Latest TCS Aptitude Question SOLUTION: Find the remainder when number represented by 22334 raised to power (1^2+2^2 +......+66^2) is divided by 5

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Find the remainder when number represented by 22334 raised to power (1^2+2^2 +......+66^2) is divided by 5

Asked In TCS Amisha Agarwal (10 years ago)

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Arpit Srivastava  (10 years ago)

1^2+2^2+.....+66^2=n*(n+1)*(2n+1)/6=98021
22334^98021/5
rem of 22334/5=4
hence 4^98021/5
=4..ans

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rohan chawla  (10 years ago)

answer is 4

we know a number with units digit as 4 raised to any power has units digit 4 or 6
so when we divide the number by 5 we have to check units digit
if units digit is 4 remainder is 4 and if units digit is 6 remainder is 1

now 1^2+2^2+.....+66^2 has 33 even terms i.e 2,4,6 etc whose square is always even
so when all these even terms are added we get another even term
this expression has 33 odd terms whose square is always odd
so when these 33 odd terms are squared and added we get sum of 33 odd terms which is odd

so we see that there is an addition of even and odd terms which give the overall result as odd
so the number is raised to odd power so its unit digit is 4
as number whose unit digit is 4 when this number is raised to odd power we get 4 as unit digit
for ex 4^1 = 4, 4^3 = 64 etc

so as the unit digit of the number is 4 we get the remainder as 5

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madhurima  (10 years ago)

ans may be 4

Is this solution Helpfull? Yes (1) | No   

Kunal Verma  (10 years ago)

check mail

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