Yes, it is indeed tricky and i too got it wrong initially.
Please see that the questions asks for different prime factors for the two numbers and not the total number of factors (that's what i did in the first attempt). Here's the expn:
Considering the stmt, where j is told to be multiple of 30
suppose, if j =30 => different prime factors(pf) are: 2,3,5
and, if j =60 => diff pf are still: 2,3,5
similarly for 210 => diff pf are: 2,3,5,7
therefore, the minimum number of diff pf for multiple of 30 are : 3
but still we don't have any info about value of k. hence, take the stmt, where k = 1000.
now, 1000 = 2^3 * 5^3
i.e. different prime factors(pf) are: 2, 5
the minimum number of diff pf for multiple of 30 are : 3
hence, (C) is the correct choice.
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Just to add on, the prime factors of a number and the prime factors of the multiple of the number will always be the same.
For example -
1. Number 30 - Prime factors - 2, 3, 5
2. Number 60 - Prime factors - 2, 2, 3, 5
3. Number 90 - Prime factors - 2, 3, 3, 5
Unique prime factors - 2, 3, 5
For example -
1. Number 30 - Prime factors - 2, 3, 5
2. Number 60 - Prime factors - 2, 2, 3, 5
3. Number 90 - Prime factors - 2, 3, 3, 5
Unique prime factors - 2, 3, 5
