how many different prime numbers are factors of the expressi

[bhumika.k.shah]

If K is a positive integer, how many different prime numbers are factors of the expression K^2?

Three different prime numbers are factors of 4K^4.
Three different prime numbers are factors of 4K.

How to even approach these kinda sums ???

[thephoenix]

is it D

[sars72]

The statements just say that "3 different primes are factors of ...." since the statements don't say that there are only 3 prime factors, can we say insufficient?

[thephoenix]

The statements just say that "3 different primes are factors of ...." since the statements don't say that there are only 3 prime factors, can we say insufficient?

even then also i think we can find out

for the s1) let k=2*3*5*7*6=1260

k^2 will have same numbers of prime factors
as k^4
if k=3*5*2*2
then 4*k^4 will have 3 prime factors
and k^2 will also have 3 prime factors

so in that way think we can find out
what does OA says

[ajith]

If K is a positive integer, how many different prime numbers are factors of the expression K^2?

Three different prime numbers are factors of 4K^4.
Three different prime numbers are factors of 4K.

How to even approach these kinda sums ???

K as well as K^2 has same no of prime factors

4K^4 has same no factors as 2K and 4K Which can be one less than the number of factors K has if K is even and equal to bo of factors k has if k is odd

For an example say k =15 = 3*5

4K^4 has 3 prime factors 3,5 and 2
4K has 3 prime factors 3 5 and 2

K has 2 prime factors
K^2 has 2 prime factors

on the other hand say if K=30 = 3*5*2

4K^4 has 3 prime factors
4K has 3 prime factors

K has 3 prime factors
K^2 has 3 prime factors

Hence E

[thephoenix]

If K is a positive integer, how many different prime numbers are factors of the expression K^2?

Three different prime numbers are factors of 4K^4.
Three different prime numbers are factors of 4K.

How to even approach these kinda sums ???

K as well as K^2 has same no of prime factors

4K^4 has same no factors as 2K and 4K Which can be one less than the number of factors K has if K is even and equal to bo of factors k has if k is odd

For an example say k =15 = 3*5

4K^4 has 3 prime factors 3,5 and 2
4K has 3 prime factors 3 5 and 2

K has 2 prime factors
K^2 has 2 prime factors

on the other hand say if K=30 = 3*5*2

4K^4 has 3 prime factors
4K has 4 prime factors

K has 3 prime factors
K^2 has 3 prime factors

Hence E

yes you are correct thanks for soln.....

just check the bold part is there a mistake

[ajith]

yes you are correct thanks for soln.....

just check the bold part is there a mistake

Thanks Phoenix,
Original post edited to correct the solution