Latest TCS Aptitude Question SOLUTION: If x^y denotes x raised to the power y, find last two digits of (1941 ^ 3843)+ (1961 ^4181). a. 02 b. 82 c. 42 d. 22

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(#M40013140) TCS Logical Reasoning question Keep an EYE

If x^y denotes x raised to the power y, find last two digits of (1941 ^ 3843)+ (1961 ^4181).
a. 02 b. 82 c. 42 d. 22

Asked In TCS (11 years ago)

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Read Solution (18) :

Deepika  (8 years ago)

Step 1: (1941^3843)
Take last two digit 41 from 1941 and raise it to the unit digit power 3 from 3843. (i.e) 41^3 = 68921. From this take only the last two digit 21.
Step 2: (1961^4181)
Take last two digit 61 from 1961 and raise it to the unit digit power 1 from 4181. (i.e) 61^1=61.
Step 3:
Add that 21 + 61 = 82

Is this solution Helpfull? Yes (40) | No (1)  

Subhashini VKR  (11 years ago)

we should use power cycle method
take last 2 digit of 1941 take last 2 digits of 1961

41^1=41 r=1 61^1=61 r=1
41^2=81(take last 2 digits of ans)r=2 61^2=21 r=2
41^3=21 r=3 61^3=81 r=3
41^4=61 r=4 61^4=41 r=4
41^5=01 r=0 61^5=01 r=0
41^6=41 61^6=61
hence power cycle is repeating and it is 5 hence for 1961 it is 5
r-remainder for 1961 powercycle-5
for 1941 powercycle-5 4181mod5=rem1=61
3843mod5=rem 3=21
therefore 21+61=82

Is this solution Helpfull? Yes (31) | No (2)  

greeshma sajive  (10 years ago)

Remember 1 raised to any power will give 1 as unit digit.
To find the digit in the 10th place, we have to multiply, 10th digit in the base and unit digit in the power.
So the Last two digits of the given expression = 21 + 61 = 82

Is this solution Helpfull? Yes (16) | No (4)  

Subhashini VKR  (11 years ago)

we should use power cycle method
take last 2 digit of 1941
41^1=41 r=1
41^2=81(take last 2 digits of ans) r=2
41^3=21 r=3
41^4=61 r=4
41^5=01 r=0
41^6=41
hence power cycle is repeating and it is 5
similarly for 1961
61^1=61 r=1
61^2=21 r=2
61^3=81 r=3
61^4=41 r=4
61^5=01 r=0
61^6=61
hence for 1961 powercycle is 5
for 1941 powercycle-5
4181mod5=rem1=61
for 1961 powercycle is 5
3843mod5=rem 3=21
therefore 21+61=82

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spandana inti  (11 years ago)

last two digits of 1941^3843 is 21
last two digits of 1961^4181 is 61
so the last two digits of the whole sum is 82

Is this solution Helpfull? Yes (13) | No (30)  

LOVENEET SALHOTRA  (9 years ago)

1941^3843
it is a rule that numbers ending with 1 has at the end 1 at unit place as it is and at tens place we get as given below
multiply tens place of base number(1941) which is 4 and unit place of power(3843) which is 3
so 4*3=12 so consider 2 only
and here 21
similarly second one1961^4181 have 81
when they add up 21+81=01 ans

Is this solution Helpfull? Yes (7) | No (2)  

VAISHALI GOSAIN  (10 years ago)

Remember 1 raised to any power will give 1 as unit digit.
To find the digit in the 10th place, we have to multiply, 10th digit in the base x unit digit in the power.

So the Last two digits of the given expression = 21 + 61 = 82

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Varsha  (9 years ago)

Can you explain last two digits of 1941^3843 is 21?? how.?

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saurabh agarwal  (11 years ago)

81+21=102
ans02

Is this solution Helpfull? Yes (3) | No (18)  

karthikeyank  (9 years ago)

ANS IS : 82
Remember 1 raised to any power will give 1 as unit digit.
To find the digit in the 10th place, we have to multiply, 10th digit in the base and unit digit in the power.
So the Last two digits of the given expression = 21 + 61 = 82

Is this solution Helpfull? Yes (3) | No   

chandra  (11 years ago)

spanda way of think that problem and getting answer is i hope correct ... thank"S spandana

Is this solution Helpfull? Yes (2) | No (3)  

SumithraRengaraj  (9 years ago)

last two digits of 1941^3843 is 21
last two digits of 1961^4181 is 61
so the last two digits of the whole sum is 82

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

Srinadh   (9 years ago)

3843 should in the form of [4n+x], therefore x=3. so find last 2 digits of [1941]^3, we get 21.
similarly for 4181., we get x=1, so [1961]^1,we get 61.
Therefore laste two digits is 21+61=82

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DURGA SATISH  (11 years ago)

explain clearly@spandana

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C BALAKRISHNA  (9 years ago)

82

Is this solution Helpfull? Yes | No (1)  

RAVI K  (8 years ago)

Remember 1 raised to any power will give 1 as unit digit.
To find the digit in the 10th place, we have to multiply, 10th digit in the base x unit digit in the power.


So the Last two digits of the given expression = 21 + 61 = 82

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Balakrishna Karusala  (7 years ago)

Here Answer is 82

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Shekhar  (5 years ago)

1+1=2 last digit
4+6=10 therefore 0 is second last digit

And : 02

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