If A and B are positive integers, does A have more prime factors

Question

If A and B are positive integers, does A have more prime factors than B?
(1) B/A is an integer 
(2) A/B is an integer

broall · Answer

(1) B/A is an integer, this means that every prime factor in A is also a prime factor of B. So B has the number of prime factors no less than A. Sufficient.

(2) Likewise (1), A/B is an integer so A has the number of prime factors no less than B. Cant say equal or greater. Insufficient.

The answer is A.

Kritisood · Answer

Hi cant A and B have the same number of prime factors? How would A be sufficient then?

Bunuel · Answer

If A and B have the same number of primes, what would be the answer to the question:  does A have more prime factors than B?

Kritisood · Answer

It would still be No

TestPrepUnlimited · Answer

Analyzing the question: 
If A has more prime factors, we answer "yes".
If A has the same amount of prime factors with B, we answer "no".
If B has more prime factors, we answer "no".

Statement 1: 
B/A is an integer, then every factor in A must be contained in B. Therefore B either has the same number of prime factors as A or more. In either case, we answer "no" to the question, therefore this is  sufficient .

Statement 2: 
Similar to above, we either have A with the same number of prime factors as B ("no" case), or A has more prime factors in which we answer "yes". Therefore this is  insufficient .

Ans: A

fireagablast · Answer

(1) B/A --> 1/1, 2/1, 6/3 .... does A have more than B? Always no --> Sufficient
(2) A/B --> 1/1 no, 2/1, 6/3...Does A have more than B? No and Yes ---> not sufficient

A

bumpbot · Answer

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If A and B are positive integers, does A have more prime factors

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