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by ashishsj » Sat Mar 07, 2009 9:49 am
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?
(2m/n)+1
(2n/m)+1
2n/(m+1)
2m/n
2n/m

I found this explaination on forum :
We are told in the question
...m is a factor of n...
So lets choose m to be 2 and n to be 6 because 2 is a factor of 6 (you can pick other numbers if you wish).
Replacing these numbers into the question we get, "how many positive multiples of 2 are less than or equal to 12?"
You can write all the multiples out, "2, 4, 6, 8, 10, 12", and then it is clear to see that there are 6 positive multiples of 2 that are less than or equal to 12.
0 is not included in the list because we are asked for positive multiples and 0 is not positive. 12 is included in the list because the question asks for multiples which are less than or equal to 12.
Check against answers
Now we can work through the answers substituting the values of m (2) and n (6) into them and we can eliminate any answer which does not evaluate to 6.
2n/m = 2x6/2 = 6, and others don't tally to 6. So answer is E.

Why is 1 not considered a factor of n?


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by cramya » Sat Mar 07, 2009 10:13 am
Why is 1 not considered a factor of n?
1 is a factor of n but this question deals with multiples and not factors.

If the question was how many multiples instead of possitve multiples the answer would be 2n/m+1 since 0 is a multiple of every number.

Since in this question we are asked positive multiples the answer is E.


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CR

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by Ian Stewart » Sat Mar 07, 2009 12:24 pm
cramya wrote: If the question was how many multiples instead of possitve multiples the answer would be 2n/m+1 since 0 is a multiple of every number.
Actually, if the question asked about 'multiples', not 'positive multiples', the answer would be infinite. The GMAT always restricts its multiples questions to positive numbers only, but in real math, multiples can be negative. -9 is a multiple of 3, for example, since -9 is equal to 3 times an integer. Not important for the GMAT however - for interest only!
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by cramya » Sat Mar 07, 2009 12:52 pm
Thanks Ian!