BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

The area of circle O is added to its diameter. . .

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 2898
Joined: Thu Sep 07, 2017 2:49 pm
Thanked: 6 times
Followed by:5 members

The area of circle O is added to its diameter. . .

by Vincen » Wed Sep 27, 2017 5:39 pm
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/pi
B) 2
C) 3
D) 4
E) 5

The OA is B.

What are the calculus needed to solve this PS question?
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Thu Sep 28, 2017 8:07 am
Vincen 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/Ï€
B) 2
C) 3
D) 4
E) 5
Let r = radius of circle
Area of circle = πr²
Diameter = 2r
Circumference of circle = 2rπ

The area of circle O is added to its diameter...
We get: πr² + 2r

...If the circumference of circle O is then subtracted from this total, the result is 4
We get: πr² + 2r - 2rπ = 4
From here, we CAN just test the answer choices.
First, we can SKIP answer choice A, since the radius cannot have a negative value.

What about B (2)
Replace r with (2) to get: π(2)² + 2(2) - 2(2)π = 4
Simplify: 4Ï€ + 4 - 4Ï€ = 4
Simplify again: 4 = 4
PERFECT!

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Thu Sep 28, 2017 8:14 am
Vincen 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/pi
B) 2
C) 3
D) 4
E) 5
Another approach:

Once we get the equation πr² + 2r - 2rπ = 4, we can also solve it algebraically.
To do so, we're going to factor the expression in parts
Here's what I mean...

We have: πr² + 2r - 2rπ = 4
Subtract 4 from both sides to get: πr² + 2r - 2rπ - 4 = 0
Rearrange terms to get: πr² - 2rπ + 2r - 4 = 0
Factor as follows: πr(r - 2) + 2(r - 2) = 0
Notice that we have (x-2) in common in both parts.
So, we can combine the parts to get: (Ï€r + 2)(r - 2) = 0
This means that EITHER πr + 2 = 0 OR r - 2 = 0
case a: πr + 2 = 0
This means: πr = -2
Since π and r are both POSITIVE, this equation has NO SOLUTION

case b: r - 2 = 0
This tells us that r = 2

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Thu Sep 28, 2017 7:30 pm
Hi Vincen,

This question can be solved rather handily by TESTing THE ANSWER (one of the approaches that Brent showed), so I won't rehash any of that here. Instead, I want to point out a Geometry relationship that you might be able to use on Test Day.

In this prompt, we needed the "Pi"s to cancel out, since we were left with the number 4.

We were dealing with (π)(r²) and 2(π)(r) and the only way for those terms to cancel out is if r=2...

(π)(2²) and 2(π)(2) =
4Ï€ and 4Ï€

The geometry pattern is in reference to the radius of the circle. When comparing the area of a circle with the circumference of that same circle, the two values will be equal ONLY when the radius is 2.

If the radius is LESS than 2, then the circumference will be LARGER than the area.
If the radius is GREATER than 2, then the area will be LARGER than the circumference.

This math relationship might be useful on certain DS prompts and on PS questions in which you might need to approximate a value based on the radius (or vice versa).

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8085
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Thu Jan 11, 2018 1:48 pm
Vincen 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/pi
B) 2
C) 3
D) 4
E) 5
We can let r = radius of the circle and create the following equation:

Ï€r^2 + 2r - 2Ï€r = 4

Ï€r^2 + 2r - 2Ï€r - 4 = 0

r(Ï€r + 2) - 2(Ï€r + 2) = 0

(r - 2)(Ï€r + 2) = 0

r = 2

or

Ï€r + 2 = 0

Ï€r = -2

r = -2/Ï€

Since r can't be negative, r must be 2.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1