Latest TCS Aptitude Question SOLUTION: what is the reminder when 6^17+17^6 is divided by 7 ? a) 3 b) 0 c) 6 d) 1

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what is the reminder when 6^17+17^6 is divided by 7 ?
a) 3 b) 0 c) 6 d) 1

Asked In TCS (12 years ago)

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Jones basker  (12 years ago)

((7-1)^17+(14+3)^6)/7 --> ((-1)^17+(3)^6)/7 --> ((-1)+remainder(1))/7 --> (remainder(6)+remainder(1))/7 --> 7/7=0

Is this solution Helpfull? Yes (22) | No (8)  

Manojkumar  (12 years ago)

unit digit of 6^17=6...
6^1=6
6^2=6
6^3=6
.
.
.
6^17=6
unit digit means calculate only last digit
therefore 6^17 reminder=6 why means (6/7)
same other part reminder=2 why means 9/7=2
reminder(6)+reminder(2)/7=1(8/7=1)
show the answer=1

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rathika  (12 years ago)

ans : d)1
consider only unit digits....

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Antony Johnson  (12 years ago)

6^2=1 mod 7 [(6^2)=36,divided by 7 gives remainder 1]
=>(6)^2*8=1^8 mod 7
=>6^16=1 mod 7 [all even power also gives 1 mod 7]
=>(6^16)*6=1*6 mod 7
So, 6^17=6 mod 7.

Likewise,

17^2=2 mod 7
=>(17)^2*3=2^3 mod 7
=>17^6=8 mod 7 [simplify: 8 is one time divisible by 7 & gives remainder 1]
So, 17^6=1 mod 7.

((6^17+17^6)/7)= ((6 mod 7)+(1 mod 7))/7
=>((6+1) mod 7)/7
=>(7 mod 7)/7
=>Hence the remainder is 0

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lala  (12 years ago)

6^17 mod 7=(7-1)^17 mod 7=(-1)^17 mod 7=-1
17^6 mod 7=(7*2+3)^6 mod 7= (3)^6 mod 7=729 mod 7=1
the remainder when 6^17+17^6 is divided by 7 is
1-1=0(ans)

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prachitrivedi  (12 years ago)

find unit place by divide power by 4 if remainder comer becomes power of unit place so
6^1+7^2=55
55/7=remainder=3

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vivek garg  (12 years ago)

ans is zero

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Varsha RameshKumar  (11 years ago)

6^17 mod 7=(7-1)^17 mod 7=-1^17 mod7=-1 mod 7=(-1+7)mod 7=6mod7=6(a mod n can range only between 0 and n-1)
(7*2+3)^6 mod 7=14^6 mod 7+ 3^6mod 7=0+729 mod 7=1
Thus 6+1=7 is remainder but value can range between only 0 and 6 so again divide by 7 so 7 mod 7=0
Hope this helped... -1 mod 7 is not -1

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