Latest Elitmus Aptitude Question SOLUTION: what is the unit digit in 27^20

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what is the unit digit in 27^20

Asked In Elitmus Harmitha (9 years ago)

Unsolved Read Solution (22)

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PUSPANJALI  (9 years ago)

unit digit of 27 is 7 having power 20 which means 4n..
7^20=1

Is this solution Helpfull? Yes (25) | No (2)  

prem  (9 years ago)

1
27^20=27^(2*10)
=27^(2*2*5 )
for unit place (7^4)^5
=1^5=1

Is this solution Helpfull? Yes (17) | No (2)  

ANUJ KUMAR  (9 years ago)

TO FIND UNIT DIGIT WE HAVE TO FOLLOW 3 RULES ....

LAST DIGIT =ANYONE OF THESE ( 0,2,3,7,8) GOES TO CYCLIC RULE DIVIDE ( POWER NO BY 4) & FIND REMDR. IF REMD =0 THEN PUT 4
= 1 THEN PUT 1
=2 THEN PUT 2
=3 THEN PUT 3

RULE ii - IF LAST DIGIT EITHER 4 OR 9 GOES TO
IF POWER EVEN ADD +2 = 4+2 =6 LIKE .124^20005554 =6
=9+2=11 LIKE 589^4500008= 1
OTHERWISE WRITE SAME
(254)^8555541 =4
( 366666666666888879)^45555555588888888893 =1

AND LAST RULE IF LAST DIGIT ONE OF (1,5,6)
UNIT DIGIT SAME I.E
(122201)^525544 =1
5555555^69887=5
4256986^653=6


NOW GOES TO THIS QWESTION - (27)^20 ie. last digit =7 goes to cyclic rule = 20/4 ,remd =0 thus write 4
7^4 = 1 anssssss

Is this solution Helpfull? Yes (9) | No   

aditya kumar  (9 years ago)

use cyclicity rule... that all

Is this solution Helpfull? Yes (4) | No   

SubbaReddy Gowru  (9 years ago)

When the given number is odd then try to get the last digit as 1.
27^4*5
7^4=1

Is this solution Helpfull? Yes (3) | No   

shailendra sethiya  (9 years ago)

(7) ^ 4*5 ans 1

Is this solution Helpfull? Yes (3) | No   

A.Mahesh Reddy  (9 years ago)

In unit place is 7 => 7^2=49
Unit place is 9 => 9*7= 63
Unit place is 3 => 3*7=21
There fore Units place of 27^4=1
there fore units place is 7^20=>7^4^(5)=1^5=>1

Is this solution Helpfull? Yes (2) | No (1)  

Shrimant  (9 years ago)

First We know the power cycle of 7 then we can solve answer fast
i.e. divide the power by power cycle i.e. 20/4 4 is power cycle of 7 unit place then
20/4=Reminder is 0 then take the hightest power of power cycle i.e. 4 then 7^4=2401 then
unit place is =1 is the correct ans.

Is this solution Helpfull? Yes (2) | No (1)  

Athena Chakraborty  (9 years ago)

Cyclicity of 7 is 4.
20/4 gives remainder 0.
So the unit digit should be 7(i.e the unit digit of 27)^0=1
:-)

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kowligi arunkumar  (9 years ago)

ans is 1
unit digits :7^1..............7
7^2.............9
7^3............3

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Paresh Kumar Nayak  (9 years ago)

Ans-:1
27^20=(3^3)^20=3^60
unit digits of 3^N repeat as =3,9,7,1...(since 3^1=3, 3^2=9, 3^3=27, 3^4=81,3^5=243....)
so, 3^60 has unit digit 1

Is this solution Helpfull? Yes (1) | No   

bravo  (9 years ago)

27^20
7 ^0 = 1

so 1

Is this solution Helpfull? Yes (1) | No   

YAMUNA DEVI MUNIGADAPA  (9 years ago)

if the unit digit is 2,3,7,8 divide the power with 4
in the above questn in units place 7 ,so divide the 20 with 4
we vil get the reminder as 0 whenevr dividing vit 4 if we get remainder as 0 we need to take last value in 4th table ie the ans is 6 (
4^1=4
4^2=6
4^3=4 repeating no need to consider)

Is this solution Helpfull? Yes | No (3)  

NISHANT BADGOTIYA  (9 years ago)

27^20
20/4 gives 0 as remainder.
therefore at unit place 7^4 gives= 7*7=49
now, 9*7=72
now, 2*7=14, therefore unit place is 4.

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RAJA  (9 years ago)

20/4 we get remainder 0 then consider as 4
7^4=81
ans unit digit is 1

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samm  (8 years ago)

Cyclicity of 7 is 4.
then 7^4=2401.
unit digit is 1.

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gattikoppula vikram  (8 years ago)

divide the base with 10 and power with 4 ,because to get units digit e divide it with 10,,,nd cyclicit of any number z 4.. i.e after every four times the unit digits are same...
cyclicit of 7 is 7,9,3,1.when we divide power with 4 the remainder is 0.i.e 4... so ans is 1

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Aakash Raj  (8 years ago)

Guys...go thru Arun Sharma (Quant ) for this type of problems ..... easy, helpful and time efficient methods are there....

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ganesh babu  (8 years ago)

27^20
20(mod 4) =0
27^20 unit digit 1

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swati  (8 years ago)

the unit digit=1

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zac  (7 years ago)

ans will be 1
becoz
if we use cyclic rule here we will get 7^4 which results in 1 at unit place

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PALASH MONDAL  (5 years ago)

27^20
To get the unit digit we only look at unit digit power

27^20
=7^20
=9^10
=1^5
=1

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