inakihernandez wrote:
Circle 1, Circle 2 and Circle 3 have the same center, and have a radius r1<r2<r3. Let A1 be the area of circle 1, let A2 be the area of the region within Circle 2 and outside Circle 1, and let A3 be the area of the region within Circle 3 and outside Circle 2. What are the values A1/A2 and A2/A3?
(1) A2=A3
(2) A2+A3 = 2 A1
Target question: What are the values A1/A2 and A2/A3? Statement 1: A2=A3 This will help us determine the value of A2/A3 (it equals 1) but, since we have no information about A1, statement 1 is NOT SUFFICIENT
Statement 2: A2+A3 = 2 A1 This tells us that the COMBINED areas of A2 and A3 are twice the area of A1
So, for example, we COULD have a scenario that looks like this...
..... in which the green area is twice the area of the A1.
Or we COULD have a scenario that looks like this...
Notice that the green area is still twice the area of the A1.
As you can see, the value of A2/A3 is different for each of the above cases.
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that A2=A3, so let's let x = the area of each part
Statement 2 tells us that A2+A3 = 2 A1, which means we can now write: x + x = 2(A1)
In other words, 2x = 2(A1), which means A1 = x
So, all 3 regions have area x:
This means
A1/A2 = x/x = 1, and A2/A3 = x/x = 1Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent