Latest TCS Aptitude Question SOLUTION: what is the last two digits of 259^66

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(#M40030109) TCS Numerical Ability question number Keep an EYE

what is the last two digits of 259^66

Asked In TCS PRIYA NAMDEO (11 years ago)

Unsolved Read Solution (9)

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Read Solution (9) :

Mahesh  (11 years ago)

The given problem can be expressed as

(250 + 9) ^ 66 = 250^ 66( that is 66 C 1) + 66 * 250^ 65 * 9 + .............
+ 66* 250 * 9 ^ 65 + 9 ^ 66

All the first 65 terms have 250 raised to at least a power of 2, so all these terms have the last two digits as zeroes
The 66 th term has 66 * 250, so the last two digits again will be zero.

So, the only term that influences the answer is the last term, 9^ 66

So, we have to simply understand the pattern of the last two digits of 9 powers

The pattern for 9 power 1, 2, 3, 4 ,5 and so on is

09, 81, 29, 61 we can observe an alternate series of increase and decrease of 20

So, the first 20 terms are
09, 81, 29, 61, 49, 41, 69, 21, 89, 01, The series again continues 09, 81, 29, 61


So, the given expression is following a cycle of 10. So, 66 th term will be same as 6 th term, 41 will be the answer.

Answer is 41.

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ritesh dewangan  (11 years ago)

259^66=67081^33
last two digit is 81.
so 81^33= 531441^11
last two digit is 41.
now....
41^2=1681
41^3=68921
41^4=2825761
41^5=115856201

means last two digit is 01

so we can write...
41^11=41^5 * 41^5 * 41
=01*01*41
=41.
so 41 WILL BE ANSWER ..

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Sam  (11 years ago)

(259)^66=(259^2)^33=(last two digit of 259^2)^33=(91)^33=last two digit of (91)^33=71

Is this solution Helpfull? Yes (3) | No (5)  

Manisha Choudhary  (11 years ago)

(259)^66=(259^2)^33=(last two digit of 259^2)^33=(91)^33=last two digit of (81)^33=41

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DEEPAK SINGHAL  (11 years ago)

ans will be 29

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

sanjeet  (10 years ago)

we have to calculate last to digit
(259)^66
means 59^66=(59^2)^33=(81)^33
i.e last digit 1
second last 8*3=24 means 4
so 41 is the ans

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avnish pandey  (11 years ago)

9^2n=(.....1).. so it will be 1!

Is this solution Helpfull? Yes | No (3)  

Punit  (10 years ago)

simply ((259)^2)^33)= (67081)^33 >>>> last two digit will be 41

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sourav saha  (8 years ago)

last digit=9^66
=(3^2)^66
=(3^4)^33
=81^33
1^3=1
8*3=24
then last two digit=41

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