Latest Elitmus Aptitude Question SOLUTION: 9^1+9^2+9^3+.........+9^n when divide by 6 what will be the reminder. n should be multiple of 11 ? 1)0 2)1 3)3 4) Can't determine

• Placement Papers
• /
• Elitmus
• /
• Numerical Ability
• /
• Number System

Elitmus Question Papers:

(#M40037441) ELITMUS Numerical Ability question Reminder Theorem Keep an EYE

9^1+9^2+9^3+.........+9^n when divide by 6 what will be the reminder. n should be multiple of 11 ?

1)0
2)1
3)3
4) Can't determine

Asked In Elitmus Radhakanta Ghosh (10 years ago)

Unsolved Read Solution (13)

Is this Puzzle helpful?   (7)   (4) Submit Your Solution Number System

Read Solution (13) :

Saraswathy  (10 years ago)

9^1 mod 6 = 3
9^2 mod 6 = 3
9^3 mod 6 = 3
So for all the powers of 9, the remainder is same . i.e. 3 only....
So 3+3+3+3... 3 mod 6
If n=11, 11(3) = 33 mod 6 = 3
If n=22, 22(3) = 66 mod 6 = 0
If n=33, 33(3) = 99 mod 6 = 3
So for all odd multiples of 11, i.e. 1*11, 3*11, 5*11, etc, the remainder ll be 3...
For all even multiples of 11, the remainder ll be 0...
Hence we can't determine without knowing the exact value of "n"...

Ans : 4) Can't determine

Is this solution Helpfull? Yes (87) | No (5)  

Amit kumar jha  (10 years ago)

9^1+9^2+9^3+.........+9^n/6
3^1+3^2+3^3+...........+3^n/6 (According to remainder theory) a/b= (a-b)/b
take two term
(3^1+3^2)+(3^3+3^4)+..........+(3) /6 ( because n multilpe of 11 so if u take two term 1 is left here)
12/6 +78/6 +............+3/6
0+0+0+.............+3
=3
Ans should be 3

Is this solution Helpfull? Yes (12) | No (18)  

Anita  (10 years ago)

In any case,
when n is add.. remainder is 3.
when n is even.. remainder is 0.

Is this solution Helpfull? Yes (10) | No   

saira fatma  (9 years ago)

ANSWER WILL BE 3
BECAUSE
on dividing 9/6=3(remainder)
final series will be
9^1+9^2+9^3..........9^n/6
will givw
=3^1+3^2+3^3...3^n
let n=11
=3+9+27+81+.......3^11/6
on adding even terms and dividing by 6 we are left with final odd term 3^11 now
=3^11/6=(9^5).3/6
=(3^5).3/6
=243.3/6
=3.3/6
=9/6
=3 ans

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

nilanjan das  (9 years ago)

(9^1+9^2)/6 the remender is 0.(9^3+9^4)/6 remender is 0.if we take n=11 thn remender is 3 bt if we take n=22 remender is 0.so the anwer shd be d) Can't determine.

Is this solution Helpfull? Yes (2) | No   

ReshmaManu  (9 years ago)

@Saraswathy
your's answer is correct but u did mistaken in 2nd line that is......
9^2 mod 6=0 plz correct it.....

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

Vaishali Gupta  (10 years ago)

2nd option is 2

Is this solution Helpfull? Yes | No (4)  

sunil kumar banjara  (10 years ago)

question was
9^1+9^2+.....9^n is divisible by 6 nd 6 is multiple of 11
answer is first option
1)o.

Is this solution Helpfull? Yes | No (6)  

sunil kumar banjara  (10 years ago)

question was
9^1+9^2+.....9^n is divisible by 6 nd "n" is multiple of 11
answer is first option
1)o.
they had asked for the value of n , not for the reminder

Is this solution Helpfull? Yes | No (3)  

saira fatma  (10 years ago)

ANS:1)0because 9^1+9^2+9^3..........+9^n/6=3^1+3^2+3^3+3^4+..........3^n/6
where n is a multiple of 11.let it be 11 for demonstration...
now,on solving powers:
=3+9+27+81..........3^11/6
on adding odd terms starting from the first and 3we will get apattern as:
=30+90+............3^11/6=0

Is this solution Helpfull? Yes | No (3)  

abhinav srivastava  (9 years ago)

what does 2^(n-1)gives?

Is this solution Helpfull? Yes | No   

omsharan sharma  (9 years ago)

As we know that last digit of odd power of 9 is 9 and last digit of even power of 9 is 1. from 1 to 11 FIVE(2,4,6,8,10) is even number i.e. last digit (1,1,1,1,1).
and SIX(1,3,5,7,9,11) is odd power i.e. last digit(9,9,9,9,9,9). mean that last two digit of this sum 9^1+9^2+9^3+.........+9^n will be (54+5)=59 and last digit
will be 9 . when we will divide this sum by 6 ,reminder will be get 3 (9/6)

Is this solution Helpfull? Yes | No   

Ehtesham  (9 years ago)

n=11k;
so if 11k is evn nuber then reainder =0;
because 3*22%6=0
3*44%6=0

but if n=11k is odd .eg:11,33,55 etc then
3*11%6=3

so ans will be (d)

Is this solution Helpfull? Yes | No   

Please Login to Read Solution.