I must say that collection of DS problems is very nice.
Hareesh this is your first question-
1) How many different prime numbers are factors of the positive integer n ?
(1) Four different prime numbers are factors of 2n.
(2) Four different prime numbers are factors of n2.
Statement1:
2n has four different prime factors.
two possibilities are there-
n already has four different prime factors and 2 is one of the factors, to say- n=2X3X5X7 so now 2n will also have only 4 different prime factors.
n has only three prime factors i.e. n=3X5X7. After multiplying with 2 we will get total 4 different prime factors.
So this information is not sufficient.
Statement2:
n2 has four different prime factors.
TO BE REMEMBERED: DIFFERENT PRIME FACTORS OF ANY POWER OF A NATURAL NUMBER WILL ALWAYS BE SAME AS THE DIFFERENT PRIME FACTORS OF THE ORIGINAL NUMBER.
so if n2 is having four different prime factors, n will also be having 4 different prime factors.
Sufficient
Answer (B)
