Latest TCS Aptitude Question SOLUTION: find the last two digits of 583^512?

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(#M40024791) TCS question Keep an EYE

find the last two digits of 583^512?

Asked In TCS pre (10 years ago)

Unsolved Read Solution (17)

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Shreya Sohan  (10 years ago)

61..
considering last two digits
83^1=83
83^2=89
83^3=87
.....
83^12=61
.....
83^19=47
83^20=01
83^21=83..
therefore we see power repeats itself after 20.. so dividing 512 by 20, we get remainder=12 so 83^12=61 last two digits..

Is this solution Helpfull? Yes (21) | No (4)  

saurabh  (10 years ago)

583^512
taking last two digit and squaring i.e (83^2)^256 = 6889...so now we have to calculate 89^256
similarly repeating the process as (89^2)^128 = 7921...now 21^128
(21^2)^64 = 441^64...so 41^64
(41^2)^32 = 1681^32...SO 81^32
(81^2)^16 =6561^16...SO 61^16
(61^2)^8 =3721^8....SO 21^8
(21^2)^4 =441^4...SO 41^4
(41^2)^2 =1681^2...SO 81^2
81^2 = 6561 SO 61 IS IN THE LAST

Is this solution Helpfull? Yes (9) | No (1)  

vikash kumar  (10 years ago)

given:( 583^512)
=( 583^4*128)
=(_21^128) (since , its hard to explain here that how it comes , better you follow the link and try to learn the concept, http://totalgadha.com/mod/forum/discuss.php?d=4405 )
= 61
hence, 61 is the ryt ans

Is this solution Helpfull? Yes (8) | No   

Mita Pan  (10 years ago)

61 will be the answer

Is this solution Helpfull? Yes (7) | No   

Nikhil kumar  (10 years ago)

given:( 583^512)
=( 583^4*128)
=(_21^128)
= 61
hence, 61 is possible.

Is this solution Helpfull? Yes (4) | No   

Aastutee sahu  (10 years ago)

61 is the ans....

Is this solution Helpfull? Yes (2) | No   

Mita Pan  (10 years ago)

@SAMANVITHA I did it in a manual way. 583^16*32=(583^4)128 Here I did square of 83 and got 6889 but I considered only 89..Then I multiplied it with another 89.Hence got the last 2 digits of 583^4 which will be 21.After that the equation will be reduced to (21^4)32..We will get the solution by solving it in the previous method.

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

Ritesh  (10 years ago)

ans will be 61.

Is this solution Helpfull? Yes (1) | No   

samanvitha  (10 years ago)

Yes 61 is the answer can u plz explain it @MITA PAN

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utkarsh bisht  (10 years ago)

WILL IT BE 69?

Is this solution Helpfull? Yes (1) | No (9)  

s.sahithi  (10 years ago)

find 83^12 we wil get 61 as last 2 digits.. i think 61 will be the answer....

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Anupam Mondal  (10 years ago)

3^2=9
8*2=16
answer will be 69

Is this solution Helpfull? Yes (1) | No   

rohit tandon  (10 years ago)

49 are the last two digits.

Is this solution Helpfull? Yes | No (6)  

kaustubh ingale  (10 years ago)

49 are the last digits..guys its very simple

Is this solution Helpfull? Yes | No (10)  

madhu  (10 years ago)

83^512=((83)^2)^255=(89)^255=(90-1)^255=(-1)^55+55*90(-1)^54(binomial expansion)=(-1)+55*90)=4950-1=4949..So,the last 2 digits=49

Is this solution Helpfull? Yes | No (4)  

dinesh  (10 years ago)

96 after real multiplication

Is this solution Helpfull? Yes | No (2)  

Guru Pranav  (10 years ago)

61 are the last two digits.

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