Latest TCS Aptitude Question SOLUTION: A number 12345678910111213141516...............3738394041424344 when divided by 45 leaves a remainder.... what is the remainder?

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A number 12345678910111213141516...............3738394041424344 when divided by 45 leaves a remainder.... what is the remainder?

Asked In TCS sruthi kaipa (11 years ago)

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Read Solution (8) :

nishant pandey  (11 years ago)

when a number is to be divided by 45 then it has to be get divided by 9 and 5
divisibility of 9 says that sum of number should get divided by 9
so,see the sequence of numbers carefully..applying formula for sum of n natural numbers:-n(n+1)/2,we get 990..n since 990 is divided by 9 hence ,remaining 5 is left to be checked n after seeing the units digit of number we get 4 as the ans.

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Rakesh Kumar  (11 years ago)

A number is divided by 45 means , it is divided by 5 as well as 9.

for divisiblity by 9, the sum of digits should be divided by 9 :
Sum of digits = 1+2+3+........+44
=990(it is divisible by 9)
For divisiblity by 5,the unit digit of number must be 0 or 5.
Here,Unit digit is 4.
so, when divided by 45 leaves the remainder 4.

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MayankKumar  (11 years ago)

my friend nishant u r consider all the number individual but
look the num carefully every digit is separated in addition
exmple=12=1+2=3 not 12
ater the concept of 1 to 44
how many 1...
2....
3...
4...
.
.
9....
&
get sum it is 270
which divisible by 9
but not with 5 so
last digit should have 0 ,5
then
replace the last 44 with 35(if we replace it with 40 sum is affected)
which not affect the sum
& divisible by 9 & 5 both so remainder is ....9 ans

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kck  (11 years ago)

answer :9
Explanation:
the sum of digits of above no. is 270...
as we know to divide a no. by 45 we must get 0 remainder if it is divided by 5 or 9..
a no is divisible by 5 if the no has either 5 or 0 at last
similarly the no is divisible by 9 if sum of digits of the no is divisible by 9
in this case 123456789101112...41424344 sum of digits of this no is 270 as 270 is not divisible by 9.so,we hav to make some arrangements.if we break no into two parts like:
1234567891011.......40414200+144
the sum of digits of first no is 261 which shows that the no is divisible by 9 and this no has zero at end so it is divisible by 45 as well.
the remainder will be equal to the remainder in 144 when we divide it by 45 i.e 9
hence answer is 9.

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kck  (11 years ago)

Let me simplify it:
we can write 1234567891011121314........4041424344 as
123456789101112......4041424335+9
now sum of d digits of the number 12345678910111213.....4041424335
is sum of digits is
1+2+3+4+5+6+7+8+9+1+0+1+1+1+2+3+.......4+3+3+5=270 which says that it is divisible by 9 again tis no. has 5 at the end hence it is divisible by 5 also that means 12345678910111213.....4041424335 is divisible by 45.
the last no which is 9 is remainder.
Note: Many of us hav taken sum of digits as:
1+2+3+4+5+6+7+8+9+10+11+12+13+14+15....+40+41+42+43+35=981 this also shows that
12345678910111213.....4041424335 is divisible by 9 and by 5(last digit =5) hence by 45 as well.
which also gives the same result

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Devidutta Mohanty  (9 years ago)

Correct me if I am wrong , people who are saying 9 is the answer dont you think 5 will divide the 9 also and the remainder will be 4.its like (a+b)/5 means a/5 + b/5.So in my opinion answer is 4.

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Amit Chawla  (11 years ago)

the number is not divisible by 5 so no chance of being divisible by 45....:)

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Saurabh Kumar Tripathi  (11 years ago)

Remainder is 0 !!
First of all understand the pattern, it is actually 1+2+3+...+9+(1+0)+(1+1)+(1+2)+...+(1+9)+(2+0)+(2+1)+....+(4+4) i.e. units' & tens' digit are separated.
Now add first 9 digis(0+1+2+...+9) => 45
As all these 9 digits appear in "units" place(from 11 to 19, from 21 to 29, from 31 to 39),thus => 45*4 = 180
Now there are 10 "1" at tens place(from 10 to 19) => 1*10 = 10
Similarily, 2*10 = 20
3*10 = 30
And 4*5 = 20(Note since there are only 5 "4" at tens' place)
Adding all these we get 180+10+20+30+20 = 270 which is divisible by 45..

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