official quant thread for cat08

[jha16june]

Originally Posted by nikunj14_83

Hi all,
One brain teaser from geometry ...I ma not able to solve the same so help me out with the sol....

1)
Hexagon ABCDEF is inscribed in a circle. The sides AB, CD, and EF are each x units in length whereas the sides BC, DE, and FA are each y units in length. Then, the radius of the circle is
a. [(x^2 + y^2 + xy)/3]^1/2
b. [(x^2 + y^2 – xy)/2]^1/2
c. [(x^2 + y^2 + xy)/2]^1/2
d. [(x^2 + y^2 – xy)/3]^1/2

Answer is option a. put x=y u must get x as the answer.
Posting other 2 soon.

[man_on_mission]

Originally Posted by nikunj14_83

Hi all,
One brain teaser from geometry ...I ma not able to solve the same so help me out with the sol....

1)
Hexagon ABCDEF is inscribed in a circle. The sides AB, CD, and EF are each x units in length whereas the sides BC, DE, and FA are each y units in length. Then, the radius of the circle is
a. [(x^2 + y^2 + xy)/3]^1/2
b. [(x^2 + y^2 – xy)/2]^1/2
c. [(x^2 + y^2 + xy)/2]^1/2
d. [(x^2 + y^2 – xy)/3]^1/2

is it a. [(x^2 + y^2 + xy)/3]^1/2

got it by taking the limiting case...put x = y and 1st option staisfies..

[shikhajejani]

Originally Posted by naga25french

can u jus explain ur approach ?
i got the answer as 2^44....

oh i corrected my ans....its 2^44...
i misinterpreted it at my first attempt...

[implex]

question 2) join BC and BD
and now just use the fact that angle subtended by arcs of equal length is equal
also angle subtended at centre is twice the angle at the segment

so we get
3(40+x)+x-180=0
x=15

[man_on_mission]

Originally Posted by nikunj14_83

Hi all,
One brain teaser from geometry ...I ma not able to solve the same so help me out with the sol....






3)
What is the value of PR?

Choose one answer.
a. 10(5)1/2 b. 5(13)1/2 c. 20
d. 24

i think answer is c. 20

given QT = 10 and TR = 15 so QR = 25.
Now we know 3:4:5 is a pythogoras triplet....so 15:20:25 is also a puthogoras triplet...and hypotenuse is 25...

So out of the given otpion only c matches so 20 is answer...

[gautamgomzi]

Q.) Find the no. pf consecutive zeroes at the ned of 72! ans- 18Q.) Find the remainder when 43^197 is divided by 7. Ans- 2Q.) Find the remainder when (2222^5555 + 5555^2222) / 7. Ans- 0Q.) Find the number of divisors of 1420. Ans- 12

[implex]

Originally Posted by man_on_mission

i think answer is c. 20

given QT = 10 and TR = 15 so QR = 25.
Now we know 3:4:5 is a pythogoras triplet....so 15:20:25 is also a puthogoras triplet...and hypotenuse is 25...

So out of the given otpion only c matches so 20 is answer...

answer is 10.sqrt(5)

it uses the fact that if two secants are drawn from the same point to a circle the products are same
PA.PB=PC.PD
using this
we get
(PR-r)(PR+R)=25.15
also right trianle
PR^2+r^2=25^2=625
2PR^2=1000
PR=10.SQRT(5)

option a is right

[man_on_mission]

Originally Posted by implex

answer is 10.sqrt(5)

it uses the fact that if two secants are drawn from the same point to a circle the products are same
PA.PB=PC.PD
using this
we get
(PR-r)(PR+R)=25.15
also right trianle
PR^2+r^2=25^2=625
2PR^2=1000
PR=10.SQRT(5)

option a is right

i don remenber tat theorem correctly ..but tat is applicable wen from xternal point two secants are drawn tat is for this problem the theorem will only be valid wen RP is extended to meet circle on circumfernece but here P is center of circle.....

Please clarify my doubt...

[implex]

Originally Posted by man_on_mission

i don remenber tat theorem correctly ..but tat is applicable wen from xternal point two secants are drawn tat is for this problem the theorem will only be valid wen RP is extended to meet circle on circumfernece but here P is center of circle.....

Please clarify my doubt...

man, its the thing you need to do
just extend from centre to the end of diameter.

constructions are important for geometry problems!!

[implex]

Originally Posted by man_on_mission

i think answer is c. 20

given QT = 10 and TR = 15 so QR = 25.
Now we know 3:4:5 is a pythogoras triplet....so 15:20:25 is also a puthogoras triplet...and hypotenuse is 25...

So out of the given otpion only c matches so 20 is answer...

they are not asking the radius !!
so pythagoras triplet theory is futile