Latest TCS Aptitude Question SOLUTION: what is the reminder when 6^17+7^16 is divided by 7

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what is the reminder when 6^17+7^16 is divided by 7

Asked In TCS RAHU SHARMA (11 years ago)

Unsolved Read Solution (8)

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Read Solution (8) :

sainath  (11 years ago)

(7-1)^17+7^16
=[17c0(7)^17-17c1(7)^16(1)+17c2(7)^15(1)^2-.......+17c16(7)^1(1)^16-17c17(1)^17]+ 7^16
in the expansion every term contains 7 which is divisible by 7 except the last term -17c17(1)^17=-1
but remainder must be positive so 7-1=6...
[for this lets consider previous term also 17c16(7)^1(1)^16-17c17(1)^17
=17(7)-1=119-1=118
when 118 devided by 7 leaves remainder 6...
hence proved...]

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Sanket Kumar  (11 years ago)

Answer is 0.Check out the latest post of the same question.

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akshya dhingra  (11 years ago)

as if 7^16 is divided by 7 it will give 0 remainder and when 6^17 is divided by 7 then the remainder will be 6 since 6 can be written as (7-1) and when(7-1)^ an odd number will be divided by 7 it will give 6 as remainder.so the total remainder=6.

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Rishi Singh  (11 years ago)

6 is the right answer

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mangzmetlida  (11 years ago)

6^17/7= 2
7^16/7= 4
6^17+7^16= 2+4= 6
so ans is 6

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chaitanya chinmoy singh  (11 years ago)

answer is 0 for sure...:):)....this same question was solved day before yesterday by our trainer of face institute...:):)

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Narendra kumar  (9 years ago)

(6^17 + 17^6)/7
=((7-1)^17)/7 + ((17^(7-1) /7)
=-1+1
=0

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gaurav tyagi  (9 years ago)

(6^17+7^16)/7 can be written as..........
(6^17)/7 +(7^16)/7
2nd term has Remainder=0.To get remainder from 1st term we can use a property of number system (ax-1)^n/a has remainder equal to (-1)^n.
Here (7-1)^17/7 gives remainder equals to (-1)^17=-1.But remainder can not be negative.Hence remainder is 7-1=6.
Ans. R=6

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