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Not able to solve this problem!!

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Not able to solve this problem!!

by aman273 » Mon Dec 27, 2010 7:14 am
I am not able to solve this simple problem, My approach is:

Since Angles in the same arc are equal, so, angle C= angle E , angle B= angle D, Angle A common,

So, by AAA property, Triangles are similar. Hence, The sides should be in proportion.

Hence, BC/DE = AC/AD = AB/AE

So, 6/DE = 5/6 = 4/AE

DE= 7.2

But the answer is 9. Could you please explain me how to solve this problem.. What i am doing wrong here ?
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by Anurag@Gurome » Mon Dec 27, 2010 7:27 am
aman273 wrote:I am not able to solve this simple problem, My approach is:

Since Angles in the same arc are equal, so, angle C= angle E , angle B= angle D, Angle A common,

So, by AAA property, Triangles are similar. Hence, The sides should be in proportion.

Hence, BC/DE = AC/AD = AB/AE

So, 6/DE = 5/6 = 4/AE

DE= 7.2

But the answer is 9. Could you please explain me how to solve this problem.. What i am doing wrong here ?
Your approach is correct, just a small error: BC/DE = AC/AE = AB/AD
This implies 6/DE = 4/6 implies DE = 36/4 = 9

[spoiler]Hence, the correct answer is D.[/spoiler]

Does that help?
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by N:Dure » Mon Dec 27, 2010 7:27 am
You're on the right track, but he's looking for DE

so AB:AC:BC is 4:5:6

Similarly AD:AE:DE is 6: (6*5/4) : (6*6/4) i.e 6: 7.5: 9

so DE = 9
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by anshumishra » Mon Dec 27, 2010 7:39 am
aman273 wrote:I am not able to solve this simple problem, My approach is:

Since Angles in the same arc are equal, so, angle C= angle E , angle B= angle D, Angle A common,

So, by AAA property, Triangles are similar. Hence, The sides should be in proportion.

Hence, BC/DE = AC/AD = AB/AE

So, 6/DE = 5/6 = 4/AE

DE= 7.2

But the answer is 9. Could you please explain me how to solve this problem.. What i am doing wrong here ?
A small mistake, You know the answer as two solutions have already been offered.

Here is where you missed :
When triangles are similar, The sides opposite to the equal angles are in the same ratio.
So,
BC/DE = AC/AE = AB/AD.

Hope that helps.
Thanks
Anshu

(Every mistake is a lesson learned )
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by Woozler » Mon Dec 27, 2010 8:30 pm
Do we need to know for GMAT that "angles in the same arc" are the same? I have never encountered a problem like this.
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by okletsdothis » Tue Dec 28, 2010 5:55 am
yes.
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