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

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

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

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 + 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

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

Posted from my mobile device

Bunuel

For PS questions, when is it safe/not safe to assume that the figures provided are made to scale?

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.

Sol:

This is a very very easy question if you read properly. (areas of the circle are equal)

So. here is a trick, in GMAT if you think C is an obvious answer then it may be a trick question.

SO check 1: we know A=c so we can write


(1) A + 2B + C = 24


or 2B+2C=24 thus B+C=12

now check 2:

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

or 2C=18 and B=3,

or C=9 and B=3 thus B+C=12.

D is good answer.

PS: if you read the questionin hurry then you might think ..oh! 1 equations 3 variables then not suff. and 2 equations 3 variables not suff.

but each is sufficient.

The make or break detail in this question is "equal areas"

If you dont read carefully, you might miss this detail and then you'll choose the wrong answer

Once you capture that detail, its a cakewalk.

Since the circles are equal, A+B=B+C => A=C

S1: Substitute C for A and the equation becomes 2B+2C=24 => B+C=12. SUFFICIENT.

S2: Since A and C are equal, they must both equal 9. We are told that B is 3 so we can find that B+C=9+3=12. SUFFICIENT.

ANSWER: D

Given,
A+B=B+C
A = C

1) A +2B+C = 24
C+ 2B + C= 24
B+C = 24 SUFF.
2. A = C SO, SUFF,

ANS. D.

I have a question: how do we know that the area on the left is equal to the area on the right?
According to the official explanation, "it is given that the area of the left circle is equal to the area of the right circle". Where exactly was it 'given' ?

Thanks!

Hi HWPO,

The prompt includes the following text describing the circles: "... the intersection of two circles of EQUAL area..." Thus, the areas of the two circles (and by extension, the radius of each circle), is the same.

GMAT assassins aren't born, they're made,
Rich

Given that, A+B=B+C, A=C

(1) A+2B+C=24 Sufficient AS A=C.

(2) Sufficient. A=C.

The answer is D.

Answer: Option D

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