Latest TCS Aptitude Question SOLUTION: 1541^1041 + 1671^2356 . find last two digits?

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1541^1041 + 1671^2356 . find last two digits?

Asked In TCS sanjeev (11 years ago)

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utkarsha  (11 years ago)

by checking the periodicity of the last two digits of each no.
for ex- periodicity of 41 in 1541= 5
periodicity of 71 in 1671= 10
therefore, 1041%5= 1 and 2356%10= 6
hence, 41^1 + 71^6(=last 2 digits=21)=62

Is this solution Helpfull? Yes (19) | No   

lucky  (11 years ago)

62,as the unit digit is 1

Is this solution Helpfull? Yes (5) | No (6)  

nirvan gupta  (11 years ago)

@utkarsha periodicity of 1741 would be 6
and ans would be 41^3+71^6=42

Is this solution Helpfull? Yes (1) | No (5)  

anand singh  (11 years ago)

(1541)^1041 + (1671)^2356
(1541)^1041 + (5041)^1178
cyclicity of 41 is 5.. so..
(1541)^1 + (5041)^3
(41)^1 + (41)^3
41 + 21
last two digit is 62.

Is this solution Helpfull? Yes (1) | No   

Maitreyi Sutradhar  (8 years ago)

1 raised to any power will give 1 as unit digit
To find the digit in 10th place,
10th digit in base*unit digit in power
1541^1041+1671^2356
so,
41+21=62
last two digit=62

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Akash Ayush  (8 years ago)

Any number whose unit digit is 1 will always give 1 as unit digit if it is multiplied by itself any number of times.

So both 1541^1041 and 1671^2356 will have 1 at its unit place.

Now to calculate the ten’s place there is a short trick. (This is applicable only in the case of number with unit digit as 1)

Multiply the ten’s place digit of the base with the unit place digit of power.

In 1541^1041 the ten’s place digit of the base is 4 and unit place digit of the power is 1. Multiply 4 x 1 which gives 4. This will be the ten’s place of 15411041.

So the last two digits of 1541^1041 is 41.

Now in 1671^2356 the ten’s place digit of the base is 7 and unit place digit of the power is 6. Multiply 7 x 6 which gives 42.The unit digit of this product which is 2 is the ten’s place digit of 1671^2356.

So the last two digits of 1671^2356 is 21.

As a result the last two digits of 1541^1041 + 1671^2356 = 41 + 21 = 62

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Somnath Yadav  (7 years ago)

people there is one more easy trick to solve this:
1541^1041 is the first function
first we multiply unit digit of 1541 i.e 1 with unit digit of 1041 i.e again 1..so we get 1..which is the unit digit of the ans of 1541^1041 ...
now for the tens place of 1541^1041 we multiply 4 of 1541 with unit digit of 1041 we get 4..
so the ans of 1051^1041 is 4&1 i.e 41....
similarly for 1671^2356 we repeat the above process ..first we take unit digit of 1671 i.e 1
next we multiply 7 of 1671 and 6 of 2356 i.e 7*6=42...from 42 we only take 2 for the tens place of the ans of 1671^2356 so we get 21 as last two digits..
now finally we add 21+41(last two digits of 1541^1041)= 62 is the ans..

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