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The area of Circle O is added to its diameter. If the circum

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The area of Circle O is added to its diameter. If the circum [#permalink] New post 15 May 2012, 12:43
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The area of Circle O is added to its diameter. If the circumference of Circle O is then subtracted from this total, the result is 4. What is the radius of Circle O?

A. 2/π
B. 2
C. 3
D. 4
E. 5
[Reveal] Spoiler: OA
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Re: The area of Circle O is added to its diameter. If the circum [#permalink] New post 16 May 2012, 02:28
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alexpavlos wrote:
The area of Circle O is added to its diameter. If the circumference of Circle O is then subtracted from this total, the result is 4. What is the radius of Circle O?

A. 2/π
B. 2
C. 3
D. 4
E. 5


Given: area+diameter-circumference=4 --> \pi{r^2}+2r-2\pi{r}=4 --> (\pi{r^2}-2\pi{r})+(2r-4)= --> \pi{r}({r-2)+2(r-2)=0 --> (r-2)(\pi{r}+2)=0 --> either r=2 or r=-\frac{2}{\pi}, which is not a valid solution since the value of the radius cannot be negative.

Answer: B.
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Re: The area of Circle O is added to its diameter. If the circum [#permalink] New post 25 Sep 2014, 12:39
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The area of Circle O is added to its diameter. If the circum [#permalink] New post 29 Sep 2014, 00:52
Area + Diameter - Circumference = 4

Just observe the above setup equation in terms of circle

Area calculation always involves the \pi factor. Example, \pi r^2 etc for whatever the radius may be.

Similarly, Circumference calculation always involves again the \pi factor. Example, 2\pi r for whatever the radius may be.

Now the resultant of all this ideally should have a \pi. However , the resultant returned = 4.

It means the \pi factor is cancelled out in the calculation which also means Area of the given circle = circumference of the given circle.

Area of Circle = Circumference of circle: Happens only when Radius = 2

In this case, Diameter = 4; so radius = \frac{4}{2} = 2

Answer = B


Bunuel/Experts: Kindly let me know if above argument holds value for calculation purpose in this question? Thank you
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Re: The area of Circle O is added to its diameter. If the circum [#permalink] New post 29 Sep 2014, 19:02
alex1233 wrote:
The area of Circle O is added to its diameter. If the circumference of Circle O is then subtracted from this total, the result is 4. What is the radius of Circle O?

A. 2/π
B. 2
C. 3
D. 4
E. 5


Bunuel/ Karishma: Although I have posted my answer earlier, want to know if this problem is "technically correct"?

Say, if the diameter is in meters, then circumference would also be in meters. However, Area would be in (meter)^2.

How can we perform addition/subtraction in dissimilar units?
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Re: The area of Circle O is added to its diameter. If the circum [#permalink] New post 30 Sep 2014, 00:01
Expert's post
PareshGmat wrote:
alex1233 wrote:
The area of Circle O is added to its diameter. If the circumference of Circle O is then subtracted from this total, the result is 4. What is the radius of Circle O?

A. 2/π
B. 2
C. 3
D. 4
E. 5


Bunuel/ Karishma: Although I have posted my answer earlier, want to know if this problem is "technically correct"?

Say, if the diameter is in meters, then circumference would also be in meters. However, Area would be in (meter)^2.

How can we perform addition/subtraction in dissimilar units?


I think it's clear that the question means adding numerical value of area to numerical value of diameter. I see no point to complicate.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: The area of Circle O is added to its diameter. If the circum   [#permalink] 30 Sep 2014, 00:01
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