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for knowing the multiples of a number, we need to know the number or the multiple of the number

now using both the statements we can figure out that J is multiple of 30 so all the primes that divide 30 also divide J and K is given to be 1000, we can figure out the # of the primes that divide 1000 and then find the relationship that both are required.

I dont understand how C is the answer.

Question is that if the total number of prime factors that J has is more than K.

From St.1 -- Since j is divisible by 30 it is divisible by 2*3*5*n. n can potentially be a prime number or a product of several prime numbers. So total number of factors of j can be anywhere between 4 or infinity. For example n can be equal to 7*11*13*17*19*23*29*31*......... so it is indeterministic what the total number of prime factors j has and if it is less than k.

From St. 2 -- We know that k=1000. But we still dont know what j is. All we know is that j 2*3*5*n. n can be a product of just 2 prime numbers or several infinite prime numbers and hence we cannot establish if total number of prime factors of j is less than 1000 or greater than 1000.

for knowing the multiples of a number, we need to know the number or the multiple of the number

now using both the statements we can figure out that J is multiple of 30 so all the primes that divide 30 also divide J and K is given to be 1000, we can figure out the # of the primes that divide 1000 and then find the relationship that both are required.

I dont understand how C is the answer.

Question is that if the total number of prime factors that J has is more than K.

From St.1 -- Since j is divisible by 30 it is divisible by 2*3*5*n. n can potentially be a prime number or a product of several prime numbers. So total number of factors of j can be anywhere between 4 or infinity. For example n can be equal to 7*11*13*17*19*23*29*31*......... so it is indeterministic what the total number of prime factors j has and if it is less than k.

From St. 2 -- We know that k=1000. But we still dont know what j is. All we know is that j 2*3*5*n. n can be a product of just 2 prime numbers or several infinite prime numbers and hence we cannot establish if total number of prime factors of j is less than 1000 or greater than 1000.

E in my opinion.

What is the OA ?

st 1 ==> j is a multiple of 30. lets take j = 30 - so 3 prime divisors (2, 3 & 5). Note that any multiple of 30 will have atleast these 3 divisors. st 2 ==> k = 1000. only divisors are 2 and 5

regardless of the actual value of j, it has more divisors than k. so the answer is (C)
_________________

Is the positive integer j divisible by a greater number of different prime numbers than the positive integer k?

1) j is divisible by 30. 2) k = 1000

1) different prime numbers are 2, 3 and 5. Insuffisient as it needs to be compared to the number of prime factors of K 2) the only different prime factors are 5 and 2. Alone insufficient because we'd have to know how many factor J has.

Together sufficient as K has 3 factors vs. J's 2 factors

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