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EIV 4th Ed. Ch. 10 problem set Question 9 -- please help

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futjim
 Post subject: EIV 4th Ed. Ch. 10 problem set Question 9 -- please help
 Post Posted: Mon Jul 05, 2010 6:55 am 
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Students


Posts: 7
Location: Japan
If mn = 3(m+1) + n and m and n are integers, m could be any of the following values EXCEPT:

- 2
- 3
- 4
- 5

The explanation at the back offered two approaches. I understand the first one but don't understand the second:

...you can notice that consecutive values of 5c + 8d differ by 3. In other words, every possible value of 5c + 8d equals a multiple of 3 plus some constant...

Question one: what is the rule here? What happens when a Multiple of 5, MO5, is added to a Multiple of 8, MO8? (I tried looking in the number properties book and found nothing)

I've also tried working this relationship out with numbers and found that if c & d in the above equation is different then the resulting number isn't a MO3. However, if c=d then the result is MO3 + some constant.

Please clarify the above relationship!!

Thanks alot!
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adiagr
 Post subject: Re: EIV 4th Ed. Ch. 10 problem set Question 9 -- please help
 Post Posted: Mon Jul 05, 2010 9:16 am 
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Students


Posts: 89
futjim wrote:
If mn = 3(m+1) + n and m and n are integers, m could be any of the following values EXCEPT:

- 2
- 3
- 4
- 5

The explanation at the back offered two approaches. I understand the first one but don't understand the second:

...you can notice that consecutive values of 5c + 8d differ by 3. In other words, every possible value of 5c + 8d equals a multiple of 3 plus some constant...

Question one: what is the rule here? What happens when a Multiple of 5, MO5, is added to a Multiple of 8, MO8? (I tried looking in the number properties book and found nothing)

I've also tried working this relationship out with numbers and found that if c & d in the above equation is different then the resulting number isn't a MO3. However, if c=d then the result is MO3 + some constant.

Please clarify the above relationship!!

Thanks alot!


separate out m and n.

mn-n = 3m +3

n*(m-1) = 3 *(m+1)

n = 3 * [(m+1) /(m-1)]

n is an integer.

it can be seen that n is integer for all given values of m except 5.

Aditya
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futjim
 Post subject: Re: EIV 4th Ed. Ch. 10 problem set Question 9 -- please help
 Post Posted: Tue Jul 06, 2010 8:13 pm 
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Students


Posts: 7
Location: Japan
Aditya, thank you so much for the reply.

I just realized the typed in the wrong question.

I'll repost it again.

Cheers,
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tim
 Post subject: Re: EIV 4th Ed. Ch. 10 problem set Question 9 -- please help
 Post Posted: Thu Jul 08, 2010 1:53 pm 
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ManhattanGMAT Staff


Posts: 2242
Location: Southwest Airlines, seat 21C
i don't know if you ever posted a corrected version of your problem, but please do when you get a chance, ALONG WITH a reference. The solution you mention looks really fishy and i don't think you typed it correctly..

_________________
Tim Sanders
Manhattan GMAT Instructor
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