Official Quant thread for CAT 2013

@jaspunit said:
3 circles touching each other, find possible radius of circle circumscribing all these, if radius of each 3 circle is 'r'?
(2r/rt3)+r
@Asfakul said:
How many ordered pairs (a, b) exist such that L.C.M. of a and b is (2^3)(5^7)(11^13) (a, b ˆˆN)?a) 2460b) 2835c) 2645d) 2840
7*15*27=2835
@catahead said:
Q1 3000
Q2 (9/2)^8/3
@mani0303 said:
It's 2835 ie (4^2 - 3^2)*(8^2 - 7^2)*(14^2 - 13^2) = 7*15*27 = 2835
@Subhashdec2 said:
7*15*27=2835
ye kaise kiya???
@Subhashdec2 said:
7*15*27=2835
ye kaise kiya??
@mani0303 said:
It's 2835 ie (4^2 - 3^2)*(8^2 - 7^2)*(14^2 - 13^2) = 7*15*27 = 2835
Sir.. I'm horribly out of touch :embarrassed:

Can you please explain the formula you have used? :neutral:
@Subhashdec2 said:
7*15*27=2835
ye kaisekiya?
@mani0303 said:
It's 2835 ie (4^2 - 3^2)*(8^2 - 7^2)*(14^2 - 13^2) = 7*15*27 = 2835
Sir I'm in horribly out of touch :embarrassed:

Can you please explain the formula you have used? :neutral:
@jaspunit said:
@Dexian3 circles touching each other, find side of triangle circumscribing all these, if radius of each 3 circle is 'r'?
(2+rt3)r
@vijay_chandola said:
Sir I'm in horribly out of touch Can you please explain the formula you have used?
hey,- good to see you old fella

Let's say a = (2^x1)(5^y1)(11^z1) and b = (2^x2)(5^y2)(11^z2)

the pair x1 and x2 can take 4 different values including 0 - so the possible pairs = 16,but we should exclude pairs that don't have 3

Hence,4^2 - 3^2 and similarly for other 2
@Dexian said:
(2+rt3)r
my ans is 2r[1+root(3)], can you please explain?
@AsihekAdhvaryu said:
my ans is 2r[1+root(3)], can you please explain?
circum radius is (2r/rt3) + r........
i think yahin par kuchh cal mistake hoga...
wat have u got as circum radius...?
@Dexian said:
circum radius is (2r/rt3) + r........i think yahin par kuchh cal mistake hoga...wat have u got as circum radius...?
I am getting as 2r/root(3)+2r
@AsihekAdhvaryu said:
I am getting as 2r/root(3)+2r
i think it shud b +r and not +2r .........
if u c ur diagram... only r needs to be added and not 2r
@Dexian ..@AsihekAdhvaryu ..approach plz ?

@priyank333333 said:
@Dexian ..@AsihekAdhvaryu ..approach plz ?
it becomes a equi triangle wid side 2r.....
now find the circumradius of this triangle and add r
@Dexian oh..ur rite ..i got equi triangle but ...lost somwhere 😛 😁 then...

@amannarang7 4 € 3 € 3! = 72

the meaning is d can be placed only in the positions 2 or 3 or 4

in a quadrilateral ABCD, BC=10, CD=14, AD=12 and /_CBD = /_BAD =60. IF AB=a+root b. where a and b are a positive integers then a+b = Options
1) 193
2) 201
3) 204
4) 207
5) none of the above

How many ordered triples (x,y,z) of integer solutions are there to the system of equations

x2+y2+z2=194
x2z2+y2z2=194=4225?


Here x2 means x sq and y2 means y sq and z2=z sq