. How many prime factors does positive integer n have?
(1) n/5 has only a prime factor.
(2) 3*n^2 has two different prime factors.
OE
(1) : n/5 has one prime factor. So we know immediately that is a multiple of 5. Either n is of the form 5^k or 5x(another_prime)^k (Eg. n=125 or n=15 both work). Hence n has either 1 or 2 prime factors ... Insufficient
(2) : 3*n^2 has two factors. Again, n could have 1 or 2 factors. Eg n=15 OR n =125 both work
(1+2) : Take the case n = 15 and n = 125 ... both statements can be true together. Hence not clear if n has one prime factor or two
Hence, Answer is (e)
My query: at stem 1; " n/5 has only a prime factor" n cant be 125 as explained in OE ,bcz if it so , no of primes 125/5 becomes two not one, however no of different primes stay one (which stem is not asking) in my opinion OA should be A
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same analogy with this one
If m is divisible by 3, how many prime factors does m have?
1) \frac{m}{3} is divisible by 3
2) \frac{m}{3} has two different prime factors
OA says C, however m= 3^2*5^2 and m = 3^2*5^3 satisfies both statements while total no of primes are different in both cases
(1) n/5 has only a prime factor.
(2) 3*n^2 has two different prime factors.
OE
(1) : n/5 has one prime factor. So we know immediately that is a multiple of 5. Either n is of the form 5^k or 5x(another_prime)^k (Eg. n=125 or n=15 both work). Hence n has either 1 or 2 prime factors ... Insufficient
(2) : 3*n^2 has two factors. Again, n could have 1 or 2 factors. Eg n=15 OR n =125 both work
(1+2) : Take the case n = 15 and n = 125 ... both statements can be true together. Hence not clear if n has one prime factor or two
Hence, Answer is (e)
My query: at stem 1; " n/5 has only a prime factor" n cant be 125 as explained in OE ,bcz if it so , no of primes 125/5 becomes two not one, however no of different primes stay one (which stem is not asking) in my opinion OA should be A
----
same analogy with this one
If m is divisible by 3, how many prime factors does m have?
1) \frac{m}{3} is divisible by 3
2) \frac{m}{3} has two different prime factors
OA says C, however m= 3^2*5^2 and m = 3^2*5^3 satisfies both statements while total no of primes are different in both cases
