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# If m is an integer greater than zero but less than integer n

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If m is an integer greater than zero but less than integer n  [#permalink]

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Updated on: 08 Apr 2014, 09:22
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If m is an integer greater than zero but less than integer n, is m a factor of n?

(1) n is divisible by all integers less than 10
(2) m is not a multiple of a prime number

Originally posted by ananthpatri on 05 Aug 2012, 23:04.
Last edited by Bunuel on 08 Apr 2014, 09:22, edited 3 times in total.
Edited the question and added the OA
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Re: If m is an integer greater than zero but less than n,  [#permalink]

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06 Aug 2012, 02:11
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ananthpatri wrote:
If m is an integer greater than zero but less than n, is m a factor of n?

(1) n is divisible by all integers less than 10.
(2) m is not a multiple of a prime number.

(1) n must be divisible by 2, 3, 4,...,9 so, n is divisible by 9! If m = 11, n is not necessarily divisible by m.
Not sufficient.

(2) m must be 1, therefore m is a factor of n. Sufficient.

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Re: If m is an integer greater than zero but less than n,  [#permalink]

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06 Aug 2012, 20:11
EvaJager wrote:
ananthpatri wrote:
If m is an integer greater than zero but less than n, is m a factor of n?

(1) n is divisible by all integers less than 10.
(2) m is not a multiple of a prime number.

(1) n must be divisible by 2, 3, 4,...,9 so, n is divisible by 9! If m = 11, n is not necessarily divisible by m.
Not sufficient.

(2) m must be 1, therefore m is a factor of n. Sufficient.

What does this mean ?
m is not a multiple of a prime number

I thought it means that M is a Prime Number itself.
Can m be 19 ?

How can m be 1 ? 1 is a multiple of one. ? All numbers are a multiple of one. It can then be 2 as well ? 3 as well ? 5 as well ?
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Re: If m is an integer greater than zero but less than n,  [#permalink]

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06 Aug 2012, 22:12
mandyrhtdm wrote:
EvaJager wrote:
ananthpatri wrote:
If m is an integer greater than zero but less than n, is m a factor of n?

(1) n is divisible by all integers less than 10.
(2) m is not a multiple of a prime number.

(1) n must be divisible by 2, 3, 4,...,9 so, n is divisible by 9! If m = 11, n is not necessarily divisible by m.
Not sufficient.

(2) m must be 1, therefore m is a factor of n. Sufficient.

What does this mean ?
m is not a multiple of a prime number

I thought it means that M is a Prime Number itself.
Can m be 19 ?

19 = 19*1, is a multiple of a prime number 19. So, m cannot be 19.

How can m be 1 ? 1 is a multiple of one. ? All numbers are a multiple of one. It can then be 2 as well ? 3 as well ? 5 as well ?

1 is not prime. 2, 3, 5 are primes and all are a multiple of themselves. Neither one can be m.
Every positive integer greater than 1 has a unique factorization, meaning it can be written as a product of prime numbers.
1 cannot.

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Re: If m is an integer greater than zero but less than n,  [#permalink]

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11 Aug 2012, 04:08
1
ananthpatri wrote:
If m is an integer greater than zero but less than n, is m a factor of n?

(1) n is divisible by all integers less than 10.
(2) m is not a multiple of a prime number.

stmt 1: n = LCM(2-9) * K - INSUFFICIENT
stmt 2: m is not a multiple of prime number means,
m can not be a composite number, because every composite number can be factorized in to product of prime numbers

m can not even be a prime number, because every prime number is a multiple of itself.

m has to be an integer greater than 0. only value n can have is 1.

coming to root question. is m a factor of n. If m = 1, yes..! As 1 is a multiple of every integer. - SUFFICIENT

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Re: If m is an integer greater than zero but less than n,  [#permalink]

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11 Aug 2012, 10:23
I reached the same conclusion hermit84 but then I realized that we are not explicitely told that n is an integer, a condition I think is necessary for statement 2 to be sufficient on its own.

Hence, C (if my assumption holds).
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Re: If m is an integer greater than zero but less than n,  [#permalink]

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11 Aug 2012, 10:49
leodesrumaux wrote:
I reached the same conclusion hermit84 but then I realized that we are not explicitely told that n is an integer, a condition I think is necessary for statement 2 to be sufficient on its own.

Hence, C (if my assumption holds).

The question is about m being a factor of n. The term factor is used only for integers.
So, n is also an integer.

I agree, it would have been better to state clearly that both m and n are positive integers.
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Re: If m is an integer greater than zero but less than n,  [#permalink]

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11 Aug 2012, 10:57
EvaJager wrote:
ananthpatri wrote:
If m is an integer greater than zero but less than n, is m a factor of n?

(1) n is divisible by all integers less than 10.
(2) m is not a multiple of a prime number.

(1) n must be divisible by 2, 3, 4,...,9 so, n is divisible by 9! If m = 11, n is not necessarily divisible by m.
Not sufficient.

(2) m must be 1, therefore m is a factor of n. Sufficient.

hermit84 is right: n must be divisible by the least common multiple of all the integers less than 10, which is not 9! as I stated in my above post.
The difference is a factor of $$2^3*3$$, so, 9! is not accurate. The rest holds, and doesn't change the conclusion.
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Re: If m is an integer greater than zero but less than n,  [#permalink]

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11 Aug 2012, 12:25
leodesrumaux wrote:
I reached the same conclusion hermit84 but then I realized that we are not explicitely told that n is an integer, a condition I think is necessary for statement 2 to be sufficient on its own.

Hence, C (if my assumption holds).

leodesrumaux, be cautious but not extra cautious.
I know there are many DS questions, which will test the same thing you pointed, but not here.
n has to be integer, if we are talking about factors here.
Even if we assume that every whole number can have a factor, we will still have to accept 1 as a universal factor.

I hope it makes sense.
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The world ain't all sunshine and rainbows. It's a very mean and nasty place and I don't care how tough you are it will beat you to your knees and keep you there permanently if you let it. You, me, or nobody is gonna hit as hard as life. But it ain't about how hard ya hit. It's about how hard you can get it and keep moving forward. How much you can take and keep moving forward. That's how winning is done!
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Re: If m is an integer greater than zero but less than n,  [#permalink]

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Updated on: 29 Aug 2012, 18:25
That one is interesting!

If m is an integer greater than zero but less than n, is m a factor of n?
what do we learn?
- m is an integer > 0 , m can be 1,2,3,4...................
- m must be less than n, n < m, note that we don't know whether n is an integer; we simply know that n is positive
Now the question: Is m a factor of n OR is n a multiple of m?

Before tackling the statements, let us give a few conditions that will make n divisible by m:
1- n is an integer, therefore
- m=1
- m has all the prime factors of n ( so m cannot be prime)

2- n is not an integer, therefore
n/m cannot be an integer.

What do the statements reveal or imply ?

1) n is divisible by all intergers less than 10
- n is an integer
- n is not prime (1,2,3,4........,9 are factors of n)
as you may notice, this statement is not sufficient: n is an integer, and is not prime. if m can be written as a product of prime factors less than 10, n/m would be sufficient; but m can be written as a product of prime factors less than 10 and a prime (n = 2*11 =22 or n = 3*17 = 51), and n/m will not necessarily be a integer. Not sufficient

2) m is not a multiple of a prime number
this clearly means that m cannot be written as the product of a prime integer
therefore m must be 1, since any non-prime can be written as the product of prime integers (2,3,5,7,11,13.....) AND a prime is a multiple of itself

clearly statement (2) is not sufficient
n can still be any number (integer, fraction etc.); if n were a fraction n/1 cannot be an integer. for n/m to be an integer, n must be an integer. But statement (2) does not give us enough information about n.

BUT COMBINING THE TWO STATEMENTS IS SUFFICIENT
- n is an integer and n can be written as the product of all integers from 2 to 9 (from statement 1)
- n< m (from the stem)
- m = 1 (statement 2)

Therefore C must the correct answer

Originally posted by silas on 29 Aug 2012, 15:39.
Last edited by silas on 29 Aug 2012, 18:25, edited 1 time in total.
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Re: If m is an integer greater than zero but less than n,  [#permalink]

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29 Aug 2012, 15:51
hermit84 wrote:
leodesrumaux wrote:
I reached the same conclusion hermit84 but then I realized that we are not explicitely told that n is an integer, a condition I think is necessary for statement 2 to be sufficient on its own.

Hence, C (if my assumption holds).

leodesrumaux, be cautious but not extra cautious.
I know there are many DS questions, which will test the same thing you pointed, but not here.
n has to be integer, if we are talking about factors here.
Even if we assume that every whole number can have a factor, we will still have to accept 1 as a universal factor.

I hope it makes sense.

@hermit84
leodesrumaux is right to be cautious or extra cautious.
We must not assume anything that is not clearly stated.
And in the question stem, it is clearly stated that m is an integer.
And they want us to decide whether a number "n" is a multiple of integer m.
Even though 1 is a universal factor, n/1 will not be an integer if n is decimal or a fraction.
And that is one the the three tricks I noticed with the question

Hope this helps
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Re: If m is an integer greater than zero but less than n,  [#permalink]

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08 Apr 2014, 09:05
What's the answer for this one? I too thought that it didn't matter whether 'n' was an integer since 1 is a factor of any number whether integer or not.

Therefore, IMHO B stands

Please let us know will ya?
Thanks
Cheers
J
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Posts: 58398
Re: If m is an integer greater than zero but less than n,  [#permalink]

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08 Apr 2014, 09:26
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jlgdr wrote:
What's the answer for this one? I too thought that it didn't matter whether 'n' was an integer since 1 is a factor of any number whether integer or not.

Therefore, IMHO B stands

Please let us know will ya?
Thanks
Cheers
J

Term "factor" is used only for integers. Also, the question was copied incorrectly, actual question says that n is in fact an integer.

If m is an integer greater than zero but less than integer n, is m a factor of n?

(1) n is divisible by all integers less than 10. Clearly insufficient.

(2) m is not a multiple of a prime number. Every positive integer is a multiple of at least one prime number except 1, thus m=1, which implies that it must be a factor of any other integer including n. Sufficient.

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Re: If m is an integer greater than zero but less than integer n  [#permalink]

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Re: If m is an integer greater than zero but less than integer n   [#permalink] 24 Aug 2019, 01:00
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