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Cool goIITian

Joined: 28 Apr 2008

Posts: 64

2 May 2008 12:30:13 IST

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Is the answer 23?

New kid on the Block

Joined: 2 May 2008

Posts: 20

2 May 2008 12:38:23 IST

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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

Hot goIITian

Joined: 24 Apr 2008

Posts: 163

2 May 2008 13:21:54 IST

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Zorro how are u saying its 23

James Bond

Hot goIITian

Joined: 14 Sep 2007

Posts: 188

2 May 2008 13:52:50 IST

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

Cool goIITian

Joined: 28 Apr 2008

Posts: 64

2 May 2008 13:59:40 IST

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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

Hot goIITian

Joined: 24 Apr 2008

Posts: 163

2 May 2008 14:00:55 IST

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u want me to give ans or let others try ???

Hot goIITian

Joined: 24 Apr 2008

Posts: 163

2 May 2008 14:04:49 IST

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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

Cool goIITian

Joined: 28 Apr 2008

Posts: 64

2 May 2008 14:16:12 IST

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no such values of a and b exists..

hence no solution.

I think soo..

what's the answer?????????

Hot goIITian

Joined: 24 Apr 2008

Posts: 163

2 May 2008 14:31:17 IST

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no solution exists
dont give up so soon
I took more than half an hour to figure out the ans

Hot goIITian

Joined: 24 Apr 2008

Posts: 163

2 May 2008 14:31:35 IST

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solution exists
dont give up so soon
I took more than half an hour to figure out the ans

Cool goIITian

Joined: 28 Apr 2008

Posts: 64

2 May 2008 14:35:58 IST

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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

Hot goIITian

Joined: 24 Apr 2008

Posts: 163

2 May 2008 14:47:22 IST

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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

New kid on the Block

Joined: 2 May 2008

Posts: 20

2 May 2008 16:05:26 IST

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min. (a+b) = 56

New kid on the Block

Joined: 2 May 2008

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2 May 2008 16:16:54 IST

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Given : a+11b=k(13) - (i)
a+13b=k'(11) - (ii)
and, (a,b) belongs to Natural no.'s
Proof : (a+11b)+2b=k'(11)
b=[k'(11)-k(13)]/2
Therefore, b(min.)=10 [because, b belongs to Natural no.)
Now, for a(min.)=46 eq. (i) & (ii) are satisfied
Hence, a+b(min.)=46+10=56

Hot goIITian

Joined: 24 Apr 2008

Posts: 163

2 May 2008 16:39:11 IST

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sorry kirpal
ur reasoning that b min is 10 is wrong

New kid on the Block

Joined: 2 May 2008

Posts: 20

2 May 2008 16:53:34 IST

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Acc. to u reasoning that b min is 10 is wrong. Could u pls. explain me how.