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Geometry for CAT 2011

Hi Guys, Geometry, Algebra and Number system form the major chunk of our QA section for CAT. Proficiency in these three sections would definitely boost our Quants scores. Contents of Geometry 1\. Plane Geometry - Basics and Tri...
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puys i have a question in which i am stuck :help

C and D are points on the circle with diameter AB such that (angle AQB) =2*(angle COD), where O the center of the circle. Q is the point of intersection of AC and DB inside the circle.The tangents at C and D meet at P. The circle has radius 1. The distance of P from its center is:
(a) (sqrt2)/3
(b) 2/(sqrt3)
(c) 3/(sqrt2)
(d) 1

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OK...i am losing the track here...in the question,it is not specified that he has to cover all the cities.Is that we are taking into account while solving??

From top city,3 routes are possible

Since there are 3 edges leading from each city and also the figure is perfectly symmetrical, these 3 routes are possible from each edge.

So,total number of routes = 4 * 3 = 12.

ps : one more ceo from Delhi
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Four cities are connected by a road network as shown in the figure. In how many ways can you start from any city and come back to it without traveling on the same road more than once
10,12,14,15
I am getting 13 as the answer..that too by calculating manually all the routes.Is there any shortcut for such questions??
Image is attached.


From top city,3 routes are possible

Since there are 3 edges leading from each city and also the figure is perfectly symmetrical, these 3 routes are possible from each edge.

So,total number of routes = 4 * 3 = 12.

ps : one more ceo from Delhi
You are not rich until you own your mistakes - Linda Poindexter
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If x, y, z are the angles of a triangle where x, y, z are integers, what is the number if values that x-y-z can take?
1. 90
2. 355
3. 178
4. 177


Please provide me with a solution.....


Quote:Solution I found on PG :
Originally Posted by quantphobic View Post
If x, y, z are the angles of the triangle ABC, where x, y, z are integers, then what isthe number of values that x - y - z can take?

x-y-z = 180-2(y+z)

y+z -> 2 to 179

So, 178 values...
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Four cities are connected by a road network as shown in the figure. In how many ways can you start from any city and come back to it without traveling on the same road more than once

10,12,14,15

I am getting 13 as the answer..that too by calculating manually all the routes.Is there any shortcut for such questions??

Image is attached.
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If x, y, z are the angles of a triangle where x, y, z are integers, what is the number if values that x-y-z can take?
1. 90
2. 355
3. 178
4. 177


Please provide me with a solution.....

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dpiict Says
my take is option b.



calculation error, 1/2
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ABC is a triangle with area 1. AF = AB/3, BE = BC/3 and ED = FD. Find the area of the shaded figure.


Choose one answer.
a. 1/2 b. 5/9 c. 1/3 d. 13/16






my take is option b.
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In an acute angle triangle all the angles are positive integers and 13 times one angle is equal to 17 times another angle then what could be the minimum angle??

Please solve it ..i dint get it after trying for 3 hrs


ans can also be 30 ,65,85..
30+65+85=180...all are positive integers....and 17*65=13*85 also..
so the ans should be 30..

That's correct!
The possible triplets are - (17,13,150),(34,26,120),(51,39,90),(68,52,60),(85,65,30).
Only last 2 satisfy the acute angled tr. criteria...so you have ur answer.
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ADE is the triangle here...not a straight line. Plz refer to original detailed solution by ravitoons!

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