The area of Circle O is added to its diameter. If the circum : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 23 Jan 2017, 20:07

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 18 Mar 2012
Posts: 48
GMAT 1: 690 Q V
GPA: 3.7
Followers: 0

Kudos [?]: 189 [0], given: 117

The area of Circle O is added to its diameter. If the circum [#permalink]

### Show Tags

15 May 2012, 12:43
1
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

82% (03:01) correct 18% (02:25) wrong based on 68 sessions

### HideShow timer Statistics

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
Math Expert
Joined: 02 Sep 2009
Posts: 36618
Followers: 7102

Kudos [?]: 93589 [1] , given: 10578

Re: The area of Circle O is added to its diameter. If the circum [#permalink]

### Show Tags

16 May 2012, 02:28
1
KUDOS
Expert's post
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.

_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13530
Followers: 577

Kudos [?]: 163 [0], given: 0

Re: The area of Circle O is added to its diameter. If the circum [#permalink]

### Show Tags

25 Sep 2014, 12:39
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1858
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 47

Kudos [?]: 1937 [0], given: 193

The area of Circle O is added to its diameter. If the circum [#permalink]

### Show Tags

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 $$radius = \frac{4}{2} = 2$$

Bunuel/Experts: Kindly let me know if above argument holds value for calculation purpose in this question? Thank you
_________________

Kindly press "+1 Kudos" to appreciate

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1858
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 47

Kudos [?]: 1937 [0], given: 193

Re: The area of Circle O is added to its diameter. If the circum [#permalink]

### Show Tags

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?
_________________

Kindly press "+1 Kudos" to appreciate

Math Expert
Joined: 02 Sep 2009
Posts: 36618
Followers: 7102

Kudos [?]: 93589 [0], given: 10578

Re: The area of Circle O is added to its diameter. If the circum [#permalink]

### Show Tags

30 Sep 2014, 00:01
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.
_________________
Director
Joined: 23 Jan 2013
Posts: 579
Schools: Cambridge'16
Followers: 1

Kudos [?]: 42 [0], given: 40

Re: The area of Circle O is added to its diameter. If the circum [#permalink]

### Show Tags

16 Mar 2015, 01:10
area+diameter-circumference=4

pi*r^2+2r=4+2pi*r

isolate r and get r(pi*r+2)=4+2pi*r

r=(4+2pi*r)/(pi*r+2) =>2(2+pi*r)/(pi*r+2)

r=2

B
Re: The area of Circle O is added to its diameter. If the circum   [#permalink] 16 Mar 2015, 01:10
Similar topics Replies Last post
Similar
Topics:
1 If the diameter of a circle is 14, then the area of the circle is 3 03 Jan 2017, 20:23
8 The area of circle O is added to its diameter. If the circumference 5 11 Sep 2015, 01:03
2 What is the area of circle O above? 3 25 Aug 2013, 16:45
What is the area of circle O? 3 23 Apr 2013, 00:35
25 In the figure, circle O has center O, diameter AB and a radi 8 20 Feb 2008, 12:25
Display posts from previous: Sort by