Latest Elitmus Aptitude Question SOLUTION: Remainder when 50^56^52 divided by 11

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Remainder when 50^56^52 divided by 11

Asked In Elitmus Amisha Agarwal (10 years ago)

Unsolved Read Solution (17)

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VISHAL JAIN  (10 years ago)

50^56^52 mod 11
56^52 mod 10
6^52 mod 10
-
10=2*5
6^52 mod 2=0
6^52 mod 5=1
2a=5b+1
remainder= 6
-
50^6 mod 11
6^6 mod 11
36^3 mod 11
27 mod 11 = 5 ans

Is this solution Helpfull? Yes (22) | No (9)  

Debabrata Nayak  (10 years ago)

ans:3
sol:50^56^52=50^2912
Rem=50^2912/11=>(5*10)^2912/11
=>5^2912*10^2912/11
=>3*1/11=3(rem) [since 5^2912 leaves rem 3 and 10^2912 leaves a rem 1 ]

Is this solution Helpfull? Yes (10) | No (9)  

hp maity  (10 years ago)

50^56^52=(44+6)^56^52
just take the following
=6^56
=36^28
=(33+3)^28
=3^4*7
=81^7
=(77+4)^7
4^7

having reminder 5
am i ri8

Is this solution Helpfull? Yes (9) | No (5)  

ARPIT SAXENA  (10 years ago)

ans=
(55-5)^56^52/11
=5^56^52/11
=5^2912/11
=5/11
=5 remainder

Is this solution Helpfull? Yes (7) | No (3)  

anirduh  (10 years ago)

THE ans IS 4
USE REMAINDER THEOREM DIRECTLY OR NEGATIVE REMAINDER THEOREM MAKES IT FURTHUR EASY
SIMPLE ONE
50*56*52/11 -R->(6)(1)(8)/11=48/11====4 ANS
NEGATIVE REMAINDER
(-5)(1)(-3)/11==15/11===4 ANS

Is this solution Helpfull? Yes (7) | No (6)  

pankaj prasad gupta  (10 years ago)

50^56^52/11=50^(55+1)^52/11
=50^1^52/11=50^1/11=50/11=6ans

Is this solution Helpfull? Yes (5) | No (13)  

chandel kumar  (10 years ago)

we can write 56^52 as (55+1)^52
here 55 is divisible by 11 but the problem is 1 so
1^52 = 1 therefore
any power of 50 will end with 1 as 50^...................1
now we can write 50^...1 as (44+6)^...1 here 44 is divisible by 11 and the remaining part is 6^.....1
now if u see
6^1=6
6^2=36
6^3=216
6^4=1296
here any power of 6 is ending with 6
so the unit digit of 6^.....1 will also be 6 and all the numbers is divisible by 11 and 6 is remain as extra which is not further divisible so the remainder is 6

Is this solution Helpfull? Yes (3) | No (6)  

soumik ghosh  (10 years ago)

50/11=6
now, euler of 11 is 10.thus dividing power of 50 by 10 we get 6 as remainder
thus 6^6/11=6 . 6 is the ans.

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

komal pandhariwal  (10 years ago)

REM (50*56*52/11)= Rem ((44+6)(55+1)(44+8)/11) =Rem (6*!*8/11)=4

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

Shantanu Mukhopadhyay  (10 years ago)

3
[50^56^52/11]=[6^(56*52)/11]=[6^2842/11]
as 11 is prime and 6,11 are co prime. [6^10n/11]=1
so
[6^2/11] matters
or [36/11]=3

Is this solution Helpfull? Yes | No (8)  

Saurabh  (10 years ago)

Ans is 3.
50 to the power anything will result in the end digits of ...250000...... .
Now, if no of 0s are even, then the rem will always be 3.
Clearly, 56^52 is even no., thus the ans is 3.

Is this solution Helpfull? Yes | No (3)  

Sourav Chandra  (10 years ago)

answer is 1.
{(50)^56^52}/11={(6)^56^52}/11={(6^4)14^52}/11={(-1)14^52}/11=1/11=1
thus remainder is 1.

Is this solution Helpfull? Yes | No (3)  

Mani kandan  (10 years ago)

Ans is 6.
where phi(11)=(1-1/11)*11=10
=> So 51^52 is to be written in the form of 10k + a.
Now unit digit of 56^52 = 6 => 56^52 = 10k + 6.
=> 50^56^52 = 5010k + 6 = 506mod11 = 6

Is this solution Helpfull? Yes | No (4)  

ASHISH MUKHERJEE  (9 years ago)

50^56^52 /11 = remainder 3 .

Is this solution Helpfull? Yes | No (4)  

Vikash kumar  (8 years ago)

5 is the correct answer.

Is this solution Helpfull? Yes | No   

sweety  (7 years ago)

5652 = 10k + 6
=> 5010k + 6 = 506mod11 = 56mod11 = 5mod11

Is this solution Helpfull? Yes | No   

steffie  (7 years ago)

We need to find out Rem [50^56^52 / 11] = Rem [6^56^52 /11]

Now, by Fermat's theorem, which states Rem [a^(p-1)/p] = 1, we know
Rem [6^10 /11] = 1
=> Rem [6^10k / 11] = 1

The number given to us is 6^56^52
Let us find out Rem[Power / Cyclicity] t0 find out if it 6^(10k +1) or 6^(10k +2). We can just look at it and say that it is not 6^10k

Rem [56^52 / 10] = 6
=> The number is of the format 6^(10k + 6)

Now, we need to calculate Rem [6^56^52 /11]
= Rem [ 6^(10k + 6) / 11]
= Rem [6^6*6^10k / 11]
= Rem[216^2/11] * Rem [6^10k / 11]
= Rem [7^2/11] * 1

= Rem [49/11]

= 5

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