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# In the above figure, the area of circle A is 144π and the area of circ

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Math Expert
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In the above figure, the area of circle A is 144π and the area of circ  [#permalink]

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25 Jun 2015, 03:40
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75% (01:10) correct 25% (01:37) wrong based on 98 sessions

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In the above figure, the area of circle A is 144π and the area of circle B is 169π. If point x (not shown above) lies on circle A and point y (not shown above) lies on circle B, what is the range of the possible lengths of line xY.

A) 0 to 169π^2
B) 0 to 144
C) 0 to 25
D) 0 to 50
E) 5 to 144

Source: Platinum GMAT
Kudos for a correct solution.
Attachment:

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Re: In the above figure, the area of circle A is 144π  [#permalink]

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25 Jun 2015, 04:27
Circle A has a Diameter of 24
Circle B has a Diameter of 26

Shortest line, if both points lie in the middle where the circles tangent = 0. If both points lie on the outer bounds, then the longest line would be their diameters 26 + 24 = 50.

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In the above figure, the area of circle A is 144π and the area of circ  [#permalink]

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25 Jun 2015, 04:52
Bunuel wrote:

In the above figure, the area of circle A is 144π and the area of circle B is 169π. If point x (not shown above) lies on circle A and point y (not shown above) lies on circle B, what is the range of the possible lengths of line xY.

A) 0 to 169π^2
B) 0 to 144
C) 0 to 25
D) 0 to 50
E) 5 to 144

Source: Platinum GMAT
Kudos for a correct solution.
Attachment:
00022-1.gif

Area of Circle = πr^2

Area of Circle A = 144π = πr^2
i.e. Radius of Circle A = 12

Area of Circle B = 169π = πr^2
i.e. Radius of Circle B = 13

Maximum Length of XY = Diameter of A + Diameter of B = 2(12+13) = 50
Minimum Length of XY = 0 (When the Two circles are tangent to each other)

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Re: In the above figure, the area of circle A is 144π and the area of circ  [#permalink]

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25 Jun 2015, 05:57
1
Bunuel wrote:

In the above figure, the area of circle A is 144π and the area of circle B is 169π. If point x (not shown above) lies on circle A and point y (not shown above) lies on circle B, what is the range of the possible lengths of line xY.

A) 0 to 169π^2
B) 0 to 144
C) 0 to 25
D) 0 to 50
E) 5 to 144

Source: Platinum GMAT
Kudos for a correct solution.
Attachment:
00022-1.gif

Area of circle A=144pie
Similarly, radius of circle B=13 and diameter=26
If both the points X and Y lie on the same point, distance=0
For max distance, we need to add the distance of diameters=24+26=50
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Re: In the above figure, the area of circle A is 144π and the area of circ  [#permalink]

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25 Jun 2015, 08:45
Area of A = 144pie = pie r^2 =? r=12; d=24
Area of B=169pie=pie R^2 => R=13; D=26
Minimum length of length of xy = 0, where both A and B touches
Maximum length of XY = d+D=50,
Hence range of length of xy = 0 to 50

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Math Expert
Joined: 02 Sep 2009
Posts: 61280
Re: In the above figure, the area of circle A is 144π and the area of circ  [#permalink]

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29 Jun 2015, 04:24
Bunuel wrote:

In the above figure, the area of circle A is 144π and the area of circle B is 169π. If point x (not shown above) lies on circle A and point y (not shown above) lies on circle B, what is the range of the possible lengths of line xY.

A) 0 to 169π^2
B) 0 to 144
C) 0 to 25
D) 0 to 50
E) 5 to 144

Source: Platinum GMAT
Kudos for a correct solution.
Attachment:
The attachment 00022-1.gif is no longer available

Platinum GMAT Official Solution:

The shortest distance of line xy will occur when x and y are at the same point (i.e., the point where the two circles come together). In this instance, the line xy will be 0 units long.

In order to determine the longest possible distance for xy, we must first recall that the longest line across a circle is the circle's diameter. In other words, it is impossible to construct a line from one point on a circle to another point on the same circle that is longer than the circle's diameter.

The longest distance of line xy will occur when x and y are at exact opposite sides of the two circles. In other words, when x is at the far left of A and y is at the far right of B. More technically, line xy will be the combined diameter of circles A and B. This makes sense given that the diameter of a circle is the longest possible line from one point on the circle to another point on the same circle.

Since the length of xy is the length of the diameter of A plus the diameter of B, we need to find the diameter of each circle.
Area of A = 144π = πr^2
rA = 12 = radius of circle A
dA = 2(12) = 24 = diameter of circle A

Area of B = 169π = πr^2
rB = 13 = radius of circle B
dB = 2(13) = 26 = diameter of circle B

Maximum distance of xy = 24 + 26 = 50.

Attachment:

00022-2.gif [ 4.61 KiB | Viewed 2416 times ]

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Re: In the above figure, the area of circle A is 144π and the area of circ   [#permalink] 29 Jun 2015, 04:24
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