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Intern  Joined: 01 Mar 2006
Posts: 21
Schools: columbia, chicago, Insead, wharton
If m and n are positive integers such that m is a factor of  [#permalink]

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Question Stats: 67% (02:06) correct 33% (02:15) wrong based on 376 sessions

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If m and n are positive integers such that m is a factor of n, how many positive multiples of m are less than or equal to 2n ?

A. 2m/n + 1
B. 2n/m + 1
C. 2n/(m+1)
D. 2m/n
E. 2n/m

Originally posted by kulki on 04 Oct 2011, 20:59.
Last edited by Bunuel on 11 Nov 2014, 03:43, edited 1 time in total.
Veritas Prep GMAT Instructor V
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Location: Pune, India
Re: If m and n are positive integers such that m is a factor of  [#permalink]

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10
1
kulki wrote:
If m and n are positive integers such that m is a factor of n, how many positive multiples of m are less than or equal to 2n ?
a. 2m/n + 1
b. 2n/m + 1
c. 2n/(m+1)
d. 2m/n
e. 2n/m

what is the best method to approach problems like these ? - Algebraic methods or substitution method ? Any advice ?

I don't think there is anything called 'the best approach'. Each person uses what works best for her/him. I jump to plugging in numbers whenever I see variables in the questions and variables in the options. I know that within 1 or 2 iterations, I should get my answer. I also like to choose the simplest possible numbers. e.g. here I would put m = 1 and n = 1 (both positive integers and m is a factor of n). But the moment I put them equal, I see that options d and e will be the same. So instead, I put m = 1 and n = 2. 2n = 4.
Number of positive multiples of 1 that are less than or equal to 4 = 4 (1, 2, 3, 4)
Only e gives me 4 when I put n = 2 and m = 1

Mind you, it is not a good idea to plug in numbers when you have 3-4 variables since you might just get lost in them.
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Re: If m and n are positive integers such that m is a factor of  [#permalink]

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kulki wrote:
If m and n are positive integers such that m is a factor of n, how many positive multiples of m are less than or equal to 2n ?
a. 2m/n + 1
b. 2n/m + 1
c. 2n/(m+1)
d. 2m/n
e. 2n/m

what is the best method to approach problems like these ? - Algebraic methods or substitution method ? Any advice ?

Lets say N=10, M=5
2N=20. so the answer should be 4 (20/5)
lets try to plug in the answers:
A-not an integer
B-not an integer
C-not an integer
D-1 (not the answer)
E-4 - the answer. (the only one).

I would choose E.

Method 2
N=M*A (A is an integer)
So - A=N/M
therefore in 2N A will be 2N/M

Again - Answer is E.

Hope it helps.

*** personally - I love the mathematical approach. Easier for me, however, many people like the plug in numbers approach. It is important to master both methods so if one doesnt work, you can try the other.
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Senior Manager  Joined: 08 Nov 2010
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Re: If m and n are positive integers such that m is a factor of  [#permalink]

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Karishma, you are the greatest. +1
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Intern  Joined: 11 Aug 2011
Posts: 4
Re: If m and n are positive integers such that m is a factor of  [#permalink]

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thank you for this!
Intern  Joined: 26 May 2011
Posts: 10
Location: United States
Re: If m and n are positive integers such that m is a factor of  [#permalink]

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VeritasPrepKarishma wrote:
kulki wrote:
If m and n are positive integers such that m is a factor of n, how many positive multiples of m are less than or equal to 2n ?
a. 2m/n + 1
b. 2n/m + 1
c. 2n/(m+1)
d. 2m/n
e. 2n/m

what is the best method to approach problems like these ? - Algebraic methods or substitution method ? Any advice ?

I don't think there is anything called 'the best approach'. Each person uses what works best for her/him. I jump to plugging in numbers whenever I see variables in the questions and variables in the options. I know that within 1 or 2 iterations, I should get my answer. I also like to choose the simplest possible numbers. e.g. here I would put m = 1 and n = 1 (both positive integers and m is a factor of n). But the moment I put them equal, I see that options d and e will be the same. So instead, I put m = 1 and n = 2. 2n = 4.
Number of positive multiples of 1 that are less than or equal to 4 = 4 (1, 2, 3, 4)
Only e gives me 4 when I put n = 2 and m = 1

Mind you, it is not a good idea to plug in numbers when you have 3-4 variables since you might just get lost in them.

In case of 3-4 variables good to use the table to track.
Manager  Joined: 13 May 2011
Posts: 191
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WE 2: Supply Chain 5 Yrs
Re: If m and n are positive integers such that m is a factor of  [#permalink]

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I think picking number is the best for this sort of problems.
i Picked m=3, n=12
Only E worked.
Manager  Joined: 09 Jun 2011
Posts: 78
Re: If m and n are positive integers such that m is a factor of  [#permalink]

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@karishma..

Same here i plugged in numbers too..m=2 and n=6..

IMO E..
Manager  Joined: 18 Jun 2010
Posts: 82
Re: If m and n are positive integers such that m is a factor of  [#permalink]

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Plugging numbers seems like the best approach here.

1. Put n = 25 and m = 5
2. Put n = 4 and m = 2.

In both the scenarios only E stands out.
Intern  Joined: 04 Oct 2011
Posts: 8
Re: If m and n are positive integers such that m is a factor of  [#permalink]

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kulki wrote:
If m and n are positive integers such that m is a factor of n, how many positive multiples of m are less than or equal to 2n ?
a. 2m/n + 1
b. 2n/m + 1
c. 2n/(m+1)
d. 2m/n
e. 2n/m

what is the best method to approach problems like these ? - Algebraic methods or substitution method ? Any advice ?

I think we can save some time here. It is a simple question asking the number of factors but in a twisted manner. For example, if I may ask how many positive multiples of 3 are less than or equal to 12 (6*2), given that 6 is multiple of 3. Its straight 12/3.
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GMAT 1: 540 Q39 V26 GMAT 2: 680 Q46 V37 Re: If m and n are positive integers such that m is a factor of  [#permalink]

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Keyword: Positive
Lets say

m=4
n=16
2n=32

Every other option except for B and E give non integer values.

B indicates the answer to be 9. That would be true if we were to consider 0 as well. However, the question asks for positive.
0 is neither positive nor negative.

Hence, E
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Manager  B
Joined: 02 Jul 2016
Posts: 121
If m and n are positive integers such that m is a factor of  [#permalink]

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Since every one has given approach in which value is placed is the variable I have an approach without putting values..
Let me know if I am wrong...
m is a factor of n
Therefore I can say
n= m*k where is the multiplying factor(For eg: if n=6 and m=3 then 6=3*2)
Hence k=n/m;
(2=6/3) Hence, we can say that the number of multiples of n less than equal to m is equal to k(multiples of 3 less than equal to 6 are 2)
Similiarly,
2m=n*k"
=>k"=2m/n

Hence, we can say that the number of multiples of n less than 2m equals to k" i.e. 2m/n;

Actually in this question we are asked that by what factor 2m will be divided by n

FOCUS ON THE CONCEPT NOT THE QUESTION
SVP  V
Joined: 26 Mar 2013
Posts: 2344
Re: If m and n are positive integers such that m is a factor of  [#permalink]

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kulki wrote:
If m and n are positive integers such that m is a factor of n, how many positive multiples of m are less than or equal to 2n ?

A. 2m/n + 1
B. 2n/m + 1
C. 2n/(m+1)
D. 2m/n
E. 2n/m

Let m=2 & n=4 ...then m=2 & 2n=8

There are 4 multiples between 2 & 8 which are 2,4,6 & 8

A. 2m/n + 1 = 1 +1 = 2..........Eliminate

B. 2n/m + 1 = 4 +1 =5............Eliminate

C. 2n/(m+1) = 8/3..................Eliminate

D. 2m/n = 4/4 =1 ..................Eliminate

Only choice left...we can check to be sure

E. 2n/m = 8/2 = 4..................Keep Re: If m and n are positive integers such that m is a factor of   [#permalink] 30 Mar 2018, 13:57
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