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# If m and n are positive integers such that m is a factor of

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If m and n are positive integers such that m is a factor of [#permalink]

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04 Oct 2011, 19:59
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Nov 2014, 02:43, edited 1 time in total.
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Re: If m and n are positive integers such that m is a factor of [#permalink]

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04 Oct 2011, 20:10
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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
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

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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Re: If m and n are positive integers such that m is a factor of [#permalink]

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06 Oct 2011, 03:25
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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 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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06 Oct 2011, 08:33
Karishma, you are the greatest. +1
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Re: If m and n are positive integers such that m is a factor of [#permalink]

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06 Oct 2011, 09:05
thank you for this!
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Re: If m and n are positive integers such that m is a factor of [#permalink]

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07 Oct 2011, 09:34
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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.
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Re: If m and n are positive integers such that m is a factor of [#permalink]

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08 Oct 2011, 23:41
I think picking number is the best for this sort of problems.
i Picked m=3, n=12
Only E worked.
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Re: If m and n are positive integers such that m is a factor of [#permalink]

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14 Oct 2011, 01:15
@karishma..

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

IMO E..
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Re: If m and n are positive integers such that m is a factor of [#permalink]

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18 Oct 2011, 20:24
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.
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Re: If m and n are positive integers such that m is a factor of [#permalink]

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03 Jun 2012, 08:18
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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Re: If m and n are positive integers such that m is a factor of [#permalink]

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10 Nov 2014, 21:44
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Re: If m and n are positive integers such that m is a factor of [#permalink]

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20 Jun 2016, 18:18
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Re: If m and n are positive integers such that m is a factor of [#permalink]

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29 Jun 2016, 16:36
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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If m and n are positive integers such that m is a factor of [#permalink]

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24 Oct 2016, 04:40
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
If m and n are positive integers such that m is a factor of   [#permalink] 24 Oct 2016, 04:40
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