Latest Elitmus Aptitude Question SOLUTION: find remainder of (9+9^1+9^2+.........+9^n)/6 n is multiple of 11. a) 2 b) 5 c) 3 d) 0

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find remainder of (9+9^1+9^2+.........+9^n)/6
n is multiple of 11.
a) 2
b) 5
c) 3
d) 0

Asked In Elitmus ranjeet singh (7 years ago)

Unsolved Read Solution (15)

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suvasree chatterjee  (7 years ago)

9 div 6=3 rem

3*11=33
33/6 =3 rem

3*22=66
66/6= 0rem

99/6= 3 rem

so 3 and 0 ill be rem( when even no. comes rem ill be 0 else 3)

Is this solution Helpfull? Yes (19) | No (5)  

Sibabrat Swain  (7 years ago)

1-IF YOU WILL TAKE COMMON 9 FROM THE EXPRESSION , IT WILL BE
9{1+1+9+9^2+....9^(N-1)}
2-IF WE WILL DIVIDE 6 FROM THE ABOVE EXPRESSION IT WILL GIVE 3 AS REMINDER .
9/6, REM = 3
3- 3 WILL BE THE ANSWER .
*DOESNT DEPEND ON VALUE OF N

Is this solution Helpfull? Yes (11) | No (6)  

Archit Agarwal  (7 years ago)

remainder will be 3
as no matter what power of 9 is...if it is divided by 6 , the remainder will be 3 only

Is this solution Helpfull? Yes (7) | No (9)  

Shubham Brat  (7 years ago)

answer will be 3. because sum of power of 9 upto even powers is divisible by 6
and upto odd powers it will give the remainder 3 everytime

Is this solution Helpfull? Yes (2) | No   

ashish  (7 years ago)

everyone is wrong here.
correct answer is 5.

9^1/6 = 3
9^2/6 = 1
likewise 9^odd/6 = 3
9^even/6 = 1

3*6+ 1*5 = 23/6 = rem = 5

Is this solution Helpfull? Yes (2) | No (4)  

PRIYANAR PERNI  (7 years ago)

=9/6+(9^1+9^2+....9^11*n)/6
=9/6+3/6
then =12/6=0

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

Anshul Nagi  (7 years ago)

It can be both 3 and 0 . If n=11 then its (9+ 3*11) /6 gives 0 remainder if n=22 then it becomes ( 9+ 3*22)/6 gives 3 as remainder

Is this solution Helpfull? Yes (1) | No   

Nitish Kumar Jha  (7 years ago)

Taking n as 11 and proceeding further, step wise
9^11 = 31381059609
9^10 = 3486784401
9^9 = 387420489
9^8 = 43046721
9^7 = 4782969
9^6 = 531441
9^5 = 59049
9^4 = 6561
9^3 = 729
9^2= 81
9^1 = 9
+ 9
-------------------
35303692063
--------------------

Now dividing these number by 6 we get remainder as 5.

So, the correct answe is b) 5

Is this solution Helpfull? Yes (1) | No (7)  

Vikash kumar  (7 years ago)

correct answer is 3.

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

pradeep  (7 years ago)

for odd multiples of 11 the answer is 3 and for even multiples of 11 ans is 0 so here the answer as per question is cant be determined as we dont know whether the power is even or odd multiple

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puja kumari  (7 years ago)

in 1 to 10 the odd no is 5
11 to 20 odd no. is 5
similarly 90 to 100 odd no is 5
so total no. is up to 100 is 50
so 50 *100=5000

Is this solution Helpfull? Yes | No (1)  

Vikash kumar  (7 years ago)

can not be determined bcz here 11 is multiple .because here we can take the value of n is even or odd .

Is this solution Helpfull? Yes | No (1)  

Nagmani Kumar  (7 years ago)

Use calculator Ans will be 3

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Vidhya Mukati  (6 years ago)

9+9^1+9^2...........+9^n=9+9(9^11-1)/9-1 formula to sum of gp series

9+9(9^11-1)/9-1 =9(1+9^11-1)/8

9*9^11/8

now we r taking 6 the is given in the question
=9*9^11/6*8
=3*9^11/16
=27*9^10/16
27/16=11 rem
9^10/16=10 rem
11+10=21/16=5


5 will be the answer

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superstar  (4 years ago)

If we divide numerator and denominator by 3 then we will get only 2 in denominator... which means only 0,1 can be remainder... so i think 0 should be the answer.

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