Official Quant thread for CAT 2013

MBA CAT 2024
15683
@TootaHuaDil said:
How many divisors of 360 are not divisors of 540 and how many divisors of 540 are not divisors of 360?
part 1-6
part 2- 6


prime factor representation of 360= (2^3)(3^2)(5)
prime factor representation of 540= (2^2)(3^3)(5)

Part 1- Now, the thing is, 8 is a factor of 360 but not 540 so all such numbers which are factors of 360 but not 540 will have 8 in them. Now the number of such numbers are

6=(2+1)(1+1).....(360)=(8)(3^2)(5)

Part 2- Now, the thing is, 27 is a factor of 540 but not 360 so all such numbers which are factors of 540 but not 360 will have 27 in them. Now the number of such numbers are

6=(2+1)(1+1).....(540)=(27)(2^2)(5)


15684
@adityaknsit said:
part 1-6part 2- 6
correct :)
15685
@ytstacks said:
Find the remainder when (123123123123..................300digits) is divided by 37.Please explain along with the method?
16?
123*100 mod 37
12*100 mod 37 = 16
15686

How many divisors of 36^36 are perfect cubes?

15687

How many numbers less than 100 have exactly 8 divisors? Any short cut for this question?

15688
@TootaHuaDil said:
How many divisors of 36^36 are perfect cubes?
36^36 = 2^72 * 3^72
= (2^3)^24 * (3^2)^24
No of factors = (24+1)(24+1) = 625?
15689
@TootaHuaDil said:
How many divisors of 36^36 are perfect cubes?
625?


36^36=

(2^72)(3^72)

=((2^3)^24)*((3^3)^24))

factors=(24+1)*(24+1)=625
15690
@adityaknsit @The_Loser said:
36^36 = 2^72 * 3^72 = (2^3)^24 * (3^2)^24 No of factors = (24+1)(24+1) = 625?
Yes right 😃 Do you have any short cut for this quoted below?
@TootaHuaDil said:
How many numbers less than 100 have exactly 8 divisors? Any short cut for this question? @
15691
@TootaHuaDil said:
Yes right Do you have any short cut for this quoted below?
trying
15692
@adityaknsit said:
nope, mine is exactly the same approach as @The_Loser 'strying the second one..
ya..that is ok...i mean the one quoted below. How many numbers less than 100 have exactly 8 divisors? I am getting it but one by one I have to check all the possiblities.
15693
@TootaHuaDil said:
How many divisors of 36^36 are perfect cubes?
625?

36^36 = 6^72 = (2*3)^72 = (2)^72*(3)^72 = (2^3)^24*(2^3)^24 = 25*25 = 625
15694
@TootaHuaDil
10 numbers
missed out the two cases
15695
@TootaHuaDil said:
How many divisors of 36^36 are perfect cubes?
625
15696
@ishu1991 said:
@TootaHuaDil8 numbers
nahi bhai more than 8.
15697
@TootaHuaDil said:
ya..that is ok...i mean the one quoted below. How many numbers less than 100 have exactly 8 divisors? I am getting it but one by one I have to check all the possiblities.
10 nos. ?
15698
@TootaHuaDil said:
Yes right Do you have any short cut for this quoted below?
don't know if its a short approach...but mine is as follows.......

8=2*2*2=2*4

therefore the number can be of the form

(p^1)(q^1)(r^1)

or (p^1)(q^3)

or p^7


case 1, the set of prime numbers that can be chosen from are


2,3,5,7,11,13

2,3,5
2,3,7
2,3,11
2,3,13
2,5,7


case 2

we can pick among

2, 3, 5, 7, 11

we can have...
2^3*3
2^3*5
2^3*7
2^3*11
3^3*2



third case, none

could not formulate any shortcuts......and I don't think this was what u wanted....








15699
@The_Loser said:
36^36 = 2^72 * 3^72 = (2^3)^24 * (3^2)^24 No of factors = (24+1)(24+1) = 625?
How to solve the question given below by the same method...

How many divisors of 21600 are perfect squares?
15700
8=4*2 -> a^3*b^1 -> 24,54,40,56,88.
2*2*2 -> a*b*c -> 30,42,66,78,70.
total --> 10 ?
15701
@adityaknsit said:
don't know if its a short approach...but mine is as follows.......8=2*2*2=2*4therefore the number can be of the form


Hehe...May be question was just for building concepts. 😁
Anyways right answer. 10 numbers (y)
15702
@rubikmath Yes 10 :)