Latest Elitmus Aptitude Question SOLUTION: what is the last four digits of (3030303)^4?

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what is the last four digits of (3030303)^4?

Asked In Elitmus zen mano (10 years ago)

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Glued Brain  (10 years ago)

Since we need the last 4 digits, consider only the last 4 digits i.e. 0303..
1. 0303 * 0303 = 91809
Now we will again consider only the last 4 digits i.e. 1809
2. 1809 * 0303 = 548127
3. 8127 * 0303 = 62481
Now, the last 4 digits are 2481 and is the required answer..

Is this solution Helpfull? Yes (53) | No (1)  

Najid  (10 years ago)

last 4 digits 2481

Is this solution Helpfull? Yes (6) | No   

P.Someshwar Reddy  (10 years ago)

The answer I gave 3481 is wrong, it is due to the calculation mistake, the correct answer is 2481.
don't multiply the whole number four times, since we need the last four digits of the result take the last three numbers,
that is from the number 3030303 take the last three they are 303, so now multiply these last three number four times you will find the result as 2481.

Is this solution Helpfull? Yes (6) | No (1)  

mithlesh dhore  (10 years ago)

the last digit is 1

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

Anusha  (10 years ago)

split the number and make it 3030300+3
So now expand (3030300+3)^4 using binomial theorem.
=3030300^4 + 4c1*(3030300^3)*3 + 4c2*(3030300^2)*(3^2) + 4c3*(3030300)*(3^3) + 3^4

Now consider the last 4 digits of each term and add them!
So we get
1st term=0000
2nd term=4*3 = 12
3rd term = 9*6 = 54
4th term= 27*4*3030300 = 2400 (last 4 digits)
5th term = 81

so adding them, the last 4 digits are = 2574

Is this solution Helpfull? Yes (3) | No (25)  

Harshal Raverkar   (10 years ago)

303*303*303*303=
Last digit is 2481

Is this solution Helpfull? Yes (3) | No (1)  

P.Someshwar Reddy  (10 years ago)

the last four digits are 3481
don't multiply the whole number four times, since we need the last four digits of the result take the last three numbers,
that is from the number 3030303 take the last three they are 303, so now multiply these last three number four times you will find the result as 3481.

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

SAMBIT KUMAR GHOSH  (10 years ago)

last four digit will be 2481

Is this solution Helpfull? Yes (1) | No   

Anusha  (10 years ago)

Sorry my previous answer was wrong, had some wrong calculations.
The correct answer is 2481.

Is this solution Helpfull? Yes (1) | No   

Hafiz Hussain  (10 years ago)

3481, 3030303*3030303 take last 4 digits 1809 then jus take the square of this number alone and take last 4 digits 3481

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sushmita nigam  (10 years ago)

its 2481 by multiplying the last 3 digits

Is this solution Helpfull? Yes (1) | No   

FRANTTO  (10 years ago)

ans is 1....

Is this solution Helpfull? Yes | No (4)  

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