from section test

[Rohan]

There are three cities: A, B and C. Each of these cities is connected
with the other two cities by at least one direct road. If a traveller
wants to go from one city (origin) to another city (destination), she
can do so either by traversing a road connecting the two cities
directly, or by traversing two roads, the first connecting the origin
to the third city and the second connecting the third city to the
destination. In all there are 33 routes from A to B (including those
via C). Similarly, there are 23 routes from B to C (including those
via A). How many roads are there from A to C directly?

a) 6
b) 3
c) 5
d) 10
e) 12

[Shrinidhi]

@rohan
I tried to solve the problem,but I got a contradiction
Let the dierect routes from A to B, B to C,C to D be x,y,z resp.
Total num of routes from B to C= dierect routes(B to C)+indierect
routes(B-C-A).
therefore,
indierect routes= 33-x----------------->>>>>>>eq1
now, No of a-c-b=>>dierct routes A to C+ dierct routes C to B;
hence
33-x=y+z
33=x+y+z;
Similarly,
Total num of routes from B to C= dierect routes(B to C)+indierect
routes(b-a-c).
therefore,
indierect routes= 23-x----------------->>>>>>>eq2
now, No of b-a-c=>>dierct routes B to A+ dierct routes A to C;
hence
23-x=y+z
23=x+y+z;
The contradiction
where am i going wrong???

[JATIN GUPTA]

i got the ans as 12..Is it correct?

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Regards,
Suvrit Chadha

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[Rohan Aggarwal]

no the answer is 6

[Shrinidhi]

Solution please

On Aug 16, 3:32 pm, Rohan Aggarwal <jiit.ro...@gmail.com> wrote:
> no the answer is 6
>
>
>
> On Mon, Aug 16, 2010 at 3:45 PM, JATIN GUPTA <jatin....@gmail.com> wrote:
> > i got the ans as 12..Is it correct?
>

> >> simple-funda...@googlegroups.com<simple-fundas%2Bunsubscribe@goog legroups.com>

> >> For more options, visit this group at
> >>http://groups.google.co.in/group/simple-fundas?hl=en-GB
>
> >> Regards,
> >> Suvrit Chadha
>
> > --
> > Regards,
> > Jatin Gupta
>
> > --
> > You received this message because you are subscribed to the Google
> > Groups "Simple fundas" group.
> > To post to this group, send email to simple...@googlegroups.com
> > To unsubscribe from this group, send email to

> > simple-funda...@googlegroups.com<simple-fundas%2Bunsubscribe@goog legroups.com>

[devanshu singhal]

Answer: 6
Soln.
AB (Direct) : d1
BC (Direct) : d2
CA (Direct) : d3

Eqn1:
d1 + d2.d3 = 33
d2 + d1.d3 = 23

Substitute value of d3 from the options.Substituting 6, we get the other variables as integers.

regards
Devanshu