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In the diagram above, the four triangles ABE, CBE, ADE, and CDE are al

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
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In the diagram above, the four triangles ABE, CBE, ADE, and CDE are al  [#permalink]

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29 May 2016, 13:02
00:00

Difficulty:

65% (hard)

Question Stats:

61% (01:42) correct 39% (01:59) wrong based on 114 sessions

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In the diagram above, the four triangles ABE, CBE, ADE, and CDE are all equal, and CD = 5. What is the area between the two circles?

Statement #1: AE = 3

Statement #2: angle BEC = 90 degrees

Geometry is beautiful, and the GMAT DS loves geometry. This problem is a from a collection of ten practice problems. For the other problems, as well as the OE for this question, see:
GMAT Data Sufficiency Geometry Practice Questions

Mike

Attachment:

quadrilateral inside circles.png [ 17.73 KiB | Viewed 3406 times ]

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Mike McGarry
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Re: In the diagram above, the four triangles ABE, CBE, ADE, and CDE are al  [#permalink]

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29 May 2016, 20:15
mikemcgarry wrote:
Attachment:

In the diagram above, the four triangles ABE, CBE, ADE, and CDE are all equal, and CD = 5. What is the area between the two circles?

Statement #1: AE = 3

Statement #2: angle BEC = 90 degrees

Geometry is beautiful, and the GMAT DS loves geometry. This problem is a from a collection of ten practice problems. For the other problems, as well as the OE for this question, see:
GMAT Data Sufficiency Geometry Practice Questions

Mike

Hi,

If you look at ABE and CBE, they are congruent triangles....
HOW?-
since B and D are at equal distance from A and C, the line drawn through B and D will also be at equal distance at every point so E will be at SAME distance from A and C..
so AE = CE...
all sides are equal so triangles are congruent..

therefore all angles will be equal and angle AEB= angle CEB = 90..

lets see the statements now..

Statement #1: AE = 3
Now we know AE and AB in right angle triangle ABE...
so $$BE^2 = AB^2-AE^2=5^2-3^2 = 4^2..................BE=4$$

radius of both circles is known we can find the differenjce in AREA..
Suff

Statement #2: angle BEC = 90 degrees
we have already derived this info
Insuff
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Re: In the diagram above, the four triangles ABE, CBE, ADE, and CDE are al  [#permalink]

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29 May 2016, 21:14
chetan2u wrote:
mikemcgarry wrote:
Attachment:

In the diagram above, the four triangles ABE, CBE, ADE, and CDE are all equal, and CD = 5. What is the area between the two circles?

Statement #1: AE = 3

Statement #2: angle BEC = 90 degrees

Geometry is beautiful, and the GMAT DS loves geometry. This problem is a from a collection of ten practice problems. For the other problems, as well as the OE for this question, see:
GMAT Data Sufficiency Geometry Practice Questions

Mike

Hi,

If you look at ABE and CBE, they are congruent triangles....
HOW?-
since B and D are at equal distance from A and C, the line drawn through B and D will also be at equal distance at every point so E will be at SAME distance from A and C..
so AE = CE...
all sides are equal so triangles are congruent..

therefore all angles will be equal and angle AEB= angle CEB = 90..

lets see the statements now..

Statement #1: AE = 3
Now we know AE and AB in right angle triangle ABE...
so $$BE^2 = AB^2-AE^2=5^2-3^2 = 4^2..................BE=4$$

radius of both circles is known we can find the differenjce in AREA..
Suff

Statement #2: angle BEC = 90 degrees
we have already derived this info
Insuff

In question stem it is given: " the four triangles ABE, CBE, ADE, and CDE are all equal". Triangles equal does not mean that they are equilateral. , Their areas are equal.

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Joined: 18 Jan 2010
Posts: 251
Re: In the diagram above, the four triangles ABE, CBE, ADE, and CDE are al  [#permalink]

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29 May 2016, 21:37
mikemcgarry wrote:
Attachment:

In the diagram above, the four triangles ABE, CBE, ADE, and CDE are all equal, and CD = 5. What is the area between the two circles?

Statement #1: AE = 3

Statement #2: angle BEC = 90 degrees

Geometry is beautiful, and the GMAT DS loves geometry. This problem is a from a collection of ten practice problems. For the other problems, as well as the OE for this question, see:
GMAT Data Sufficiency Geometry Practice Questions

Mike

Each of the 4 equal triangles is such that the bigger radius forms one the sides, the smaller radius forms the other side and the length of hypotenuse is given (CD = 5).

Statement 1

AE =3, AB = CD = 5, Therefore BE is 4 (3, 4, 5 is a Pythagorean pair. Triangle ABE is a right angled $$/triangle$$)

The bigger radius is known. Area of bigger circle is known.
Smaller radius is known. Area of smaller circle is known.
We can calculate the area of the space between two circles

Sufficient.

Statement 2
This information is already known and does not give any additional information. Further, we cannot calculate the radius of the two circles.

Hence not sufficient

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Re: In the diagram above, the four triangles ABE, CBE, ADE, and CDE are al  [#permalink]

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29 May 2016, 21:59
robu wrote:
chetan2u wrote:
mikemcgarry wrote:
Attachment:

In the diagram above, the four triangles ABE, CBE, ADE, and CDE are all equal, and CD = 5. What is the area between the two circles?

Statement #1: AE = 3

Statement #2: angle BEC = 90 degrees

Geometry is beautiful, and the GMAT DS loves geometry. This problem is a from a collection of ten practice problems. For the other problems, as well as the OE for this question, see:
GMAT Data Sufficiency Geometry Practice Questions

Mike

Hi,

If you look at ABE and CBE, they are congruent triangles....
HOW?-
since B and D are at equal distance from A and C, the line drawn through B and D will also be at equal distance at every point so E will be at SAME distance from A and C..
so AE = CE...
all sides are equal so triangles are congruent..

therefore all angles will be equal and angle AEB= angle CEB = 90..

lets see the statements now..

Statement #1: AE = 3
Now we know AE and AB in right angle triangle ABE...
so $$BE^2 = AB^2-AE^2=5^2-3^2 = 4^2..................BE=4$$

radius of both circles is known we can find the differenjce in AREA..
Suff

Statement #2: angle BEC = 90 degrees
we have already derived this info
Insuff

In question stem it is given: " the four triangles ABE, CBE, ADE, and CDE are all equal". Triangles equal does not mean that they are equilateral. , Their areas are equal.

Hi robu ,
Triangles are all equal means they are congruent .
If two or more triangles are congruent, then all of their corresponding angles and sides are congruent as well.
Here Since AE= 3 , EC= 3
Also, AB = BC = CD = AD = 5
and $$\angle$$ BEA = $$\angle$$ BEC = $$\angle$$ CED = $$\angle$$ DEA = 90

Hope this helps!!
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Re: In the diagram above, the four triangles ABE, CBE, ADE, and CDE are al  [#permalink]

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05 Jan 2018, 12:52
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Re: In the diagram above, the four triangles ABE, CBE, ADE, and CDE are al   [#permalink] 05 Jan 2018, 12:52
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