Latest TCS Aptitude Question SOLUTION: what is the remainder when 4^29 is divided by 63? a)16 b)12 c)61 d)none of these.

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(#M40152730) TCS Numerical Ability question puzzle Keep an EYE

what is the remainder when 4^29 is divided by 63?
a)16
b)12
c)61
d)none of these.

Asked In TCS Juwairiya Siraj Khan (8 years ago)

Unsolved Read Solution (14)

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Read Solution (14) :

Sharad Kumar Pani  (8 years ago)

as 4^3 is 64 so when devided by 63 we get remainder 1 .. So 4^27 rmainder is 1 4^2 is 16 so the remainder is 16.. so the net remainder is 16

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

anup  (8 years ago)

16*64*64*64*64*64*64*64*64*64
.............................................................
63
from negative remainder method.
(64-63=1) that is 9 times one.
so.
16*1*1*1*1*1*1*1*1*1
........................................
63
so the remainder is 16.
OPTION (A).

Is this solution Helpfull? Yes (3) | No   

Juwairiya Siraj Khan  (8 years ago)

As it's given,
4^29 mod 63 = (4^2)*(4^27) mod 63 = 16*(4^3)^9 mod 63 = 16*(64)^9 mod 63
so,above expression can be written as,
=16*(63+1)^9 mod 63
now, 63^9 would give remainder 0,when divided by 63
therefore, 16*(1)^9 mod 63 can only be considered
1^9 = 1
so, 16 mod 63 = 16
hence,the answer is 16.

Is this solution Helpfull? Yes (3) | No (1)  

raghavendra  (8 years ago)

4^2 * 4^3 * 4^3 *4^ 3* 4^3 * 4^3 *4^ 3*4^ 3*4^ 3*4^ 3
=16*4^3 *64*64*64*64*64*64*64*64/63-----(1)
take one 64 from the above
64/63=1(remainder) and so on we get eight ones as remainders for 63
and 16*64/63=1024/63=16(remainder)
note:if we talke 4^3=64 in equ (1) we get 16/63 =which is not possible

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salauddin  (8 years ago)

(4^3)^9*4^2/63
4^3/63 remainder is 1
4^2/63
so remainder is 16

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Shashank Sourabh Singh  (8 years ago)

4^29=64^9x16
when divided by 63 give remainder 1^9x16=16
so a)16 is correct

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Golluru Lalitha  (8 years ago)

4^29/63=((4^3)^9 * 4^2 )/63 ( when 4^3=64 divided by 63 we get remainder as 1 , when we divide
= (1)^9 * 16 4^2=16 with 63 we get remainder as 16 )
=16

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Reena Sangwan  (8 years ago)

The ans is 16

Is this solution Helpfull? Yes | No (1)  

SARASWATHI SIVAGURU  (8 years ago)

16*64*64*64*64*64*64*64*64*64
.............................................................
63
from negative remainder method.
(64-63=1) that is 9 times one.
so.
16*1*1*1*1*1*1*1*1*1
........................................
63
so the remainder is 16.
OPTION (A).

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Rajanikanta Pradhan  (8 years ago)

4^29= [ (4^3)^9 *4^2 ] /63
= 1^9 *16/ 63
=16 reminder

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shubham tank  (8 years ago)

4^29/63= 4^2*4^27/63= 4^27/63=1 and 4^2 /63= 16 . hence ans is 16.

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Rajesh Gurjar  (7 years ago)

when 64/63 gives remainder 1, so in every 2^6 the remainder will be 1.
4^29= 2^58
the closest factor of 6 is 54 so we have to check only for 2^(58-54) i. e. 16
because 2^54 will give remainder 1.
I hope it helped.

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CHINNASANI BHARGAVI  (7 years ago)

((4^3)^9 *4^2)/63
((1)^9*16)/63
16/63
so 16

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  (5 years ago)

none of these

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