Latest CTS Aptitude Question SOLUTION: Q. What will be in unit\\\'s place digit of 3 to the power 34. option: A) 1 B) 6 C) 3 D) 0 E) 9

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Q. What will be in unit\'s place digit of 3 to the power 34.
option:
A) 1
B) 6
C) 3
D) 0
E) 9

Asked In CTS SOUVIK TALUKDAR (10 years ago)

Solved Juhi Kumari Read Solution (15)

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Read Solution (15) :

Juhi Kumari  (10 years ago)

9 is the answer... as the unit place digit of 3 to the power of 1 is 3, to the power of 2 is 9.to the power of 3 is 7 ,to the power of 4 is 1 and it'll be repeated again in the same order.... so the unit place digit of 3 to the power of 34 is 9..

Is this solution Helpfull? Yes (19) | No (3)  

palas pore  (10 years ago)

to find unit digit take last two digit of the power and then divided it by 4
and use remainder as a power of no
like 3^34
34/4 remainder will be 2
then 3^2=9
ans E) 9

Is this solution Helpfull? Yes (19) | No   

DHAKAD NEETENDRA SINGH  (10 years ago)

units place of 3 repeats after four places 3 9 7 1 3.....
s0,
= 34/4
= 2 remainder
now, 3^2=9 ans...

Is this solution Helpfull? Yes (7) | No   

Sourav Das  (10 years ago)

we know 3^4=81 & 81^any value = number with 1 at unit place
so ((3^4)^8)*3^2= number with 1 at unit place * 9 = number with 9 at unit place.
so option E is right

Is this solution Helpfull? Yes (6) | No   

S.SHAFI  (10 years ago)

ans) E
Unit's place digit of 3 to the power 34 is 9
3^34 = 3^(4*8)x3^2 ==> 3^2 ==> 9

Is this solution Helpfull? Yes (6) | No   

Rituparna Chakraborty  (10 years ago)

3^34
=(3^2)^17
=(9)^17
=(9)^16*9
=(9^2)^8*9
=(1)^8*9 [(9^2)=81,so we take unit place digit so (9^2)^8=(1)^8]
=1*9
=9
So 9 is the answer.

Is this solution Helpfull? Yes (6) | No (2)  

K.Prasanna  (10 years ago)

3^34=(3)^4*8+2
=(3)^2
=9
As by formula a^4k+2=a^2

Is this solution Helpfull? Yes (4) | No   

Parul  (10 years ago)

cycle of 3 is 3,9,7,1 it is repeated after every fourth intrval. so the ans is 9

Is this solution Helpfull? Yes (2) | No   

AMIT KUMAR  (10 years ago)

3^x follow a patten unit place

3^1 = 3 3
3^2 =9 9
3^3 = 27 7
3^4 = 81 1
3^5 = 243 3
3^6 = 729 9
34/4 = remainder will be 2
ans>>>>>>>>>>>>(e)9

Is this solution Helpfull? Yes (2) | No   

vishalsenapati  (10 years ago)

3^32*3^2=3^34
the unit digit of 3^32 is 1(3*3*3*3=81)and 3^2 is 9
so 1*9=9(ans)

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shweta das  (10 years ago)

9, as 3^4=1 always.so,3^34 can be written as (3^4)^8 *3^2.so, by this we get,1*9=9

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rakesh bhagat  (8 years ago)

its based on cycle of a number.
cycle of 3 is 3,9,7,1
now devide the power by 4 we get 2 as reminder
it means the 2nd no in cycle is at unit place

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shweta kumari  (7 years ago)

e is the right ans becaz 1,3,9,7 is repeadted

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suryacsr  (6 years ago)

Cyclicity of 3 is 4 that means 3^4=81 here last digit is '1'
then find out last digit of 3^34
3^32 get last digit is 1 remaining 3^2 =9
therefore 3^32*3^2=1*9=9

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Trishita Nath  (5 years ago)

(3)^34=((3)^2)^17
=(9)^17
We know that for odd power of 9 unit digit is 9 and for even power unit digit is 1.
Here power is odd so unit digit=9

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