Official Quant thread for CAT 2013

MBA CAT 2024
13703
@shinoda said:
the OA is other way round..4!*4!had a lot of discussion yesterday with fellow puys..go through some previous post and check if we are right or not !!
I am wrong actually..because No where in the question it is mentioned FLOWERS ARE ALIKE .so its 4!*4!
13704
@bs0409 said:
Yes. OA is 29. it is pigeon hole problem........Find the unit digit of 7^23 x 4^21
2
13705
R walked a descending escalator and took 40 steps to reach the bottom.. S stareted simultaneously from the bottom, taking 2 steps for every 1 step of R. time taken for both to reach at the bottom and top are same. how many steps more than R did S take before they crossed each other? If R were to walk at the speed of S, what % of the initial time would he be able to save?
13706
@pirateiim478 said:
R walked a descending escalator and took 40 steps to reach the bottom.. S stareted simultaneously from the bottom, taking 2 steps for every 1 step of R. time taken for both to reach at the bottom and top are same. how many steps more than R did S take before they crossed each other? If R were to walk at the speed of S, what % of the initial time would he be able to save?
let x be no.of steps moved by escalator in the time R moves 40 steps.

so 40+x=80-x
x=20

total steps =40+x=60



when they cross aech other..

r+e+2r-e=length of escalator=60
3r=60
r=20 so R has taken 20 steps before they cross and S has taken 40 steps before they cross..

if r has walked at the speed of s he would cover 4e in the time escalator covers e

5e=60

e=12

e=20 in the initial case.

so he has saved (1-(12/20)) % of initial journey time=40%
13707
@pirateiim478 said:
R walked a descending escalator and took 40 steps to reach the bottom.. S stareted simultaneously from the bottom, taking 2 steps for every 1 step of R. time taken for both to reach at the bottom and top are same. how many steps more than R did S take before they crossed each other? If R were to walk at the speed of S, what % of the initial time would he be able to save?
R - 1step/sec
S - 2steps/sec
escalator = x steps/sec

R comes down at - (1+x); S at 2-x
to cover 40 steps R takes 40 sec
escalator moves 40x steps
total distance covered by R= 40 +40x
similarly S covers 80 steps in the same time but escalator has moved 40x in opp dirn
hence S covers 80 - 40x

=> 40 +40x = 80 -40x
=> 40 = 80x
=> x = 1/2 step/sec
total length = 60 steps (putting value of x in either)

now R comes down at 1+ 1/2 =3/2 and S at 2- 1/2 = 3/2
relative speed = 3steps/sec
they meet after 60 /3 = 20sec
in this while R has covered 20steps. while S has covered 40 steps.
hence S has covered 20 steps more.?


If R = 2 steps/sec
then total speed of R = 2+1/2 = 5/2 steps /sec
time taken to cover = 60/5/2 = 24 sec

initially time takne = 60/3/2 = 40sec

he would save 16sec
=> 16/40 = 40% ?

13708
@ravi.theja said:
5!??
@Brooklyn said:
6!/2 ??
OA is 5!/2..= 60..
13709
Find the total number of sets of factors of 264 which are co-prime to each other.
post approach?
13710
@negiSannu said:
Find the total number of sets of factors of 264 which are co-prime to each other.post approach?
264 = 2^3 * 3 * 11

Number of Co Prime factors is given by (a+1)(b+1)(c+1) + ab + bc + ca +3abc - 1

=> 4*2*2 + 3 + 1 + 3 + 9 - 1
= 31 Sets. :)
13711
@Estallar12 said:
264 = 2^3 * 3 * 11Number of Co Prime factors is given by (a+1)(b+1)(c+1) + ab + bc + ca +3abc - 1=> 4*2*2 + 3 + 1 + 3 + 9 - 1 = 31 Sets.
how do we get this formula...?
13712
@negiSannu said:
Find the total number of sets of factors of 264 which are co-prime to each other.
post approach?
Is it 31??
264 = 2^3*3*11
((2a+1)(2b+1)(2c+1) - 1)/2 = (7*3*3 - 1)/2 = 31 sets...
13713
@negiSannu said:
how do we get this formula...?
Method I -

264 = 2^3*3*11
(1,other) = 15 (total factors -1)
(2,other) = 2
(4,other) = 2
(8,other) = 2
{(2*3,11),(4*3,11),(8*3,11),(2*11,3),(4*11,3),(8*11,3),(2,3*11),(4,3*11),(8,3*11)} = 9
(3,11) = 1
Total = 15+6+9+1=31

Method II -

Condition for two divisors of any number n to be co-prime to each other
(i) Let N=a^m*b^n has (m+1)(n+1)-1+mn numbers of factors which are co-prime to each other.
If N=12, then as 12=2^2*3,so it has (2+1)*(1+1)-1+2=7 sets which are co-prime to each
other. They are: (1,2),(1,3),(1,4),(1,6),(1,12),(2,3),(3,4).

(ii) Similarly we can deduce the formula for higher orders.If N=a^m*b^n*c^p then it will have (m+1)(n+1)(p+1)-1+mn+np+mp+3mnp co prime factors.

13714
@negiSannu said:
Find the total number of sets of factors of 264 which are co-prime to each other.post approach?
31 only
13715
@negiSannu said:
Find the total number of sets of factors of 264 which are co-prime to each other.post approach?
31 sets?
13716
There are 5 thieves (Different age )with 100 Diamonds.Oldest thieve among 5 will propose a distribution of diamonds.If 50% of the votes( do not take oldest thief in account) are in favor then oldest one will survive otherwise rest of the thieves will kill the oldest one.
All the thieves are rational thinkers and good at maths.Nobody wants to die.
So you are the oldest thief and come out with a nice proposal so that you can survive and take away the maximum share..:)

13717
@gyrodceite said:
There are 5 thieves (Different age )with 100 Diamonds.Oldest thieve among 5 will propose a distribution of diamonds.If 50% of the votes( do not take oldest thief in account) are in favor then oldest one will survive otherwise rest of the thieves will kill the oldest one.All the thieves are rational thinkers and good at maths.Nobody wants to die.So you are the oldest thief and come out with a nice proposal so that you can survive and take away the maximum share..
is it 97??
13718
@gyrodceite said:
There are 5 thieves (Different age )with 100 Diamonds.Oldest thieve among 5 will propose a distribution of diamonds.If 50% of the votes( do not take oldest thief in account) are in favor then oldest one will survive otherwise rest of the thieves will kill the oldest one.All the thieves are rational thinkers and good at maths.Nobody wants to die.So you are the oldest thief and come out with a nice proposal so that you can survive and take away the maximum share..
34?
13719
@gyrodceite said:
There are 5 thieves (Different age )with 100 Diamonds.Oldest thieve among 5 will propose a distribution of diamonds.If 50% of the votes( do not take oldest thief in account) are in favor then oldest one will survive otherwise rest of the thieves will kill the oldest one.All the thieves are rational thinkers and good at maths.Nobody wants to die.So you are the oldest thief and come out with a nice proposal so that you can survive and take away the maximum share..
clever one.
Is it 32?
13720
@gyrodceite said:
There are 5 thieves (Different age )with 100 Diamonds.Oldest thieve among 5 will propose a distribution of diamonds.If 50% of the votes( do not take oldest thief in account) are in favor then oldest one will survive otherwise rest of the thieves will kill the oldest one.All the thieves are rational thinkers and good at maths.Nobody wants to die.So you are the oldest thief and come out with a nice proposal so that you can survive and take away the maximum share..
34 ??
13721
@sails said:
34 ??
approach?
13722

100 diamonds are there so if the older thief is not to be killed he must give 2 thieves(coz this will make 50% votes in his favour) approximately equal diamonds as his so
34 for him
33 for 2nd
33for another....so he will get 2 votes in his favour...
But is the answer right?

if the thieves are too intelegent then the answer could also be 32...for oldest theif
34 and 34 for the other theieves...so not sure..either 34 or 32..