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# Remainder and gcf concept

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Manager
Joined: 10 Apr 2008
Posts: 53

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29 Jun 2009, 22:32
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I found this on another forum

Question is -

The integers m and p are such that 2 1?

1) the greatest common factor of m and p is 2.
2) the least common multiple of m and p is 30.

One of the explanations says

Quote:
when a number X is divided by number Y then the remainder left is always a multiple of HCF of X and Y ( provided x and y are integers) hence A is sufficient

Can someone please explain this? Why is this always true?

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Senior Manager
Joined: 23 Jun 2009
Posts: 355
Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago
Re: Remainder and gcf concept [#permalink]

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30 Jun 2009, 00:25
1
KUDOS
n = x*GCF(m,n)
m = y*GCF(m,n)

since m>n; y>x

m = t*n + r

since m>n; t>=1

r must be greater than 0 else GCF(m,n) would be n. And it is given that n is not a factor of m.

m = t*x*GCF(m,n) + r
y*GCF(m,n)=t*x*GCF(m,n) + r
(y-t*x)*GCF(m,n)=r

y-t*x>0 because r>0
Than r is divisible by GCF(m,n)
Manager
Joined: 10 Apr 2008
Posts: 53
Re: Remainder and gcf concept [#permalink]

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30 Jun 2009, 09:47
1
KUDOS
thanks! very good explanation.
Senior Manager
Joined: 23 Jun 2009
Posts: 355
Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago
Re: Remainder and gcf concept [#permalink]

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30 Jun 2009, 23:12
Thanks to you. You gave me an opportunity to think about a question that I've never tought about before.
Manager
Joined: 28 Jan 2004
Posts: 201
Location: India
Re: Remainder and gcf concept [#permalink]

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03 Jul 2009, 23:32

Whenever we divide a bigger number with a smaller don't you agree that the remainder will be always > 1???
Senior Manager
Joined: 23 Jun 2009
Posts: 355
Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago
Re: Remainder and gcf concept [#permalink]

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04 Jul 2009, 04:00
730 divided by 9; remainder is 1
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1346
Re: Remainder and gcf concept [#permalink]

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04 Jul 2009, 06:39
mdfrahim wrote:

Whenever we divide a bigger number with a smaller don't you agree that the remainder will be always > 1???

* When you divide 4 by 3, the remainder is 1.
* When you divide 6 by 3, the remainder is 0.

When you divide an integer x by a positive integer d, all you can be sure of, without more information, is that the remainder is an integer between 0 and d-1, inclusive.
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Manager
Joined: 28 Jan 2004
Posts: 201
Location: India
Re: Remainder and gcf concept [#permalink]

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04 Jul 2009, 11:44
hx. maliyeci and Ianstewart. I got the point now.
Manager
Joined: 28 Jan 2004
Posts: 201
Location: India
Re: Remainder and gcf concept [#permalink]

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04 Jul 2009, 22:55
A.

There is pattern to remainders. Please verify as this is my own finding , no source to quote

1. EVEN/EVEN = EVEN REMAINDER
2. EVEN/ODD = ODD REMAINDER
3. ODD/ODD = CAN BE ANYTHING
4. ODD/EVEN = ODD REMAINDER

Stmt 1 -
This tells us that both the numbers are even hence there remainder had to be even so it had to be >1 .

Stmt 2 -
Plug the numbers.

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: Remainder and gcf concept   [#permalink] 04 Jul 2009, 22:55
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