Latest Elitmus Aptitude Question SOLUTION: (32^32^32)/9 give the remainder.. Options a) 6 b) 4 c) 7 d)1

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(#M40038704) ELITMUS Numerical Ability question Number System Keep an EYE

(32^32^32)/9 give the remainder..
Options
a) 6
b) 4
c) 7
d)1

Asked In Elitmus NEERAV NIKUNJ (9 years ago)

Unsolved Read Solution (6)

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Read Solution (6) :

Dhaval  (9 years ago)

32 = 2⁵
(2⁵)³² = 2¹⁶⁰
(2¹⁶⁰)³² = 2⁵¹²⁰
2¹ mod 9 = 2
2² mod 9 = 4
2³ mod 9 = 8
2⁴ mod 9 = 7
2⁵ mod 9 = 5
2⁶ mod 9 = 1
2⁷ mod 9 = 2
2⁸ mod 9 = 4
---
2⁵¹²⁰ mod 9 = 4

Is this solution Helpfull? Yes (29) | No (2)  

veer kumar  (9 years ago)

32^32^32=(36-4)^32^32
according to remainder theorem remainder will be (-4)^32^32
now 32^32 will be an even number so we can say that remainder will be 4^32^32
we know that 4^3=64 and 9*7=63 so we need to write 32^32 in terms of 3
so 32^32/3=(33-1)^32/3 remainder will be (-)^32=1
so we can write 32^32=3k+1
32^32 is even so 3k+1 must also be even
=>3(odd)*k(odd)+1(0dd)=even so we can say that k is odd
4^32^32=4^(3k+1)=4^3k*4
64^k*4
((63+1)^k*4)/9 so as per remainder theorem will be +1^k*4=1*4= 4 ans

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saurabh agarwal  (9 years ago)

4 is the right answer

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saira fatma  (9 years ago)

unit digit=32^32=2*32=6
thus 32^6/9=2^30/9=8^10/9=(-1)^10=1 ans

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

Anjana Kumari  (9 years ago)

ans is 7
=32 %9 =5
=5^ 32.32. 32. . 32 times /9
=5^ 2. 2.2.2... 32 times /9
= 7 ans

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Animesh Gupta  (7 years ago)

(32pow32pow32/9)
=(5pow1024)/9
=gives -5 as remainder
Hence 9-5=4

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