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My doubt is when we analyse stat. 1, aren’t we left with 7,11,13,17,19,23,25,29 out of which isn’t 25 has a different answer to the question than the other numbers? don’t we need stat. 2 to answer it?

Re: divisibility problem [#permalink]
26 Apr 2012, 02:08

1

This post received KUDOS

Expert's post

kashishh wrote:

If m is a positive odd integer between 2 and 30, then m is divisible by how many different positive prime numbers?

(1) m is not divisible by 3. (2) m is not divisible by 5.

OA is A My doubt is when we analyse stat. 1, aren’t we left with 7,11,13,17,19,23,25,29 out of which isn’t 25 has a different answer to the question than the other numbers? don’t we need stat. 2 to answer it?

No, since 25 (as well as all other possible values of m from statement (1)), is divisible only by one prime number - 5.

If m is a positive odd integer between 2 and 30, then m is divisible by how many different positive prime numbers?

Since the range is not that big we can write down all possible value of m for each statement.

(1) m is not divisible by 3 --> m can be: 5, 7, 11, 13, 17, 19, 23, 25, and 29. Each has only one distinct prime in its prime factorization. Sufficient.

(2) m is not divisible by 5 --> m can be: 3, 7, 9, 11, 13, 17, 19, 21, STOP. Each but 21 has one prime in its prime factorization, while 21 has two primes: 3 and 7. Not sufficient.

Re: If m is a positive odd integer between 2 and 30, then m is [#permalink]
26 Apr 2012, 03:26

1

This post received KUDOS

Expert's post

kashishh wrote:

If m is a positive odd integer between 2 and 30, then m is divisible by how many different positive prime numbers?

(1) m is not divisible by 3. (2) m is not divisible by 5.

OA is A My doubt is when we analyse stat. 1, aren’t we left with 7,11,13,17,19,23,25,29 out of which isn’t 25 has a different answer to the question than the other numbers? don’t we need stat. 2 to answer it?

The question asks for "... how many different prime numbers?" If you are thinking that 25 is divisible by 5 and 5, it still counts as one.

(1) m is not divisible by 3 m is not divisible by 2 anyway since we are talking about odd numbers. Next prime number is 5. The next one is 7 but 5*7 = 35 which is greater than 30. So even if we take the two smallest possible primes, no odd number in the given range can have both as factors. So m must have only one prime number as a factor.

(2) m is not divisible by 5 m could be divisible by 3 and 7 (since 3*7 = 21 which lies in our range). So m could be divisible by one prime or by two different primes. So this statement is not sufficient.

Re: divisibility problem [#permalink]
20 Jan 2014, 04:52

Bunuel wrote:

kashishh wrote:

If m is a positive odd integer between 2 and 30, then m is divisible by how many different positive prime numbers?

(1) m is not divisible by 3. (2) m is not divisible by 5.

OA is A My doubt is when we analyse stat. 1, aren’t we left with 7,11,13,17,19,23,25,29 out of which isn’t 25 has a different answer to the question than the other numbers? don’t we need stat. 2 to answer it?

No, since 25 (as well as all other possible values of m from statement (1)), is divisible only by one prime number - 5.

If m is a positive odd integer between 2 and 30, then m is divisible by how many different positive prime numbers?

Since the range is not that big we can write down all possible value of m for each statement.

(1) m is not divisible by 3 --> m can be: 5, 7, 11, 13, 17, 19, 23, 25, and 29. Each has only one distinct prime in its prime factorization. Sufficient.

(2) m is not divisible by 5 --> m can be: 3, 7, 9, 11, 13, 17, 19, 21, STOP. Each but 21 has one prime in its prime factorization, while 21 has two primes: 3 and 7. Not sufficient.

Answer: A.

Hope it's clear.

Sorry Bunuel but I don't quite get it, we are asked it is divisible by how many different positive prime numbers.

So from Statement 1 I understand that it can be divisible by all of them because they are all distinct prime numbers so that will be 9 numbers

But from Statement 2, I don't understand it that well. OK we have 21 that has two primes 3, and 7 but we had already considered them early in the list, so what's the deal with having them again? Since we are asked for different primes then we just ignore these.

Are we being asked to count them all even with repetitions?

Re: divisibility problem [#permalink]
20 Jan 2014, 05:00

Expert's post

jlgdr wrote:

Bunuel wrote:

kashishh wrote:

If m is a positive odd integer between 2 and 30, then m is divisible by how many different positive prime numbers?

(1) m is not divisible by 3. (2) m is not divisible by 5.

OA is A My doubt is when we analyse stat. 1, aren’t we left with 7,11,13,17,19,23,25,29 out of which isn’t 25 has a different answer to the question than the other numbers? don’t we need stat. 2 to answer it?

No, since 25 (as well as all other possible values of m from statement (1)), is divisible only by one prime number - 5.

If m is a positive odd integer between 2 and 30, then m is divisible by how many different positive prime numbers?

Since the range is not that big we can write down all possible value of m for each statement.

(1) m is not divisible by 3 --> m can be: 5, 7, 11, 13, 17, 19, 23, 25, and 29. Each has only one distinct prime in its prime factorization. Sufficient.

(2) m is not divisible by 5 --> m can be: 3, 7, 9, 11, 13, 17, 19, 21, STOP. Each but 21 has one prime in its prime factorization, while 21 has two primes: 3 and 7. Not sufficient.

Answer: A.

Hope it's clear.

Sorry Bunuel but I don't quite get it, we are asked it is divisible by how many different positive prime numbers.

So from Statement 1 I understand that it can be divisible by all of them because they are all distinct prime numbers so that will be 9 numbers

But from Statement 2, I don't understand it that well. OK we have 21 that has two primes 3, and 7 but we had already considered them early in the list, so what's the deal with having them again? Since we are asked for different primes then we just ignore these.

Are we being asked to count them all even with repetitions?

Please clarify Thank you! Cheers! J

For (2):

If m=3, then m is divisible by ONE prime factor, 3. If m=21, then m is divisible by TWO prime factors, 3 and 7.

So, we have two different answers, which means that the statement is not sufficient.