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

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If A and B are positive integers, does A have more prime factors [#permalink] New post   22 Nov 2016, 08:24
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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
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A
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Re: If A and B are positive integers, does A have more prime factors [#permalink] New post   22 Nov 2016, 09:35
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stonecold wrote:
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


(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.
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Re: If A and B are positive integers, does A have more prime factors [#permalink] New post   02 Apr 2020, 09:43
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broall wrote:
stonecold wrote:
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


(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.


Hi cant A and B have the same number of prime factors? How would A be sufficient then?
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Re: If A and B are positive integers, does A have more prime factors [#permalink] New post   02 Apr 2020, 09:48
Expert Reply
Kritisood wrote:
broall wrote:
stonecold wrote:
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


(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.


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


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?
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Re: If A and B are positive integers, does A have more prime factors [#permalink] New post   02 Apr 2020, 09:55
Bunuel wrote:
Kritisood wrote:

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


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?


It would still be No :facepalm:
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Re: If A and B are positive integers, does A have more prime factors [#permalink] New post   04 Apr 2020, 10:01
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stonecold wrote:
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


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
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Re: If A and B are positive integers, does A have more prime factors [#permalink] New post   05 Apr 2020, 23:46
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(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
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Re: If A and B are positive integers, does A have more prime factors [#permalink] New post   12 Oct 2023, 02:06
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Re: If A and B are positive integers, does A have more prime factors [#permalink]
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