Bunuel wrote:
In the figure above, if A, B, and C are the areas, respectively, of the three nonoverlapping regions formed by the intersection of two circles of equal area, what is the value of B + C ?
(1) A + 2B + C = 24
(2) A + C = 18 and B = 3
Attachment:
2019-04-26_1348.png
Key concept: We're told that the area of the BLUE circle = the area of the RED circle
This means we can say:
A + B = B + CNow onto the question.....
Target question: What is the value of B + C ? Statement 1: A + 2B + C = 24 Rewrite this as: (A + B) + (B + C) = 24
Since we already know that
A + B = B + C, we can take the above equation and replace (A + B) with (B + C)
We get: (
B + C) + (B + C) = 24
Simplify: 2B + 2C = 24
Divide both sides by 2 to get:
B + C = 12Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: A + C = 18 and B = 3This means: (A + C) + B + B = (18) + 3 + 3 = 24
In other words, A + 2B + C = 24
HEY!!! We've seen that information before!!
Statement 1 told us that A + 2B + C = 24
Since statement 1 is SUFFICIENT, it must be the case that statement 2 is SUFFICIENT (since both statements provide the SAME information)
Statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
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