Official Quant thread for CAT 2013

MBA CAT 2024
12441
@bhatkushal said:
Q A tennis player computes her win ratio by dividing the number of matches she has won by the total number of matches played by her.At start of the weekend her win ratio is 500.During weekend she plays 4 matches, winning three and loosing one.At the end of weekend her win ratio is greater than 503.What is largest number of matches she could have won before the weekend began.........
How could the win ratio be integer if we divide the matches won/matches played?
12442
In a circle of diameter 40 cm,the length of a chord is 20 cm.find the length of the minor arc of the chord.?
12443
@bhatkushal said:
Guys stuck on this one:-Que)Given that x^2+y^2=14x+6y+6 what is the largest possible value of 3x+4y?
72?

getting at
x=y=10.29xx

12444
@veertamizhan said:
In a circle of diameter 40 cm,the length of a chord is 20 cm.find the length of the minor arc of the chord.?
2*pi*20/6 = 20/3pi
12445
@veertamizhan said:
a circle of diameter 40 cm,the length of a chord is 20 cm.find the length of the minor arc of the chord.?
( 60/360)*2*pi*20 = (20/3)*pi
12446
@veertamizhan said:
In a circle of diameter 40 cm,the length of a chord is 20 cm.find the length of the minor arc of the chord.?
60/360*2pi*20=20/3pi
12447
@mani0303 thanks, bro, I feel like an ass now.
12448

how can we take 60 degree ?

@mani
12449
@mani0303 why 60 degree ?
12450
Two circles with radius 8 cm and 3 cm. The distance between their centers is 13 cm. The direct common tangents and the transverse common tangents intersect at A,B,C,D. What is the area of the quadrilateral ABCD ?

PS: You are allowed to use a calculator for this :D, and post the approach also 😐 .. No OA :|
12451
@bhatkushal said:try doing it this wayx2-14x+y2-6y=6;x2-14x+49+y2-6y+9=6+49+9;(x-7)^2+(y-3)^2=64;hence centre ofcircle is (7,3) with radius 8.....
bt by dis we dint get any optn...


right approach there....infact this is the easiest way of solving such questions.....

here they have asked you the value of 3x+4y maximum....

let that value be C
3x+4y = c which is a line depending on the value of c.....
what we have here is a line which would move towards the circle , pass through the centre, and then again move from the circle depending on the value of c....
now c would be maximum when the line is a tangent at the extreme ( since (x,y) lies on both circle and line )

so 3x+4y -c = 0 is a tangent to the circle u just discovered....


length from centre to the line = radius

=> mod( 3(7) + 4(3) -c ) / sqrt(9+16) = 8

=> 21 + 12 - c = +40 or -40
=> 33 - c = 40 => c = - 7
and c = 33 + 40 = 73


so this method gives you both maximum and minimum value of 3x+4y i.e -7 and 73 :D

Ek teer se do nishaane 😃

Coordinate geometry rocks !!!

12452
@mr.ashutsoh.kr said:
@mani0303 why 60 degree ?
IF you join the end of chord with the center,you can see all the sides of the triangle are equal,which means the angle substended by chord at the center is 60...

So,the minor arc's length = 60/360 * circumference
12453
@mani0303 Correct da !
12454
@YouMadFellow my take 286
0.5(6+16)* 26
12455
@sagarcat said:
@YouMadFellow my take 2860.5(6+16)* 26
Nope, I don't think so :)

How are you getting 6,16,26 ?
12456
@Crysis said:
right approach there....infact this is the easiest way of solving such questions.....here they have asked you the value of 3x+4y maximum....let that value be C3x+4y = c which is a line depending on the value of c.....what we have here is a line which would move towards the circle , pass through the centre, and then again move from the circle depending on the value of c....now c would be maximum when the line is a tangent at the extreme ( since (x,y) lies on both circle and line ) so 3x+4y -c = 0 is a tangent to the circle u just discovered....length from centre to the line = radius=> mod( 3(7) + 4(3) -c ) / sqrt(9+16) = 8 => 21 + 12 - c = +40 or -40=> 33 - c = 40 => c = - 7 and c = 33 + 40 = 73so this method gives you both maximum and minimum value of 3x+4y i.e -7 and 73 Ek teer se do nishaane Coordinate geometry rocks !!!
nice to have u here sir. badia solution.
12457
@DarkHorse25k.yeah the triangle would be formed by diagonals only coz we can not use the sides of a polygon.
sorry i couldn't reply then.had some urgent work.
12458
Q: 36^24^12 div 101 R=?
12459
@viewpt said:
Q: 36^24^12 div 101 R=?


My take is 36.

E(101) = 100.
24^12 mod 100.
100 = 4*25.
24^12 mod 4 = 0.
24^12 mod 25 = (-1)^even mod 25 = 1.
=> 4k = 25x+1 -> 76.

36^76 mod 101.
(36^2)^38 mod 101 = 84^38 mod 101 = 87^19 mod 101 = 87*95^9 mod 101 = 87*(-6)^9 mod 101 = 87*-6*36^4 mod 101 = 87*-6*87 mod 101 = 87^2*-6 mod 101 = -6*-6 mod 101 = 36
12460
@viewpt said:
Q: 36^24^12 div 101 R=?
36?