Latest Capgemini Aptitude Question SOLUTION: units digit in expansion os 2 raised to 51 is:

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units digit in expansion os 2 raised to 51 is:

Asked In Capgemini poompavai (11 years ago)

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JAGADEESWARA RAO P  (11 years ago)

ANS :: 8


2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256
....
last digits are {2,4,8,6...,2,4,8,6} i.e.,for every 4 sets the last digits are repeated so 12*4+3 digits so 2^51 has last digit is "8".

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Maths Maths  (11 years ago)

51/4 -> remainder is 3 ,2^3 = 8
therefore unit's place digit is 8
to find unit's place digit
2^1 = 2,2^2 = 4,2^3 =8,2^4 =6 and again the cycle repeats i.e 2^5 =2
This cycle repeats after 4 period therefore the power is divided by 4.

Is this solution Helpfull? Yes (18) | No (1)  

Tejaswini  (11 years ago)

units digit of 2^1=2;2^2=4;2^3=8;2^4=6;2^5=2 AND THIS REPEATS
so 2^48=6;2^51 units place is 8
ans is 8

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Maths Maths  (11 years ago)

51/4 -> remainder is 3 ,2^3 = 8
therefore unit's place digit is 8
to find unit's place digit
2^1 = 2,2^2 = 4,2^3 =8,2^4 =6 and again the cycle repeats i.e 2^5 =2
This cycle repeats after 4 period therefore the power is divided by 4.

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

Amarender  (11 years ago)

2^51=2^48*2^3
units digit in 2^48 is 6
...6*8=....8

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anchal  (11 years ago)

Ans: 8
2^51=(2^48)x 2^3
=(2^4)^12x8 = 16^12 x 8
since 6 to the power of anything gives 6 so the product is 48
unit digit=8

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Shivani Jha  (8 years ago)

8,
Related to cycle of 2

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Sandeep  (7 years ago)

8.
because
first we divide 51 by 4 then the reminder is 3
so 2^3=8

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revanth suryadevara  (7 years ago)

answer :8
In order to solve this question, Firstly you have to know the power cycles concept::
2^1=2(ending digit)
2^2=4(ending digit)
2^3=8(ending digit)
2^4=6(ending digit)
from next the same cycle repeats for all like 2^5=2(ending digit),2^6=4(ending digit),2^7=8(ending digit),2^8=6(ending digit)...........
now coming to the solution ,,let us find the ending digit of 2^10:::find 10%4 which gives 2 from above cycle [mod value 1 represents ending digit 2,mod value 2 represents ending digit 4,mod value 3 represents ending digit 8, mod value 0 represents ending digit 6], so answer is 4.
2^20::20%4=0; mod value 0=6 so answer is 6;
2^51;;;;;51%4=3 mod value 3=8 ::so answer is 8

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y.nikhil  (7 years ago)

cilicity of 2 is 4,divide the power with the remainder will be 3,
make the remainder power of 2 ,it gives the unit digit that is 8.

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K.Sireesha  (6 years ago)

ans=8
because for every after 2^4 the last digit is 2
so 4*12=48 and then remaining 51-43=3
then 2^3 is 8.

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Mohankumar  (6 years ago)

2^51=51/4 here 4 is the unit cycle of 2
remainder is 3
substitute 3 in 51
2^3=8
ans is 8

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Rajaboina Radhika  (6 years ago)

unit digit is 8

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