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


DS59502.01
OG2020 NEW QUESTION



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While most DS questions are solved faster using the Logical approach, in this question we are given equations which can be simplified, and thus the Precise approach should be faster.
Since the circles are equal, A = C (they are the difference between the area of a full circle and B).
In statement (1) we can substitute A with C and get:
C + 2B + C = 24
2B + 2C = 24 (divided by 2:)
B + C = 12
That's enough!
In statement (2) we can substitute A with C again and get:
C + C = 18
C = 9
And since we have the value of B, that's enough as well.
The correct answer is D.

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Hi All,

We're told that in the figure above, A, B, and C are the areas, respectively, of the three non-overlapping regions formed by the intersection of two circles of EQUAL area. We're asked for the value of B + C. While this question might look like it might be step-heavy, there are some Geometry patterns that we can use to our advantage. To start, it's worth noting that the question is asking for the area of one of the circles (and since we're told that the circles have the SAME area, if we can determine the area of EITHER circle, then we can answer the question). Second, since B is an 'equal part' of both circles, we know that A=C.

(1) A + 2B + C = 24

With the equation in Fact 1, we can break the calculation into 2 equal 'pieces': (A+B) and (B+C). We know that those pieces are the SAME, so they each have HALF the total area - an area of 12 (and that is the answer to the question).
Fact 1 is SUFFICIENT

(2) A + C = 18 and B = 3

Fact 2 gives us the exact values we need to find the area of either circle. Since A=C, with the equation A+C = 18, we know that A=C=9. When combined with B=3, we know the area of each circle (re: 9+3 = 12)
Fact 2 is SUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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Because two circles are equal in size, so
A+B=B+C
=>A=C

1. C+2B+C=24
=>B+C=12
2. C+C=18
=>C=9
B+C=9+3=12

SO, Answer is D

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OFFICIAL GUIDE:

Problem Solving
Figures: All figures accompanying problem solving questions are intended to provide information useful in solving the problems. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

Data Sufficiency:
Figures:
• Figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2).
• Lines shown as straight are straight, and lines that appear jagged are also straight.
• The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero.
• All figures lie in a plane unless otherwise indicated.

Hope it helps.
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