Official Quant thread for CAT 2013

MBA CAT 2024
30523
@Dexian said:
ye kaisekiya?
let a=2^x1*5^y1*11^z1
b=2^x2*5^y2*11^z2

either of x1 and x2 have to be 3
let x1=3
x2 will have 4 choices 0-3

x2=3
x1 will have 4 choices 0-3
4+4-1(both equal to 3 counted twice)=7


aise hee baki ke saath karle


30524
@Tusharrr vo f(x) vala question kaha he bhai ?

30525
@priyank333333 Deleted mene solve kr diya
Ok IF you want to give answer then give
30526
@Tusharrr said:
@priyank333333 Deleted mene solve kr diyaOk IF you want to give answer then give
2 root to mil gaya +1 and -1 please share the rest approach
30527

@Tusharrr whats the answer ur getng ?
30528
@Tusharrr said:
How many ordered triples (x,y,z) of integer solutions are there to the system of equationsx2+y2+z2=194x2z2+y2z2=194=4225? Here x2 means x sq and y2 means y sq and z2=z sq
8??
(5,12,5)
(12,5,5)
(0,13,5)
(13,0,5)
(3,4,13)
(4,3,13)
(5,0,13)
(0,5,13)
30529
@AsihekAdhvaryu F (f (f (x)))=0
F (x^4-2x^2)=0
=(x^4-2x^2)^2-1
Using a^2-b^2
=(x^4-2x^2-1) (x^4-2x^2+1)
=(x-1)(x+1)(x-1)(x+1) (x^4-2x^2+-1)
2 real roots are +1 ,-1
And rest let x^2 be =t
(T^2-2t-1)
Use quaratic IT has 2 real roots For x becoz 1 for t
Total Distinct roots 2+2
30530
@heylady All are correct but the answer IS not 8 I dont know why
30531
@priyank333333 4
30532

In triangle ABC, we have a point D such that ∠DAC=10∘, ∠DCA=20∘, ∠DAB=30∘ and ∠ABC=40∘. What is ∠BDC?

30533
@Tusharrr said:
@heylady All are correct but the answer IS not 8 I dont know why
@heylady said:
8??(5,12,5)(12,5,5)(0,13,5)(13,0,5)(3,4,13)(4,3,13)(5,0,13)(0,5,13)
I would edit since I didn't consider negative values...
for 1st case: 8
2nd case: 8
3rd case: 4
4th case: 4
5th case: 8
6th case: 8
7th case: 4
8th case:4
Total: 48 solutions?? is it correct??
30534
@Tusharrr ..4 ROOTS :)

30535
@jaspunit said:
3 circles touching each other, find possible radius of circle circumscribing all these, if radius of each 3 circle is 'r'?
R= (2/_/3 + 1) r.
30536
@psk.becks said:
90 hai kya..
Koi theorem hai kya if D is any point inside an Isosceles triangle..??
30537
@heylady said:
8??(5,12,5)(12,5,5)(0,13,5)(13,0,5)(3,4,13)(4,3,13)(5,0,13)(0,5,13)
Integers can be negative too...?

Edit: Oops sorry, didn't see your edit!

regards
scrabbler
30538
@scrabbler said:
Integers can be negative too...?regardsscrabbler
Yes, I have edited the post...please verify if it is correct..getting 48??
30539
@Tusharrr said:
In triangle ABC, we have a point D such that ∠DAC=10∘, ∠DCA=20∘, ∠DAB=30∘ and ∠ABC=40∘. What is ∠BDC?
I feel it is 80. But my figure is a mess so I could be wrong 😞 There must be a simpler way of doing it?

regards
scrabbler
30540
@scrabbler how did you get 80 thats correct
30541
@heylady too good 48 is answer
30542
@Tusharrr said:
@scrabbler how did you get 80 thats correct
OK managed to draw it more neatly (attached). But little cumbersome approach. Anyone with a better way? @ChirpiBird zara dekhna?

regards
scrabbler