Latest Elitmus Aptitude Question SOLUTION: Sn=1^8+2^8+3^8+----------n^8 find the unit digit of S29

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(#M40155175) ELITMUS Numerical Ability question number system Keep an EYE

Sn=1^8+2^8+3^8+----------n^8
find the unit digit of S29

Asked In Elitmus as (8 years ago)

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Ramen Guchhait  (8 years ago)

unit digit of-
1^8=1
2^8=6
3^8=1
4^8=6
5^8=5
6^8=6
7^8=1
8^8=6
9^8=1

so 1+6+1+6+5+6+1+6+1=33 so from here we get 3 as unit digit for 1^8+2^8+.....+9^8

now for 11 to 19 same way unit digit is 3
then from 21 to 29 unit digit is 3
so 3+3+3=9

so unit digit is 9

Is this solution Helpfull? Yes (17) | No (1)  

Yamini Kant Mahato  (8 years ago)

unit digit will be 9

Is this solution Helpfull? Yes (10) | No   

Dibyashree  (8 years ago)

S29^8= 29^8
9^8=9*9*9*9*9*9*9*9
we know 9*9=81
So even number of 9 when multiplied together give 1 in unit place so unit digit for s29 is 1
ans-1

Is this solution Helpfull? Yes (5) | No (10)  

Amit Sankhyan  (8 years ago)

Unit digit will be 9. Use Cyclicity principle.

Is this solution Helpfull? Yes (2) | No   

Yamini Kant Mahato  (8 years ago)

Crypto Was:
X D L
H A E
-----------
D E P H
3 P K P
__ A D __
------------
P __ __ K D H I AM UNABLE TO FLASH BACK THE EXACT 2 CHARACTERS SO I LEFT BLANK.BUT I AM GIVING THE EXACT SOLUTION OF THE ABOVE CRYPTO:

5 4 7
3 6 9
________
4 9 2 3
3 2 8 2
1 6 4 1
___________
2 0 1 8 4 3 SO SIMPLY YOU HAVE TO PUT THE VALUE OF 1 AND 0.I CAN'T CALL BACK THE VALUE OF 0
AND 1.
Q.1 WAS:D*H*E=4*3*9=108
Q.2 WAS:P*D*K=2*4*8= 64
Q.3 WAS:X*P*__=5*2*1= 10 THE VALUE OF 1 CAN'T CALL FRIENDS.

Is this solution Helpfull? Yes (2) | No   

sonali raj  (8 years ago)

unit digit of 1^8=1
unit digit of 2^8=6
unit digit of 3^8=1
unit digit of 4^8=6
;;;;;;;

similarly find up to 9^8=1
similar for 11 to 19 also and similar for 21 to 29 also then add all the unit digits. then ans will be 9

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Bharat Ratna  (8 years ago)

Any even no raised to any power which is multiple of 4 that is (even no)^(4 n) gives 6 as the unit digit while any odd no raised to any power which is multiple of 4 gives 1 as the unit digit.Exception to the above rules are (0,1,5,6).
Unit digit of :
1^8= 1
2^8=6(even no having power multipe of 4)
3^8=1(odd no having power multiple of 4)
...similarly upto 29^8
3 Number having 5 as unit digit are
5^8=5
15^8=5
25^8=5
Number having 0 as unit digit are:
10^8=0
20^8=0
No having 1 and 6 as unit digit are 29- (no having 0 and 5 as unit digit)=29-5=24
Now, Number having 1 and 6 as the unit digit are alternately so they must be 12 and 12 in pairs.
Sum of all the no having 1 and 6 as unit digit:
Sum of No having 1 as unit digit=12*1=12
Sum of no having 6 as unit digit=12*6=72
No having 5 as unit digit=3
sum=5*3=15
No having 0 as unit digit=2
Their sum=0
Total sum of all unit digit no from 1^8 to 29^8=12+72+15+0=99
So, unit digit of S^29=9

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akanksha   (8 years ago)

Unit digit will be 9 .all the unit digit form 1^3to9^3will multiplied for times like 1^3*3+2^3×3.....
=3+8....till unit digit of 9^3 *3
=9answer

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Vanitha  (8 years ago)

i cant understand this solution...anyone give an explanation..how ans will come 9....

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Bharat Ratna  (8 years ago)

Any even number multiple of 4 always gives 6 as unit digit while any odd number multiple of 4 always gives
1 as the unit digit.In the above question ,we have to find unit digit of S29.
#Alternately ,we get 1 and 6 as the unit digit upto S29.(that is 1+6+1+6+1.....)
Now, since no are continuous so no of 1's digit in 1 to 29 will be 29-1=28 and divide by 2=14(we are subtracting 1 as total no upto 29 is odd so to form pair we do so and add 1 ) .14+1=15
No of number containing 1 as unit digit =15 and 29-15=14 are the no containing 6 as the unit digit.
Afterthat , calculate the sum of all 15 no having 1 as unit digit=15
sum of all 14 no having 6 as unit digit=84
Lastly, add the values 15+84=99
So, unit digit of S29=9

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Amitkumar  (8 years ago)

unit digit of 1^8 = 1
similarly 2^8=6
3^8=1
4^8=6
5^8=5
6^8=6
7^8=1
8^8=6
9^8=1
10^8=0
addition=33
...so on
above repeats for 11.......29
33+33+33=99/10
reminder=9

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shivang pathak  (8 years ago)

A=18
b=10
c=2
put these values get a answer, after solve a question get these values

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