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In the figure above, if A, B, and C are the areas, respectively, of th

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In the figure above, if A, B, and C are the areas, respectively, of th  [#permalink]

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New post 26 Apr 2019, 02:50
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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


Attachment:
2019-04-26_1348.png
2019-04-26_1348.png [ 12.14 KiB | Viewed 3401 times ]

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In the figure above, if A, B, and C are the areas, respectively, of th  [#permalink]

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New post 26 Apr 2019, 21:05
Bunuel wrote:
Image
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


Given that the areas of the two circles are equal.
Hence, A+B=B+C or, A=C

Question stem:- B+C=?

St1:- A + 2B + C = 24
Or, (A+B)+(B+C) or, (B+C)+(B+C)=24 or, 2(B+C)=24
Therefore, the value of B+C can be determined.
Sufficient.

St2:- A + C = 18 and B = 3

Or, C+C=18 or C=9

Therefore, the value of B+C can be determined.
Sufficient.

Ans. (D)
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Re: In the figure above, if A, B, and C are the areas, respectively, of th  [#permalink]

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New post 27 Apr 2019, 05:56
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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Re: In the figure above, if A, B, and C are the areas, respectively, of th  [#permalink]

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New post 07 May 2019, 18:36
Bunuel wrote:
Image
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


Attachment:
2019-04-26_1348.png


We are given that the areas of the two circles are equal, so A = C. We need to determine B + C.

Statement One Alone:

A + 2B + C = 24

Substituting we have:

C + 2B + C = 24

2C + 2B = 24

C + B = 12

Statement One alone is sufficient to answer the question.

Statement Two Alone:

A + C = 18 and B = 3

Again substituting we have:

C + C = 18

2C = 18

C = 9

B = 3

So B + C = 3 + 9 = 12

Statement two alone is sufficient to answer the question.

Answer: D
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Re: In the figure above, if A, B, and C are the areas, respectively, of th  [#permalink]

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New post 12 May 2019, 13:58
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

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Re: In the figure above, if A, B, and C are the areas, respectively, of th  [#permalink]

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New post 17 May 2019, 10:38
Top Contributor
Bunuel wrote:
Image
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:
Image
We're told that the area of the BLUE circle = the area of the RED circle
This means we can say: A + B = B + C

Now 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 = 12
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: A + C = 18 and B = 3
This 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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Re: In the figure above, if A, B, and C are the areas, respectively, of th  [#permalink]

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New post 17 May 2019, 22:37
Bunuel wrote:
Image
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


Attachment:
2019-04-26_1348.png


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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Re: In the figure above, if A, B, and C are the areas, respectively, of th   [#permalink] 17 May 2019, 22:37
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