) x = y
The area of the semicircle can be found as the radius from the figure is 1. We now need to find the area of the triangle ABC
Statement 1: The length of AB is 2 units.
From this we only get to know that Triangle ABC is isosceles with AB = AC = 2 units.
We cannot find the area of the triangle without knowing the value of the 3rd side (BC)
Therefore Statement 1 Alone is Insufficient. Answer options could be B, C or E
Statement 2: x = y
From this, we get that BC = AC = 2 (Sides opposite equal angles)
We cannot find the area of the triangle without knowing the value of the 3rd side (AB)
Therefore Statement 2 Alone is Insufficient.
Combining Both Statements:We get that AB = BC = AC = 2. This forms an equilateral triangle and we can find the area of the triangle.
Therefore Both Statements together are sufficient.
Option CArun Kumar
Hi Arun, I am a bit confused.
So for statement 1, you deduced that Triangle ABC is isosceles with AB = AC = 2 units.
However, the only way you could do that is if you assumed angle C is also x.
Statement1 is clearly insufficient.
However, if we can assume that angle C is x in statement 1, why can't we do the same in statement 2?
In which case we know x = y implies that all three angles are 60 degrees thus making statement 2 sufficient.
Can someone explain?