m can be 3,6,9,12,15,18 ...

St1: m/3 is divisible by 3
So m can be: 9 or 18 and corresponding m/3 would be 3 and 6 (div. by 3)
# prime factors of 9 = 1 {3}
# prime factors of 18 = 2 {2,3}
Not sufficient

St2: m/3 has 2 different prime factors
if m/3 = 10 {prime factors 2 and 5}, then m = 30 and # prime factors of 30 = 3 {2,3,5}
if m/3 = 6 {prime factors 2 and 3}, then m = 18 and # prime factors of 18 = 2 {2,3}
Insufficient

Together: m/3 is divisible by 3 and m/3 has 2 prime factors
if m = 18, # prime factors of 18 = 2 {2,3}
if m = 36, # prime factors of 36 = 2 {2,3}
Sufficient

Ans C

Thanks I considered that before but my query remains same


qustion asking: If m is divisible by 3, how many prime factors does m have?
Note that NOT differant prime factors

here in your solution 18 have 3 (2x3x3) total factors and 2 differant factors
and 36 have 4 total factors (2x2x3x3) and 2 differant prime factors

18 = {1,2,3,6,9,18}
Total # of factors = 6
# prime factors = 2 {2 and 3} = # Distinct prime factors

18 -Total no of prime factors 2x3x3 = 3; distinct prime factors = 2
36 - Total no of prime factors 2x2x3x3 = 4 ; distinct prime factors = 2

Qustion asking total no of prime factors not distinct prime factors ;since 3 not equal to 4 hence my ans remain same E

vipulgoyal wrote:18 -Total no of prime factors 2x3x3 = 3; distinct prime factors = 2
36 - Total no of prime factors 2x2x3x3 = 4 ; distinct prime factors = 2

Qustion asking total no of prime factors not distinct prime factors ;since 3 not equal to 4 hence my ans remain same E

I think we need to check the definition of prime factor.
From the top of my head we dont distinguish between distinct prime factors and prime factors i.e. we dont count them twice.

I ll have to agree with srcc25anu

I am sure experts might have come across couple of qustions where Total number of prime factors and dictinct no of prime factors didnt mean same, but my query still dangling

Yup expert reply would be great!

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