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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: find min a + b such that a+11b and a+13b are multiples of 13 and 11 resp. a,b>0
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[Post New]2 May 2008 12:09:09 IST
    Subject: find min a + b such that a+11b and a+13b are multiples of 13 and 11 resp. a,b>0
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celestine (76)

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find min a + b such that a+11b and a+13b are multiples of 13 and 11 resp. a,b>0
    
[Post New]2 May 2008 12:30:13 IST
    Subject: find min a + b such that a+11b and a+13b are multiples of 13 and 11 resp. a,b>0
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zorro (106)

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Is the answer 23?
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[Post New]2 May 2008 12:38:23 IST
    Subject: Re:find min a + b such that a+11b and a+13b are multiples of 13 and 11 resp. a,b>0
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kirpal_06391 (0)

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No I'm also getting 7.


a+11b = k(13)


a+13b= k'(11)


(a+11b) + 2b =k'(11)


b = k'(11) - k(13) (but b>0)  => b = 9/2 and therefore, a = 5/2


Hence a + b = 7
Kirpal Singh
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[Post New]2 May 2008 13:21:54 IST
    Subject: find min a + b such that a+11b and a+13b are multiples of 13 and 11 resp. a,b>0
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celestine (76)

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Zorro how are u saying its 23
IM NO BABY
I HAVE THE SEVENTH SENSE
NONSENSE!!!!!!!!!!!
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[Post New]2 May 2008 13:52:50 IST
    Subject: Re:find min a + b such that a+11b and a+13b are multiples of 13 and 11 resp. a,b>0
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12121212 (338)

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@ KIRPAL.....plz make a correction....

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[Post New]2 May 2008 13:59:40 IST
    Subject: find min a + b such that a+11b and a+13b are multiples of 13 and 11 resp. a,b>0
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zorro (106)

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let a + b = y ........(1)



now,



a + 11b = 13x............(2)



and a + 13b = 11z ..............(3)



where x and z r integeres >=1



sovle above 3 equations to get



y = 78x - 55z

therefore



a + b = 78x - 55z



for min value x=z=1



so, min(a+b ) = 23

 
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[Post New]2 May 2008 14:00:55 IST
    Subject: find min a + b such that a+11b and a+13b are multiples of 13 and 11 resp. a,b>0
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celestine (76)

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u want me to give ans or let others try ???
IM NO BABY
I HAVE THE SEVENTH SENSE
NONSENSE!!!!!!!!!!!
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[Post New]2 May 2008 14:04:49 IST
    Subject: find min a + b such that a+11b and a+13b are multiples of 13 and 11 resp. a,b>0
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celestine (76)

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gud try Zorro
But I forgot to mention that a,b are natural nos
if u put a+b as 23 ull get a,b asfractions
TRY NOW
IM NO BABY
I HAVE THE SEVENTH SENSE
NONSENSE!!!!!!!!!!!
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[Post New]2 May 2008 14:16:12 IST
    Subject: find min a + b such that a+11b and a+13b are multiples of 13 and 11 resp. a,b>0
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zorro (106)

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no such values of a and b exists..



hence no solution.


I think soo..


what's the answer?????????
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[Post New]2 May 2008 14:31:17 IST
    Subject: find min a + b such that a+11b and a+13b are multiples of 13 and 11 resp. a,b>0
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celestine (76)

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no solution exists
dont give up so soon
I took more than half an hour to figure out the ans
IM NO BABY
I HAVE THE SEVENTH SENSE
NONSENSE!!!!!!!!!!!
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[Post New]2 May 2008 14:31:35 IST
    Subject: find min a + b such that a+11b and a+13b are multiples of 13 and 11 resp. a,b>0
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celestine (76)

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solution exists
dont give up so soon
I took more than half an hour to figure out the ans
IM NO BABY
I HAVE THE SEVENTH SENSE
NONSENSE!!!!!!!!!!!
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[Post New]2 May 2008 14:35:58 IST
    Subject: find min a + b such that a+11b and a+13b are multiples of 13 and 11 resp. a,b>0
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zorro (106)

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in equation a + b = 78x - 55z


substitute diff values of x and z and see for which values a and b are natural nos.

and I m not having so much patience to solve like this..
so, will not do this..

hehe
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[Post New]2 May 2008 14:47:22 IST
    Subject: find min a + b such that a+11b and a+13b are multiples of 13 and 11 resp. a,b>0
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celestine (76)

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No Zorro I would say your method of approch is wrong
There is a more intelligent way of solving this
HE HE
IM NO BABY
I HAVE THE SEVENTH SENSE
NONSENSE!!!!!!!!!!!
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[Post New]2 May 2008 16:05:26 IST
    Subject: Re:find min a + b such that a+11b and a+13b are multiples of 13 and 11 resp. a,b>0
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kirpal_06391 (0)

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min. (a+b) = 56
Kirpal Singh
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[Post New]2 May 2008 16:16:54 IST
    Subject: find min a + b such that a+11b and a+13b are multiples of 13 and 11 resp. a,b>0
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