Latest TCS Aptitude Question SOLUTION: what is remainder when 6^17+17^6+169^235 is diveded by 7

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what is remainder when 6^17+17^6+169^235 is diveded by 7

Asked In TCS nikhil saxena (10 years ago)

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RAKESH  (10 years ago)

(6^17+17^6+169^235)/7
6^17/7=(7-1)^17/7=(-1)^17=-1
17^6/7=(2*7+3)^6/7=3^6/7=27^2/7=(4*7-1)^2=(-1)^2=1
169^235/7=(24*7+1)^235=1^235=1
so (6^17+17^6+169^235)/7 gives a remainder -1+1+1/7=1/7
remainder=1

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ganesh chemanchula  (10 years ago)

remainder is 1
(6^17)/7=(7-1)^17/7=(-1)^17=-1
(17^6)/7=(1)6=1
169^235/7=(24*7+1)^235=1^235=1
by adding=-1+1+1=1

Is this solution Helpfull? Yes (21) | No (3)  

k.v.v.varun  (10 years ago)

6^(any number)=6 as unit digit
next 17^6 means 7^6 gives =1 as unit digit
next 169^235 means 9^235=9^234.9=9 as unit digit then lastly
6+1+9=16;by this 17/7 gives remainder 2

Is this solution Helpfull? Yes (3) | No (13)  

DON  (10 years ago)

@GANESH CHEMANCHULA & NIKHIL SAXENA
remainder will be 6
consider the above question as three parts
1.6^17/7
2.17^6/7
3.169^235/7
in first part
when 6 divided by 7 remainder is -1 so it will become (-1)^17=-1
in 2nd part
when 17 divided by 7 remainder will be 3 so (3)^6/7=(3^2)^3/7
when 9(3^2) divided by 7 gives remainder -2 so (-2)^3/7=-(8)/7
when 8 divided by 7 gives remainder is -1
BUT HERE THERE IS NEGATIVE REMAINDER SO IT SHOULD BE SUBTRACTED FROM DENOMINATOR
SO IT WILL BE 7-1=6
3RD PART
WHEN 169 DIVIDED BY 7 GIVES REMAINDER 1 SO (1^235)/7=1(REMAINDER)
SO OVER ALL REMAINDER =(-1+6+1)=6

Is this solution Helpfull? Yes (3) | No (15)  

vishakha chourasia  (10 years ago)

remainder is 0

Is this solution Helpfull? Yes (2) | No (19)  

shwetabh suman  (10 years ago)

remainder is 2.

Is this solution Helpfull? Yes | No (12)  

Midhun golla  (10 years ago)

6^17=6
17^6=1
169^235=9
so (6+1+9)/7= 16/7;
so,remainder is 2;

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tallapakavasavi  (10 years ago)

Remainder is 2

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yamini  (5 years ago)

remainder 3
the unit digit 6^7 is 6
the unit digit 7^6 is 9
the unit digit 9^5 is 9
6+9+9=24/7=3

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