Latest Elitmus Aptitude Question SOLUTION: Find the reminder when 50^51^52 is divided with 11

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Find the reminder when 50^51^52 is divided with 11

Asked In Elitmus shuvaranjan dash (10 years ago)

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Saraswathy  (10 years ago)

use reminder theorem. here it is given as 50^51^52. but consider it as 50*51*52 so when it is divided by 11 it gives -ve remainder of (-5)*(-4)*(-3) = 20*(-3) again use remainder theorem so now it becomes (-2)*(-3) = 6. so the ans is 6. But note that it is valid only in case of consecutive no. i.e 50,51,52 or 34,35,36 but not in case when it is given 30^72^87 etc

Is this solution Helpfull? Yes (63) | No (17)  

shilpi  (10 years ago)

6 is the reminder

Is this solution Helpfull? Yes (18) | No (5)  

saurabh agarwal  (10 years ago)

3 is the remainder.
50^2652
(44+6)^2652/11
6^2652/11
36^1326/11
(33+3)^1326/11
3^1326/11
.........
........
........
-8/11
3

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

Harish yadav  (9 years ago)

50^51^52/11 can be written as 50^N/11=6^N/11(As remainder is 6 when 50 is divided by 11).
=Remainder
6^1/11=6
6^2/11=3
6^3/11=7
6^4/11=9
6^5/11=8
6^6/11=4
6^7/11=2
6^8/11=1
i.e in cycle of 8 we get 1 as a remainder.
Again,
N/8=51^52/8=3^52/8
again find the remainder as above way
3^1/8=3
3^2/8=1
cycle is 2
i.e 52/2=0 remainder means we take last term of a cycle i.e:3^2/8=1.
so here the remainder is 1.
Now this(remainder 1) means take the 1st term of the cycle 6 i.e;6^1/11=6. as a final remainder.
therefore 50^51^52/11=6(Answer)

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AVIJIT  (10 years ago)

: Fermat little theorem says, a^p−1/p remainder is 1.
ie., 30^10 or 8^10when divided by 11 remainder is 1.
The unit digit of 51^52 is 1 (using cyclicity of unit digits) Click here

So 51^52 = 10K + 1
50^(10K+1) %11=(50^10)K.50^1%11=3^5.k*6%11
so, 45*6%11=1.6=6
so rem =6. where 10 = phi(11)=(1-1/11)*11

Is this solution Helpfull? Yes (6) | No (2)  

SUDHIR SHARMA  (10 years ago)

3 will be the answer

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

jitin taneja  (10 years ago)

the answer will be 6 because 50 and 11 are coprime to each other so by euler thoerem, we can find out the euler no. of 11 , since it is prime no. the euler no. of 11 will be 10 , so divide the power of 50 by 10 then we will get remainder as 1
now we r left with 50^1/11 so when we divide 50^1 by 11 we will get the remainder as "6".

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SUDHIR SHARMA  (10 years ago)

6 will be the correct answer because 51^52 will give unit digit as 1.
Therefore, When 50^1 is divided by 11 will give a remainder 6

Is this solution Helpfull? Yes (2) | No (8)  

Paras Sachdeva  (10 years ago)

6 because 50 divided by 11 gives 6 remainder

Is this solution Helpfull? Yes (2) | No (8)  

utkarsh gupta  (10 years ago)

Just check the inter most no. Here 50 find the remainder that will be the result because as many times u power it factors will be same...check for any small,value the answer will always be the same depending on the central number.so,ans will be 6. @s 50/11 gives 6 as remainder

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kodali kranthi  (9 years ago)

50 power 51*52 = 50 power 2652 => 50 power 2652 => 50 power 2650 will exaclty divided by 11 and remaining 2500/11 gives remainder is 3

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Prakash Singh  (9 years ago)

answer is 3

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Nitin  (9 years ago)

if expression is like 50^(51^52) then remainder is 6.
BUT if expression is like (50^51)^52 OR you can say 50^2652 then remainder is 3.

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ASHISH MUKHERJEE  (9 years ago)

reminder will be 3.
whoever getting the answer apart from 3 please do proper calculation.

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JUGAL KHAJURIYA  (8 years ago)

reminder= 3

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CHAITANYA  (10 years ago)

50^51^52/11==(50^50^52)50/11
SO, 11)((50^50^52)*50)(4
44
--------------------
06

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Mahendra   (10 years ago)

6 is the correct answer

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Mani kandan  (10 years ago)

Ans is 6.
where phi(11)=(1-1/11)*11=10
=> 50^10k = 1mod11
So 51^52 is to be written in the form of 10k + a.
Now unit digit of 5152 = 1 => 5152 = 10k + 1.
=> 5051^52 = 50(10k + 1) = 50mod11 = 6 mod11

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Shimul chakraborty  (9 years ago)

using cyclicity of unit digits 51^52=51^0=1=50^10k+1 [cyclicity of 1 is 1 & 52/1 gives reminder 0].
Fermat little theorem says, a^ (p−1)/ p remainder is 1. therefore
50^(10k+1)/11= ((50^10)^k . 50^1)/11
= 50/11=rim 6

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Ravi  (8 years ago)

In these typ que...
1. 50 %11 =6
2.now eq will be 6^51^52 divide 11'
3. now try to get no. of 6 for which we can get 1 reminder after divide 11 here let see
6*6/11 gives 3 reminder
6*3/11 gives 7 rem
7*6/11 gives 9
9*6/11 gives 10
10*6/11 gives 5
5*6/11 gives 8
8*6/11 gives 4
4*6/11 gives 2
"2*6/11 gives 1 " thats situation we want .... upto these we have used 10 sixes.......
4. now we can write eq like that.............
now 51 =10*5+1
so 6^(50+1)^52 /11
6^(10*5+1)^52/11
in these situation we know 6^10/11 will give 1 remainder so 6^50/11 will also give 1 remainder so 6^51^52 will give 1 reminder now remaining
6^1^52/11 and you know 1^52 always gives 1 so now eq will be
6^1/11=6 reaminder ans...................

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nitin singh senger  (8 years ago)

STEP(1) 52 is deivided by 4 =means no remainder
STEP(2) 51 is devided by 10= 1 as remainder
STEP(3) 50 is devided by 11= 6 as remainder

now combining all in equation= 6^1^0= 6 will be the answer

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