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Re: If m and n are positive integers such that m is a factor of [#permalink]
04 Oct 2011, 20:10

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. _________________

Re: If m and n are positive integers such that m is a factor of [#permalink]
06 Oct 2011, 03:25

6

This post received KUDOS

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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 Answer (E).

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. _________________

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

2

This post received KUDOS

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 Answer (E).

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.

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

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

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