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remainder and mod

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remainder and mod [#permalink] New post 27 Feb 2006, 22:13
hi all

I have heard about the mod and the remainder chinese theorem in some posts dealing with remainder I did not learn this at school
Can anyone help me with this exercise using the remainder chinese theorem so i can notice i did understood it . plz explain your working
THANKS

The teacher has some apples to distribute to her students. If she
gives all of the apples to the 13 students in her first class she will
have 4 left. If she gives all of the apples to the 29 students in her
second class she will have 9 left. If she gives all of the apples to
the 37 students in her third class she will have 16 left. Whichever
class she gives the apples to, she will give each student the same
number of apples. What is the smallest number of apples the teacher
can have?
_________________

when there is a will there is a way

best regards

Manager
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 [#permalink] New post 27 Feb 2006, 22:26
My trial x be the number of apples the teacher has
k be the number of apples per student

x=13K+4
x=29K+9
x=37K+4


SMALLER NUMBER OF APPLESTEACHER CAN HAVE

x=4 MOD 13
x=9 MOD 23
x= 16 MOD 37
Since 13 ,29 ,37 Are coprime we can use the chinese remainder theorem
13x29x37
is it right ?

THANKS
_________________

when there is a will there is a way

best regards

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 [#permalink] New post 27 Feb 2006, 22:41
mand-y wrote:
My trial x be the number of apples the teacher has
k be the number of apples per student

x=13K+4
x=29K+9
x=37K+4


SMALLER NUMBER OF APPLESTEACHER CAN HAVE

x=4 MOD 13
x=9 MOD 23
x= 16 MOD 37
Since 13 ,29 ,37 Are coprime we can use the chinese remainder theorem
13x29x37
is it right ?

THANKS
how did u get x=9 MOD 23 and x= 16 MOD 37?
Manager
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Joined: 05 Oct 2005
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Re: remainder and mod [#permalink] New post 27 Feb 2006, 22:52
mand-y wrote:
hi all

I have heard about the mod and the remainder chinese theorem in some posts dealing with remainder I did not learn this at school
Can anyone help me with this exercise using the remainder chinese theorem so i can notice i did understood it . plz explain your working
THANKS

The teacher has some apples to distribute to her students. If she
gives all of the apples to the 13 students in her first class she will
have 4 left. If she gives all of the apples to the 29 students in her
second class she will have 9 left. If she gives all of the apples to
the 37 students in her third class she will have 16 left. Whichever
class she gives the apples to, she will give each student the same
number of apples. What is the smallest number of apples the teacher
can have?


x=9 MOD 23 sorry typo
corrected

x=9 MOD 29
_________________

when there is a will there is a way

best regards

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 [#permalink] New post 10 Mar 2006, 21:14
Mand-y, Answer is definitely not 13*29*37 since when the teacher distributes the apples equally to 13 students, 4 apples remain => the number of apples is not divisible by 13. But, I do not know how to answer this question. If answer choices were there, we would substitute and find out.
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Re: remainder and mod [#permalink] New post 11 Mar 2006, 15:23
mand-y wrote:
hi all

I have heard about the mod and the remainder chinese theorem in some posts dealing with remainder I did not learn this at school
Can anyone help me with this exercise using the remainder chinese theorem so i can notice i did understood it . plz explain your working
THANKS

The teacher has some apples to distribute to her students. If she
gives all of the apples to the 13 students in her first class she will
have 4 left. If she gives all of the apples to the 29 students in her
second class she will have 9 left. If she gives all of the apples to
the 37 students in her third class she will have 16 left. Whichever
class she gives the apples to, she will give each student the same
number of apples. What is the smallest number of apples the teacher
can have?



The answer is 3605 applying modular algebra, but I agree it would be easier just backsolving
Re: remainder and mod   [#permalink] 11 Mar 2006, 15:23
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