Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 18 Jun 2012
Posts: 44
GMAT Date: 09172012

If m is an integer greater than zero but less than integer n [#permalink]
Show Tags
05 Aug 2012, 22:04
1
This post received KUDOS
3
This post was BOOKMARKED
Question Stats:
28% (01:31) correct 72% (01:14) wrong based on 146 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 08 Apr 2014, 08:22, edited 3 times in total.
Edited the question and added the OA



Director
Joined: 22 Mar 2011
Posts: 608
WE: Science (Education)

Re: If m is an integer greater than zero but less than n, [#permalink]
Show Tags
06 Aug 2012, 01:11
2
This post received KUDOS
2
This post was BOOKMARKED
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. Answer B
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Manager
Joined: 05 Jul 2012
Posts: 75
Location: India
Concentration: Finance, Strategy
GMAT Date: 09302012
GPA: 3.08
WE: Engineering (Energy and Utilities)

Re: If m is an integer greater than zero but less than n, [#permalink]
Show Tags
06 Aug 2012, 19:11
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. Answer B 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 ?



Director
Joined: 22 Mar 2011
Posts: 608
WE: Science (Education)

Re: If m is an integer greater than zero but less than n, [#permalink]
Show Tags
06 Aug 2012, 21:12
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. Answer B 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.
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Intern
Joined: 02 Sep 2010
Posts: 44
Location: India

Re: If m is an integer greater than zero but less than n, [#permalink]
Show Tags
11 Aug 2012, 03:08
1
This post received KUDOS
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(29) * 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 So answer is B.
_________________
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!



Intern
Joined: 18 Jul 2011
Posts: 1

Re: If m is an integer greater than zero but less than n, [#permalink]
Show Tags
11 Aug 2012, 09:23
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).



Director
Joined: 22 Mar 2011
Posts: 608
WE: Science (Education)

Re: If m is an integer greater than zero but less than n, [#permalink]
Show Tags
11 Aug 2012, 09:49
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.
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Director
Joined: 22 Mar 2011
Posts: 608
WE: Science (Education)

Re: If m is an integer greater than zero but less than n, [#permalink]
Show Tags
11 Aug 2012, 09:57
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. Answer B 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.
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Intern
Joined: 02 Sep 2010
Posts: 44
Location: India

Re: If m is an integer greater than zero but less than n, [#permalink]
Show Tags
11 Aug 2012, 11:25
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.
_________________
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!



Intern
Joined: 17 Apr 2010
Posts: 8

Re: If m is an integer greater than zero but less than n, [#permalink]
Show Tags
29 Aug 2012, 14:39
That one is interesting! Read the question stem carefully:
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 nonprime 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
Last edited by silas on 29 Aug 2012, 17:25, edited 1 time in total.



Intern
Joined: 17 Apr 2010
Posts: 8

Re: If m is an integer greater than zero but less than n, [#permalink]
Show Tags
29 Aug 2012, 14:51
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



Current Student
Joined: 06 Sep 2013
Posts: 1954
Concentration: Finance

Re: If m is an integer greater than zero but less than n, [#permalink]
Show Tags
08 Apr 2014, 08:05
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



Math Expert
Joined: 02 Sep 2009
Posts: 43830

Re: If m is an integer greater than zero but less than n, [#permalink]
Show Tags
08 Apr 2014, 08:26
3
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
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. Answer: B.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



NonHuman User
Joined: 09 Sep 2013
Posts: 13818

Re: If m is an integer greater than zero but less than integer n [#permalink]
Show Tags
25 Jan 2018, 01:35
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If m is an integer greater than zero but less than integer n
[#permalink]
25 Jan 2018, 01:35






