In a maThematic there are 1,2,3,....9 cities  and each number corresponds to a city. Now an airflight route is to be established between two cities such that the numeral formed is divisible by 3. (eg. if 1 and 2 are connected then it satisfies the condition). Find out the number of cities which are connected to city 8, either directly or indirectly.

5 cities
  • Interview Candidate
  • 89
  • 2162

Showing Answers 1 - 75 of 89 Answers

sankar

  • Aug 10th, 2005
 

3rd anal

  Was this answer useful?  Yes

Srujana

  • Aug 19th, 2005
 

ans by rohit looks wrong... 
wat bout the combinations like:1-2-8,2-7-8,3-6-8,3-9-8 etc???

  Was this answer useful?  Yes

Vijay

  • Sep 3rd, 2005
 

Hi srujana, 
The combinations you have specified are not divisible by 3. so they are not considered. so the answer 5 is correct.  

  Was this answer useful?  Yes

antolo

  • Sep 6th, 2005
 

1-8,4-8,7-8 
2-1-8,5-4-8 
The divisiblity of 3 will be only for 2 no. and not three. 
so according to the above routes, 1,4,7,2,5 are connected either directly or indirectly. 

  Was this answer useful?  Yes

Julius Thomas

  • Sep 10th, 2005
 

All the other 8 cities r connected either directly or indirectly. 8-1,8-4,8,7,8-1-3,8-2-5, 8-5-2,9-1-7,8-1-6

  Was this answer useful?  Yes

shiv

  • Sep 13th, 2005
 

there are 9 cities interlinked directly or indirectly1-84-87-82-1-82-4-82-7-85-4-85-1-85-7-8

  Was this answer useful?  Yes

Prasanna

  • Sep 27th, 2005
 

The Possible routes are:

18 - 81
28 - 82
38 - 83
48 - 84
58 - 85
68 - 86
78 - 87
98 - 89

With the condition, 5 routes are possible


 

  Was this answer useful?  Yes

swathi

  • Sep 29th, 2005
 

8 cities

  Was this answer useful?  Yes

anil

  • Oct 4th, 2005
 

I feel the correct answer is 5.

Direct Linkages:

1-8, 4-8, 7-8  = cities 1,4,7

Indirect Linkages

2-1-8, 5-1-8, 2-4-8, 5-4-8, 2-7-8, 5-7-8 = 2 more cities... 2,5

Finally the cities that may be linked are 1,4,7 directly and 2,5 indirectly...thank you

  Was this answer useful?  Yes

Devanathan.J

  • Oct 15th, 2005
 

All the 8 cities connected with the city named as 8

1 ---->directly

2----->indirectly by 5(5 is also included here).

3----->indirectly by 4(4 is included here).

6------>indirectly come by 1.

7------>directly.

8------>is the city

9------>indirectly come by 1or4or7 etc.

final conclusion.

All the 8cities other than the city named "8" is connected with 8.

  Was this answer useful?  Yes

raju kumar

  • Feb 28th, 2006
 

7 cities are connected with city 8 directly n indirectly.directly connect by - 1-8, 4-8, 7-8, i.e. 1, 4, 7indirectly connected by- 1-3-8, 3-4-8, 2-5-8, 1-6-8 i.e. 2,3,5,6

  Was this answer useful?  Yes

Baskar

  • Mar 24th, 2006
 

combinations are

1000000003, 1000000030 ....... 1300000000  = 9
2000000002, 2000000020 ........2200000000  = 9
3000000001, 3000000010 ........3100000000  = 9
4000000000  = 1

total 28 ten digit numbers that have sum 4

answer is 28

  Was this answer useful?  Yes

yusufqtv

  • Jun 11th, 2006
 

Anil,

Ur answer for Direct Linkage is Ok ie 1-8, 4-8, 7-8 corresponds to 3 cities

In indirect linkage u have showed that only first two cities should be divisible by 3, but to my opinion it is the all numerals used in route.

So according to me in indirect linkage it should be like this:

2-5-8

3-4-8

5-2-8

6-7-8

9-1-8

So the total cities linked directly or indirectly is 1,2,3,4,5,6,7,9= 8 cities.

Let me know if there is any doubt

yusuf_qtv@yahoo.com

i

  Was this answer useful?  Yes

crazysantu

  • Jul 6th, 2006
 

hi prasanna,

urs is wrong.

2-1-1 can be arranged only in 2*(9c2) ways but not 3*(9c2) ways.=72

and 1-1-1-1 can be arranged in1*9c3 ways.=84.

so total,

1+18+18+72+84=193 ways.

  Was this answer useful?  Yes

TARUN BANSAL

  • Jul 16th, 2006
 

we have nine cities and we make an undirected graph and from graph it is clear that 3,6and9 make isolated graph while 1,2,4,5,7,8make connected graph so we can easily deduce that 8 is connected directly to 1,4,7 and indirectly to 2 and 5

  Was this answer useful?  Yes

vamshi

  • Jul 25th, 2006
 

i didn't get the above answers . how can u justify tht the answer is 5.

The possible routes may be 1-2-3-4-8 , 1-6-8 , 1-9-8 , 1-2-3-4-5-6-7-8 , 1-8 etc., and many more also.so can anyone justify the answer clearly.

  Was this answer useful?  Yes

Divya

  • Aug 19th, 2006
 

My Ans is:

1-8

4-8

7-8

1-3-8,3-1-8

2-5-8,5-2-8

1-6-8,6-1-8

3-4-8,4-3-8

  Was this answer useful?  Yes

ipn_jaspirant

  • Jul 16th, 2007
 

10 numbers means total combinations which means 10 factorial ie..
1*2*3*4*5*6*7*8*9*10=3628800.10 combinations of 10 numbers=3628800*10=36288000.total combinations with sum of digits =4 means  combinations ie..1+1+1+1,1+2+1,2+1+1,1+1+2,3+1,1+3,4.1st 4 ie.. 4*10digits =40 combinations.2nd (1+2+1,2+1+1,1+1+2)3 combinations of 3 digits 30%*3628800*3=3265920.3rd 1 Combination of 4 numbers(1+1+1+1)ie..1*40%*3628800=1451520. 4th 2 combinations2 numbers(3+1,1+3) ie.. 2* 20%*3628800=1451520.Total=1st+2nd+3rd+4th ie.. 40+3265920+1451520+1451520=
'6169000'

  Was this answer useful?  Yes

dinesha.cit

  • May 23rd, 2008
 

I feel the given answer 5 is rght since

direct connection b/w two cities thru 8 that the result was divisible by 3 
                                  1+8=9
                                  4+8=12
                                  7+8=15                 

no of possibilities=3    
         
Indirect connection thru 8 that the result was divisible by 3 
                                  7+8+3=18
                                  4+8+9=21
no. of possibilities=2

                  Total possibilities=5

  Was this answer useful?  Yes

Bhoomika sharma

  • Dec 3rd, 2008
 

There are 6 combinations possible according to me:

a :2 c: 1 e:1

a:1 c:1 e:2

a:2 c:0 e:2

a:3 c:0 e: 1

a:3 c:1 e:0

a:1 c:0 e:1
because as u can see b=0 as b gives all gifts to a nd thus total gifts with a are 8 ,if he does not give and with e as 7 c has 1 as it gives 3 to e tus above

PLEASE RESPOND IF ANSWER IS WRONG(If u feel)

  Was this answer useful?  Yes

kandukurisunil2005

  • Jun 8th, 2009
 

The Answer is : All the remaining Cities are Interlinked directly or indirectly. There are 8 Remaining Cities.

We should not go for Permutations and Combinations..

Citiy 1 is linked Directly (1-8)

City 2 is linked indirectly (2-5-8)

City 3 is linked indirectly (3-1-8)

City 4 is linked directly (4-8)

City 5 is linked indirectly (5-2-8)

City 6 is linked indirectly (6-1-8) or (6-4-8)

City 7 is linked directly (7-8)

City 9 is linked indirectly (9-4-8) or (9-1-8) or (9-5-2-8) etc

so All the other 8 citier are interlinked with 8.

so the Answer is 8 Cities.

jkuppal26

  • Dec 4th, 2009
 

Left most digit Rest of the 9 digits
         1              three 1's  rest 0's                         9c3=84
         1              one 2 and one 1, rest 0's           9c1 * 8c1 * 2 =144
         1              one 3 , rest 0's                             9c1= 9
         2              two 1's, rest 0's                            9c2= 36
         2              one 2 rest 0's                                9c1= 9
         3              one 1  rest 0's                               9c1=9
         4              all zeros                                         1

adding them, you get 292

      

  Was this answer useful?  Yes

hirenshirke

  • Dec 6th, 2009
 

See there are 8 cities and obviously 8 cannot be included so in any case the max no. of combos are 7.  Now since there are 3 direct routes satisfying that it is divisible by 3, these are 1-8, 7-8 and 4-8.  Apart from that, every city is indirectly linked as given 8-2-5 (which gives both 2 and 5 linkages. 8-4-3 which gives for 3 and 8-1-6...for 6
Thus if you count properly, there are in all those 7 cities not 5 and if its wrong then the way in which the question is potrayed in wrong I feel because if you are told to figure out by say on direct and indieract linkages then my answer is correct and for those who feel that 5 is the correct answer, post why are you leaving combos with 3 and six.

  Was this answer useful?  Yes

keermal

  • Dec 16th, 2009
 

The answer is 7
8+1
8+4
8+7
8+4+3
8+6+1
8+3+1
8+5+2
and only combinations in which 8 is one of the cities should be taken and I think it is not permutations.

  Was this answer useful?  Yes

shivanand_jha

  • Oct 9th, 2010
 

Here we just have to check the no. divisible by 2. i.e. if ab is divisible then ba is also divisible.
Now, checking for 8-
18
28
38
48
58
68
78
98.

only 18,48,78 are divisible by 3.
hence answer is 3 cities

  Was this answer useful?  Yes

vijay_1437143

  • Dec 22nd, 2010
 

Possible combinations
4    0   no of ways to arrange =1
3    1   no of ways to arrange =2*9
2    2   no of ways to arrange =2*9
2     1   1   no of ways to arrange =3*9*8
1     1   1    1   no of ways to arrange =4*9*8*7              remaining digits are zero's

Total no's are:  2269

  Was this answer useful?  Yes

Give your answer:

If you think the above answer is not correct, Please select a reason and add your answer below.

 

Related Answered Questions

 

Related Open Questions