Latest TCS Aptitude Question SOLUTION: the first 44 positive integers are written in order to form the largest number N=12345678910111213..424344. what will be the he remainder when N is diveded by 45?

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the first 44 positive integers are written in order to form the largest number N=12345678910111213..424344. what will be the he remainder when N is diveded by 45?

Asked In TCS giri (11 years ago)

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indrajit hui  (11 years ago)

i am sorry..my prev ans was wrong..it will be like this
no will be div by 45 when it is divided y both 9 and 5
a no is div by 9 if sum of digits is div by 9
now sum of digits of given no is 270
so the no is div by 9
and since last digit is 4 when div by 5 it leaves rem 4
let us say numbers such as 9,54...
we see they are div by 9 but leaves rem 4 when div by 5..
so when div by 45 they leave rem 9
so req ans=9

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indrajit hui  (11 years ago)

no will be div by 45 when it is divided y both 9 and 5
a no is div by 9 if sum of digits is div by 9
now sum of digits of given no is 270
so the no is div by 9
and since last digit is 4 when div by 5 it leaves rem 4
so req rem=4

Is this solution Helpfull? Yes (5) | No (7)  

kiruba visvanath  (11 years ago)

i cant get it how 270 came

some one pls explain :(

Is this solution Helpfull? Yes (3) | No (1)  

vinay kumar  (11 years ago)

After adding the digits we get the no. divisible by 9 but it is not divisible by 45 as not divisible by 5.
To make it divisible by 5 while keeping it divisible by 9 also, subtract 9 from the no.The resultant no. will have 35 in place of 44.So, the resultant no. is divisible by 45. Hence the original no. leaves remainder 9 when divided by 45.

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vignesh  (8 years ago)

I want to give similar exampe for proper understanding, take 279
If u add 2+7+9=18 which is divisible by 9 ,
Now divided 279 by 5 ,u will get 4 as remainder ,
Now divide the 279 by 45, u will get 9 as remainder (6*45=270), so remainder 9.
Similarly, when the above number is divisible by 9 and leave remainder 4 then when it is divided by 45 it will give remainder as 9.

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pratap kumar sahoo  (8 years ago)

N=1234......414344
sum=270;
IF N divided by 45,it should divided by 9 & 5.
N is divisible by 9.

9/9=1&1/5=>rem=1
18/9=2&2/5=>rem=2
27/9=3&3/5=>rem=3
36/9=4&4/5=>rem=4
45/9=5&5/5=>rem=0
54/9=6&6/5=>rem=1
63/9=7&7/5=>rem=2
72/9=8&8/5=>rem=3
81/9=9&9/5=>rem=4
90/9=10&10/5=>rem=0
....so on..
so, rem=(1,2,3,4,0 & again repeated)
so rem is =4(according to option) (option is:4,9,14,18)

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semanti dey  (11 years ago)

how is it comming??plsssss xplain.

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snehil  (11 years ago)

4 will be ans

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diptangshu paul  (11 years ago)

the sum of all digits are 310
55+10+55+20+55+30+4+4+4+4+4+1+2+3+4=310
310/9= reminder 4
number - 4 = divsible by 9 nd 5
so reminder is 4

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dkn  (11 years ago)

Ans=0
when we sum up those integers the total =270 and it is divisible by 45.
Note: 1st 9 digits sum=45
then while summing 10 to 19 consider 10 as 1+0=1 and 1+9 as 10.so sum=55
similarly for others

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dkn  (11 years ago)

Sorry i hurriy calculated .
The sum =270
And if 9 and 5 divides N then 45 will divide it.
So 270 is divided by 9 .
And when w divide it by 5 N will leave 4 as reminder(as last digit is 4).
So ans=4

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devi vara prasad mudili  (8 years ago)

Hi friends can anyone explain this briefly ?

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vishwam  (4 years ago)

the sum of n numbers= n(n+1)/2 =44(45)/2=990
990 divisible by 9
also 45 divisible by 9
hence denominator is 5... by the option 4 is only remainder of 5...therefore 4 is answer

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