Don't know how to approach this problem. Started off by assuming basic values for r1 and r2, but got stuck. Please help.
TIA.
GMAT Prep Exam Pack 2 DS Problem
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- Srishti_15
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Question stem, rephrased:
What is A� : A₂ : A₃?
Statement 1: A₂ = A₃
Thus, A₂ : A₃ = 1:1.
No information about A�.
INSUFFICIENT.
Statement 2: A₂ + A₃ = 2A�
Case 1: A�=2, A₂=1, A₃=3
In this case, A� : A₂ : A₃ = 2:1:3.
Case 2: A�=2, A₂=2, A₃=2
In this case, A� : A₂ : A₃ = 2:2:2 = 1:1:1.
Since A� : A₂ : A₃ can be different values, INSUFFICIENT.
Statements combined:
Substituting A₂ = A₃ into A₂ + A₃ = 2A�, we get:
A₂ + A₂ = 2A�
2A₂ = 2A�
A₂ = A�.
Since A� = A₂ and A₂ = A₃, A� = A₂ = A₃.
Thus:
A� : A₂ : A₃ = 1:1:1.
SUFFICIENT.
The correct answer is C.
What is A� : A₂ : A₃?
Statement 1: A₂ = A₃
Thus, A₂ : A₃ = 1:1.
No information about A�.
INSUFFICIENT.
Statement 2: A₂ + A₃ = 2A�
Case 1: A�=2, A₂=1, A₃=3
In this case, A� : A₂ : A₃ = 2:1:3.
Case 2: A�=2, A₂=2, A₃=2
In this case, A� : A₂ : A₃ = 2:2:2 = 1:1:1.
Since A� : A₂ : A₃ can be different values, INSUFFICIENT.
Statements combined:
Substituting A₂ = A₃ into A₂ + A₃ = 2A�, we get:
A₂ + A₂ = 2A�
2A₂ = 2A�
A₂ = A�.
Since A� = A₂ and A₂ = A₃, A� = A₂ = A₃.
Thus:
A� : A₂ : A₃ = 1:1:1.
SUFFICIENT.
The correct answer is C.
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The answer to this seemed pretty straightforward, but I was wondering whether, since we are dealing with concentric circles, there is some way that one both of the statements could be sufficient on its or their own.
I proved that neither is sufficient by using the following ideas.
Statement 1: A₂ = A₃
Even if there is some reason that A�, A₂ and A₃ have to be related, A� could be 0, clearly. In that case A�/A₂ would be 0 and A₂/A₃ would be 1.
Meanwhile, A� does not have to be 0. If A� is not 0, then A�/A₂ is not 0. So already we have two different values for one of the ratios.
Insufficient.
Statement 2: A₂ + A₃ = 2A�
In this case, either A₂ or A₃ could be 0. If A₂ = 0, we get a different set of ratios from what we get if A₃ = 0.
Insufficient.
So, no, the fact that they are concentric circles does not make either statement sufficient on its own.
What a funny question, having all that stuff about circles, radii, cm and areas obscuring what is essentially the most basic ratio question ever. The question could have been simply, "A�, A₂ and A₃ are numbers. What is the ratio A� : A₂ : A₃?", but noooo. They give you all that other information, and you have to prove that it's useless. LOL
I proved that neither is sufficient by using the following ideas.
Statement 1: A₂ = A₃
Even if there is some reason that A�, A₂ and A₃ have to be related, A� could be 0, clearly. In that case A�/A₂ would be 0 and A₂/A₃ would be 1.
Meanwhile, A� does not have to be 0. If A� is not 0, then A�/A₂ is not 0. So already we have two different values for one of the ratios.
Insufficient.
Statement 2: A₂ + A₃ = 2A�
In this case, either A₂ or A₃ could be 0. If A₂ = 0, we get a different set of ratios from what we get if A₃ = 0.
Insufficient.
So, no, the fact that they are concentric circles does not make either statement sufficient on its own.
What a funny question, having all that stuff about circles, radii, cm and areas obscuring what is essentially the most basic ratio question ever. The question could have been simply, "A�, A₂ and A₃ are numbers. What is the ratio A� : A₂ : A₃?", but noooo. They give you all that other information, and you have to prove that it's useless. LOL
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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."
I found your explanation helpful, GMATGuruNY.
However, wanted to ask about the condition provided in the question stem that states, "r1<r2<r3."
Given the definition of a circle is πr^2, and substituting the definition of a circle into the ratio of the three circle's areas, I inferred that:
= A1 : A2 : A3
and replacing area with the definition of a circle:
= π(radius 1)^2: π(radius 2)^2 : π(radius 3)^2
results in the inequality below, given what we know about the relative sizes of the radii.
= A1 < A2 < A3
However, my logic is not correct given A2 = A3 in Statement 1.
How can A2 = A3 when the radii cannot be equal?
Thanks
I found your explanation helpful, GMATGuruNY.
However, wanted to ask about the condition provided in the question stem that states, "r1<r2<r3."
Given the definition of a circle is πr^2, and substituting the definition of a circle into the ratio of the three circle's areas, I inferred that:
= A1 : A2 : A3
and replacing area with the definition of a circle:
= π(radius 1)^2: π(radius 2)^2 : π(radius 3)^2
results in the inequality below, given what we know about the relative sizes of the radii.
= A1 < A2 < A3
However, my logic is not correct given A2 = A3 in Statement 1.
How can A2 = A3 when the radii cannot be equal?
Thanks
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A₂ and A₃ do not represent the areas of the two larger circles.Ovid wrote:Circle 1, Circle 2 and Circle 3 have the same center, and have a radius r1<r2<r3. --, 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."
I found your explanation helpful, GMATGuruNY.
However, wanted to ask about the condition provided in the question stem that states, "r1<r2<r3."
Given the definition of a circle is πr^2, and substituting the definition of a circle into the ratio of the three circle's areas, I inferred that:
= A1 : A2 : A3
and replacing area with the definition of a circle:
= π(radius 1)^2: π(radius 2)^2 : π(radius 3)^2
results in the inequality below, given what we know about the relative sizes of the radii.
= A1 < A2 < A3
However, my logic is not correct given A2 = A3 in Statement 1.
How can A2 = A3 when the radii cannot be equal?
Thanks
Reread this portion of the prompt:
Let A� be the area of circle 1.
Let Aâ‚‚ be the area of the region within Circle 2 and outside Circle 1.
Let A₃ be the area of the region within Circle 3 and outside Circle 2.
These statements imply the following figure:
In accordance with the prompt:
A� = the green portion above.
Aâ‚‚ = the red portion above.
A₃ = the blue portion above.
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For more information, please email me (Mitch Hunt) at [email protected].
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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