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If a six digit number abcdef is multiplied with 6,the resulting number is defabc.Find c+f?

#Mathematics #Algebra

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9 Answers

591

Akshay Ginodia ·2013-02-21 23:39:30

May be my solution is a bit long but still...

Divide the number abcdef into 2 parts...abc and def..
Let abc=x
def=y
So the number abcdef can be written as 1000x+y and defabc =1000y+x
so ... 6(1000x+y)=(1000y+x)
from here we get..
6000x +6y = 1000y +x
so 5999x=994y
y=5999x/994
=5964x+35x/994
=6x+35x/994
=6x+5x/142

since y is integer so 5x/142 must also be an integer..
Least value of x for which it is an integer=142
so x=142
which gives y=857
hence the unique number is 142857
thus c+f=9 :)

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Akshay Ginodia actually this qstn ws probably asked in IMO and someone had asked me this a couple of weeks ago..so i had done it then..thats y it took me so little time today :P
Upvote·0· Reply ·2013-02-21 23:41:13
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79

Tanumoy Bar ·2013-02-21 23:23:13

142857

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591

Akshay Ginodia ·2013-02-21 23:26:36

is d answer 9??

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1057

Ketan Chandak ·2013-02-21 23:28:21

yeah...answer is 9....solution?

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79

Tanumoy Bar ·2013-02-21 23:30:44

Is this the number 142857???

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383

Soumyabrata Mondal ·2013-02-21 23:31:20

MATH OLYMPIAD IN TAIWAN (IMSO) ka question hain....

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383

Soumyabrata Mondal ·2013-02-21 23:32:41

solution is available @

http://mathforum.org/library/drmath/view/53296.html

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1057

Ketan Chandak ·2013-02-21 23:33:14

this is the number....you can check that for yourself....i need the approach to do such problems.

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1057

Ketan Chandak ·2013-02-21 23:34:39

thanks banda! :P

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Soumyabrata Mondal welcum chanddu :P
Upvote·0· Reply ·2013-02-21 23:36:05
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