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Math Expert V
Joined: 02 Sep 2009
Posts: 58465
The two circles above have centers at A and B, and their circumference  [#permalink]

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Difficulty:   5% (low)

Question Stats: 89% (01:07) correct 11% (01:05) wrong based on 62 sessions

HideShow timer Statistics The two circles above have centers at A and B, and their circumferences are x and y respectively. If the two circles touch at one point, what is the distance between A and B?

A. $$2\pi x + 2\pi y$$

B. $$\frac{x+y}{2\pi}$$

C. $$\frac{\pi}{x+y}$$

D. $$\pi x + \pi y$$

E. $$\frac{x+y}{\pi}$$

Attachment: 2018-01-18_1414.png [ 12.06 KiB | Viewed 998 times ]

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Marshall & McDonough Moderator D
Joined: 13 Apr 2015
Posts: 1682
Location: India
Re: The two circles above have centers at A and B, and their circumference  [#permalink]

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2*pi*R = x
2*pi*r = y

Distance between the 2 centers = R + r = (x + y)/2*pi

Board of Directors D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
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Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Re: The two circles above have centers at A and B, and their circumference  [#permalink]

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Bunuel wrote: The two circles above have centers at A and B, and their circumferences are x and y respectively. If the two circles touch at one point, what is the distance between A and B?

A. $$2\pi x + 2\pi y$$

B. $$\frac{x+y}{2\pi}$$

C. $$\frac{\pi}{x+y}$$

D. $$\pi x + \pi y$$

E. $$\frac{x+y}{\pi}$$

Attachment:
2018-01-18_1414.png

$$2πR = x$$
$$2πr = y$$

So,$$R = \frac{x}{2π}$$ & $$r = \frac{y}{2π}$$

Distance between A and B = Radius of A + Radius of B

So, Distance between A and B = $$\frac{x}{2π} + \frac{y}{2π}$$

Or, Distance between A and B = $$\frac{x+y}{2\pi}$$, answer will be (B)
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Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8137
Location: United States (CA)
Re: The two circles above have centers at A and B, and their circumference  [#permalink]

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Bunuel wrote: The two circles above have centers at A and B, and their circumferences are x and y respectively. If the two circles touch at one point, what is the distance between A and B?

A. $$2\pi x + 2\pi y$$

B. $$\frac{x+y}{2\pi}$$

C. $$\frac{\pi}{x+y}$$

D. $$\pi x + \pi y$$

E. $$\frac{x+y}{\pi}$$

Attachment:
2018-01-18_1414.png

The distance from A to B is the sum of the radii of Circles A and B.

We use the circumference formula C = 2πr. For circle A, we are given that the circumference is x, so we have:

x = 2πr
r =x/2π

Similarly, for Circle B, we solve for its radius:

y = 2πr
r = y/2π

The radius of circle A is x/2π, and the radius of circle B is y/2π, so the distance between A and B is:
x/2π + y/2π = (x + y)/2π

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Scott@TargetTestPrep.com

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Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8137
Location: United States (CA)
Re: The two circles above have centers at A and B, and their circumference  [#permalink]

Show Tags

Bunuel wrote: The two circles above have centers at A and B, and their circumferences are x and y respectively. If the two circles touch at one point, what is the distance between A and B?

A. $$2\pi x + 2\pi y$$

B. $$\frac{x+y}{2\pi}$$

C. $$\frac{\pi}{x+y}$$

D. $$\pi x + \pi y$$

E. $$\frac{x+y}{\pi}$$

Attachment:
2018-01-18_1414.png

The radius of circle A is x/2π, and the radius of circle B is y/2π, so the distance from A to B is x/2π + y/2π = (x + y)/2π.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: The two circles above have centers at A and B, and their circumference   [#permalink] 12 Jul 2019, 19:02
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