Latest TCS Aptitude Question SOLUTION: 369^77/7 What is the remainder?

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(#M40033941) TCS Numerical Ability question power cycle Keep an EYE

369^77/7

What is the remainder?

Asked In TCS ABHINAV PUSHPAM (10 years ago)

Solved RAKESH Read Solution (17)

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Read Solution (17) :

RAKESH  (10 years ago)

139^77/7
=> (7*20-1)^77/7
=> (-1)^77/7
=> -1/7 => rem = 6

Is this solution Helpfull? Yes (18) | No (25)  

Krishnakanth  (10 years ago)

answer is 3,because for every 6 powers (7-1,I.e.,divisor -1) reminder is 1,so 77%7=5,

so for 369%7=5
5
(369^2)%7=(5*5)%7=4

369^3)%7=(4*5)%7= 6


369^4)%7=(6*5)%7=2

369^5)%7=(2*5)%7=3

so for (369 ^ 5)%7 reminder is 3
and if we observe for 369^6)%7 = 3*5)%7 =1 so if n is divisor for (n-1)the power reminder is 1
you can check this for (135^77)%7, (76^77)%7

so answer is 3

Is this solution Helpfull? Yes (16) | No   

Kundan Dhande  (10 years ago)

139^77/7= (53*7-2)/7
so remainder = (-2)/7
remainder= 5

Is this solution Helpfull? Yes (11) | No (2)  

Dhruv gupta  (10 years ago)

ans is 3

Is this solution Helpfull? Yes (6) | No   

MRITUNJAY  (10 years ago)

According to rule of power cycle divide the power by four,here 77 is divided by 4 it gives 1 as remainder.last digit is 9.so 9^1 is 9,then divide 9/7= 2 remainder. so ans is 2.

Is this solution Helpfull? Yes (5) | No (2)  

Krishnakanth  (10 years ago)

answer is 3,because for every 6 powers (7-1,I.e.,divisor -1) reminder is 1,so 77%7=5,

so for 369%7=5
5
(369^2)%7=(5*5)%7=4

369^3)%7=(4*5)%7= 6


369^4)%7=(6*5)%7=2

369^5)%7=(2*5)%7=3

so for (369 ^ 5)%7 reminder is 3
and if we observe for 369^6)%7 = 3*5)%7 =1 so if n is divisor for (n-1)the power reminder is 1
you can check this for (135^77)%7, (76^77)%7

so answer is 3

Is this solution Helpfull? Yes (5) | No   

MUDIT SHARMA  (10 years ago)

For 139^77/7
Rem=6

Is this solution Helpfull? Yes (4) | No (1)  

Sahanur Mondal  (10 years ago)

3 is the right answer
(364+5)^77/7-->5^77/7-->5*(5^2)^38/7-->5*(21+4)^38/7-->5*2^76/7-->5*2*(7+1)^25/7-->10/7-->3

Is this solution Helpfull? Yes (4) | No   

PRAMIT SINHA  (10 years ago)

9^1/7=2
9^2/7=4
9^3/7=1
9^4/7=2

so,,77/3=2
r=2,,ans 4

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

Girish Jambkar  (10 years ago)

Problem wasnt like this !
it was 139^77/7

Is this solution Helpfull? Yes (2) | No   

avishek sen  (10 years ago)

(371-2)^77/7
=-2^77/7
=(-2^2*2^75)/7
=(-4*8^15)/7
=(-4*1^15)/7
-4/7
=7-4
=3 (ans)

Is this solution Helpfull? Yes (2) | No   

vipul pachauri  (10 years ago)

9^77/7=[(9^3)^25]*(9^2)/7=rem(1)*81/7=rem is 4
ans is 4

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krishnendu sen  (10 years ago)

the cylicity of the last digit in 369 i.e of 9 is 2..
then we devide 77/2 the remainder is 1..then the last digit of the no. 369^77
is= 9^1=9 so the remainder is 9/7=2

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mano ranjitha  (10 years ago)

can any one tell me which is the correct answer 6 or 2

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PAVI  (10 years ago)

Is 2 correct answer??

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ramesh  (10 years ago)

question is not 139 guys....
its 369....

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prashant subba  (10 years ago)

369/7 gives the remainder is 5. now we have to simply calculate 5^77/7 to find the answer.
again, 5^7/7 will give remainder 5. Similarly 5^11/7 will give remainder 3.
So the remainder is 3.

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