Latest TCS Aptitude Question SOLUTION: Q. What is the reminder of 6^17+17^6 is divided by 7?

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Q. What is the reminder of 6^17+17^6 is divided by 7?

Asked In TCS G.Nagasri (10 years ago)

Solved Prayosha panchal Read Solution (24)

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Read Solution (24) :

Prayosha panchal  (10 years ago)

6^17+17^6
=(7-1)^17 +(14+3)^6
dividing by 7 then for reminder
-1^17 + 3^6
=728/7
=104 So, reminder =0

Is this solution Helpfull? Yes (37) | No (2)  

RAKESH  (10 years ago)

Ans : 0
6^17/7 =(7-1)^17/7=(-1)^17/7 gives rem= -1
17^6/7 =(7*2+3)^6/7=(3)^6/7 =(27)^2/7=(28-1)^2/7=(-1)^2/7 gives rem =1
hence,remainder when 6^17+17^6 is divided by 7 is
(-1)+1 = 0

Is this solution Helpfull? Yes (20) | No   

ratnakar mani  (10 years ago)

6^17/7+17^6/7
for 6^17 remainder is 6 and for 17^6 remainder is 1
so 6+1/7=1 so resultant remainder =0

Is this solution Helpfull? Yes (12) | No (3)  

Girish Jambkar  (10 years ago)

6^7=unit place digit 6 & 17^6=unit place digit is 9
9+6=15
15/7 gives remainder=1
So answer is 1

Is this solution Helpfull? Yes (6) | No (3)  

Ankit Kedia  (10 years ago)

In order to solve such remainder problems try to get the form ((aN + 1)^x)/N or ((aN-1)^x)/N where a and x are any numbers
when this form is attained we can replace it by (-1)^x or (1)^x respectively.
here 6^17 + 17^6 /7 can be separated as 6^17/7 + 17^6/7
= (7-1)^17/7 + (35-1)^6/7
= -1^17 + -1^6
= -1 + 1
= 6 + 1
= 7
since 7 is >= the denominator so we further divide it by 7
= 0

Is this solution Helpfull? Yes (5) | No (5)  

Ramesh  (10 years ago)

the final digit obtained by solving the above expression is 304 so when u divide that number with 7 the remainder is 3
so the remainder is 3

Is this solution Helpfull? Yes (2) | No (3)  

Sajib Ghosh  (10 years ago)

the remainder is 2.
as,,(6^17 + 17^6)=(7-1)^17 +(14+3)^6
the actual remainder will be for (-1)^17 + (3)^6 = 1+ 729 = 730
so, 730/7 remainder is 2
so the answer is 2

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

Chinarayudu Yalakanti  (10 years ago)

reminder of 15/7=1
so ans is 1

Is this solution Helpfull? Yes (1) | No (1)  

janani  (9 years ago)

POWER CYCLE OF 6 IS 6...Hence the unit digit is 6..and the power cycle of 7 in 17 is 9..hence 6+9/7=1

Is this solution Helpfull? Yes (1) | No (1)  

Priyanka Mishra  (9 years ago)

reminder=0

Is this solution Helpfull? Yes (1) | No   

Sarvjeet Rajvansh  (9 years ago)

6^17+17^6
(7-1)^17+(7+10)^6
-1^17+10^6
-1+10^6
-1+(7+3)^6
-1+(3^2)^3
-1+2^3
-1+1^6; remainder=0

Is this solution Helpfull? Yes (1) | No   

Narendra Nath Banerjee  (10 years ago)

6^17+17^6=(7-1)^17+(14+3)^6
then reminder for 7 is (1^17+3^6)/7
=730/7
reminder = 2

Is this solution Helpfull? Yes | No (1)  

Midhun golla  (10 years ago)

the remainder is 0.
(6^17 + 17^6)/7 = (6^17)/7 + (17^6)/7
the remainder for (6^17)/7 is 6 and the remainder for (17^6)/7 is 1.
when they are added we get 7... the remainder for 7/7 is 0
so the answer is 0

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gautam  (10 years ago)

(6^2*6^2*6^2*6^2*6^1)+(17^2*17^2*17*2)=4

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ajay jain  (10 years ago)

6^17+17^6
easy method = first we need to find reminder to make digit small digit make 1
6divide by 7 =reminder is -1
so it become
(-1)^17=-1
now see second part = 17^6
find reminder of 17divide by 7 = 3
(3)^6
again 6 divide 7 = -1
it become
(3)^-1= 1/3
reminder of 1/3=1

so -1+1 = 0 answer

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Arpita  (9 years ago)

6^17+17^6
(7-1)^17+(7+10)^6
-1^17+10^6
-1+10^6
999999/7 remainder=0

Is this solution Helpfull? Yes | No (3)  

Tarun Sinha  (9 years ago)

ans =1
6^17+17^6 = 6^(4*4+1) + 17^(4*1+2) = 6^1 + 17^2
Now we check the units place we get , 6 and 9 for 6^1 and 17^2
6+9=15/7 remainder is 1

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anuj gupta  (9 years ago)

6^something=6
17^6=9
6+9/7=1

Is this solution Helpfull? Yes | No (1)  

ANMOL ANAND  (9 years ago)

6^17=6*36^8 now 6*36^8+17^6/7=6*1^8+3^6/7 now 3^6=^3 noe 6+9^3/7=6+2^3/7=14/7 remainder 0 by using remainder theorem...

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Pooja Navin  (9 years ago)

ans is 2
bcoz remainder of 6^17 is 6
remainder of 17^6 is 9

(7+9)/7= remainder 2

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Harshita Tiwari  (9 years ago)

Please give the Admin Solution for these question?

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pranjal srivastava  (9 years ago)

unit digit of 6^17 is 6 and unit digit of 17^6 is 9.
so 6+9=15
15/7 gives remaider 1 .so ans is 1

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Renu Pawar  (8 years ago)

first step (7-1)^17+(14+3)^6
now divide this equation by 7 u will got
(-1)^7+(3)^6
(-1+729)/7
728/7
104 so remainder =0 answer

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Arunima   (8 years ago)

6^17%7=( -1)^17 = 6
17^6%7=3^6%7=3^2^3%7=2^3%7=1
1+6=7%7=0

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