Latest MBA Aptitude Question SOLUTION: Find the remainder when 50^56^52 is divided by 11? Plzz explain the procedure..as im not sure of the answer...

1) 2
2) 3
3) 4
4) 5

• Placement Papers
• /
• MBA

MBA Question Papers:

(#M40015712) MBA question number systems, progressions Keep an EYE

Find the remainder when 50^56^52 is divided by 11? Plzz explain the procedure..as im not sure of the answer...

1) 2
2) 3
3) 4
4) 5

Asked In MBA (11 years ago)

Unsolved Read Solution (1)

Is this Puzzle helpful?   (2)   (0) Submit Your Solution

Read Solution (1) :

Shireesh Mehta  (10 years ago)

50^56^52=50^.....6 i.e.some number ending in 6 as unit's digit[since all powers of 6 end in 6 as unit's digit.
Now, 50^....6 can be written as (50^.....0)*(50^6) [simple addition of exponents]
By Fermat's Little Theorem, we know that (a^(p-1))/p=1 when a and p are co-prime and p is a prime number.
Here, 50 and 11 are co-prime ans 11 is a prime number.
Hence, 50^10/11=1 or 50^(10*n)/11=1 where n is any positive integer.
Applying this particular principle here,
50^.....0=1
This leaves 50^6/11
=rem[50*50*50*50*50*50/11]
=rem[6*6*6*6*6*6/11]
=rem[36*36*36/11]
=rem[3*3*3/11]
=rem[27/11]=5
Thus, answer is 5.

Is this solution Helpfull? Yes (3) | No   

Please Login to Read Solution.