Latest TCS Aptitude Question SOLUTION: find the remainder when 32^33^34 is divided by 11 ? a)5 b)10 c)4 d)1

• Placement Papers
• /
• TCS
• /
• Numerical Ability
• /
• Permutation and Combination

TCS Question Papers: TCS Interview Experience(90) TCS Company Profile

(#M40022335) TCS Numerical Ability question Keep an EYE

find the remainder when 32^33^34 is divided by 11 ?
a)5
b)10
c)4
d)1

Asked In TCS Shreyansh Jain (10 years ago)

Unsolved Read Solution (16)

Is this Puzzle helpful?   (54)   (21) Submit Your Solution Permutation and Combination

Read Solution (16) :

Avisek  (10 years ago)

as i have explained earlier we can use remainder theorem when consecutive no. are there...so here we cosider it as 32*33*34 but as 33 divisible its not required so 32*34 so taking -ve and +ve remainder i.e. (-1)*(1) = -1 now the remainder is
11-1 = 10.(bcoz when the remainder is -ve we subtract it from no. dividing) so ans is 10.

Is this solution Helpfull? Yes (82) | No (30)  

sameer singh  (10 years ago)

32^33=(-1)^33=(-1)
and (-1)^34=1
so ans is 1

Is this solution Helpfull? Yes (27) | No (42)  

Shreyansh Jain  (10 years ago)

is there any method to solve these type of questions when powers are not consecutive.?

Is this solution Helpfull? Yes (15) | No (10)  

VIKAS SINGH  (10 years ago)

32^33^34 now 33^34 can be written in form (10k+9)(coz unit digit iz 9)
so 32^(10k+9)/11..remainder=(-1)^(10k+9)=mod(-1)
so remainder will be 10.
ans b)10.

Is this solution Helpfull? Yes (12) | No (22)  

cippy agarwal  (8 years ago)

32/11 = 10
32^2 /11 = 1
32^3 /11 = 10

33^34 is odd number
when 32^(oddnumber) is divided by 11 remainder is 10


Answer is 10

Is this solution Helpfull? Yes (6) | No   

LAXMI DURAI  (10 years ago)

@Mr.AVISEK- plz explain find the remainder when 33^34^35 divided by 7

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

Joyprakash Khanra  (8 years ago)

lets 32^33=32*32*32*....33th time.
y=32^33^34=(32*32*32*....33th time.)*(32*32*32*....33th time.)........34times.
so,y=32*something.
y/11 remainder 10
so finally remainder will 10.

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

Shivali Raghav  (8 years ago)

Look for the cycle..!
33^34 is going to give an odd number since the unit digit will be 9...
NOW,32^1 when divided by 11 gives remainder 10..
32^2 when divided by 11 gives remainder 1..
32^3 when divided by 11 gives remainder 10..
So this means if 32^odd,we'll get remainder 10..!

Is this solution Helpfull? Yes (4) | No   

Saloni Singh  (10 years ago)

@vikas can u plz xplain y n where to use this kinda fundas??? :- {(10k+9)(coz unit digit iz 9)}
and ny1 plz help me with the soln of 50^56^52 wen divided by 11 wil gv a remainder of?? n plz xplain in detail as m helpless in solving qns wid powerr based on remainder theorem.

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

prakash kumar  (10 years ago)

10 is correct answer

Is this solution Helpfull? Yes (2) | No (14)  

Ritesh  (10 years ago)

10 z d right answer

Is this solution Helpfull? Yes (2) | No (5)  

Deep  (9 years ago)

@SALONI SINGH
for 50^56^52 /11 ans will be ...5

Is this solution Helpfull? Yes (2) | No   

munna  (8 years ago)

32^33=last two digits 92, then 92^34=last two digits 21, than 21/11=1-10/11
so here remainder is 10

Is this solution Helpfull? Yes | No   

RM ARUNACHALAM  (4 years ago)

If the question is R(32^33^34/11)=?

32^33^34≡(33−1)^33^34≡(−1)^33^34≡(−1)≡(11−1)≡10

Is this solution Helpfull? Yes | No   

venkatrao  (4 years ago)

answer is 10

Is this solution Helpfull? Yes | No   

Sasi  (4 years ago)

(32*32*......33 times)*(32*32*......33 times)*.........................*34 times
32%11 is 10. (10*10)%11 is 1. so, in first (32*32*......33 times), 10 is remainder 33 times
==> 1 is remainder 12 times and 10 is remainder one time
==> 10 is remainder 1 time
==> 34 times the expression (32*32*......33 times) means 34 times 10
==> 17 times 1 i.e., 1*1*1..........17 times
==> the remainder will be 1

Is this solution Helpfull? Yes | No   

Please Login to Read Solution.