Official Quant thread for CAT 2013

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@badwal.aman said:
Three players A, B and C play the following game. • There are three cards, each marked with a different single-digit positive numbers. • In each round the cards are randomly dealt to the players and each receives the number of marbles equal to the integer on his card. • Result after two or more rounds:players A B Ctotal marbles 20 10 9 • In the last round the player B received the largest number of marbles.Ques. If cards are arranged according to descending order of the numbers written on them, who got the middlemost card in the first round????..plz explain.. (Ans. C)
A->8 ,7,5
B->9,1,0
C->2,3,4

0 1 2 3 4 5 7 8 9

4->C
@gnehagarg said:
d. 50 cards from card 51 to 100 are true.

1st card cannot be true since if it true then 0 cards are true which inturn contradicts that it is true.
if 2nd is true then atmost 1 card is true....but if that is compatible with the statements on 3rd to 100th cards then 99 cards are true. so false.
this argument can be applied to all cards upto 50.
after that if statement on 51st card is true then atmost 50 cards are true. this statement is compatible with 51 to 100 and no contradiction arises.
so 50 cards are true.
@manasvr -2x+y+y+y+2z+2z=36
applying AM>=GM
36/6>=(8xy^3z^2)^1/6
xy^3z^2>=6^6/8
=5832
@maddy2807 said:
I am taking xy3z2 as xy^3z^2 2x/1= 3y/3 = 4z/2use the above relation, and with the given equation,2x+3y+4z=36calculate the respective value, which will be,x=3y=6z=3ans= 5832
2x/1= 3y/3 = 4z/2 -------------> bhai....can u explain dis step ....
@karan20 said:
2x/1= 3y/3 = 4z/2 -------------> bhai....can u explain dis step ....
it is like this
if equation is given, in form of x y and z
ax+by+cz= n
x^p*y^q*z^r

then min or max value exist at,
ax/p = by/q = cz/r
put it in equation and obtain the values receptively.
This hold true for 2 variables also

if v,w,x,y And z are non-negative integers less then 11 then how many distinct combination of (v,w,x,y,z) satisfy v(11^4)+w(11^3)+x(11^2)+y(11)+z=151001
a-1
b-2
c-3
d-0
The circle o having a diameter 2 cm,has a square inscribed in it.Each side of the square is then taken as a diameter to form 4 smaller circles O".Find the total area of all four O" cicles which is outside the circleO :I dnt knw ans...Plz provide solutions..
@hari_bang Option
Are
a-2
b-2-pi
c-2-pi/2
d-2-pi/4

how many 6 dig no.can be formed using dig 1 to 6,without repition such that number is divisible by the digit at unit places...:)

402
528
648
720
@hari_bang said:
how many 6 dig no.can be formed using dig 1 to 6,without repition such that number is divisible by the digit at unit places...402528648720
@hari_bang said:
if v,w,x,y And z are non-negative integers less then 11 then how many distinct combination of (v,w,x,y,z) satisfy v(11^4)+w(11^3)+x(11^2)+y(11)+z=151001a-1b-2c-3d-0
@hari_bang said:
how many 6 dig no.can be formed using dig 1 to 6,without repition such that number is divisible by the digit at unit places...402528648720
648 ?
@hari_bang said:
The circle o having a diameter 2 cm,has a square inscribed in it.Each side of the square is then taken as a diameter to form 4 smaller circles O".Find the total area of all four O" cicles which is outside the circleO :I dnt knw ans...Plz provide solutions..
a-2
orange colored area is ur ans...
area of yellow portion =area of bigger circle-area of square
which is (pi-2)-
now area of orange portion =4*(area of semicircle of smaller circle-area of yellow portion/4)
@hari_bang said:
@hari_bang OptionArea-2b-2-pic-2-pi/2d-2-pi/4
@rubikmath i dnt knw bro
@venomizer said:
a-2orange colored area is ur ans...area of yellow portion =area of bigger circle-area of squarewhich is (pi-2)-now area of orange portion =4*(area of semicircle of smaller square-area of yellow portion/4)
i try to understnd
@hari_bang said:
if v,w,x,y And z are non-negative integers less then 11 then how many distinct combination of (v,w,x,y,z) satisfy v(11^4)+w(11^3)+x(11^2)+y(11)+z=151001a-1b-2c-3d-0

a. 1

LHS of the equation can be viewed as a number written in the number system with base 11.....you just need to find whether 151001 can be converted into a unique number in number system with base 11.....it turns out that we can do that.....
we get v=10, w=3, x=4, y=10, z=4....
@hari_bang u understood it or not bro..
well see
given that
a circle of radius of 2cm has a square inscribed in it that means the diagonal of the square is also the diameter of the circle
from there we can find the side of the square which we vl get as _/2(root2 )
area of square=2
now the radius of the the smaller circle vl be _/2by 2
i hope now its clear ..if not ask again