Latest TCS Aptitude Question SOLUTION: 2988^687,what will be the last 3 digit

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2988^687,what will be the last 3 digit

Asked In TCS pre (10 years ago)

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Sambit Panda  (10 years ago)

988=(990-2)^687
if we subtract last 3 digits of 2^687 from the last 3 digits of 990^687(which will be 000) then we get the last 3 digits of 2988^687
The last 3 digits of 2^687=8*2^684=8*16^171=8*16^(5*34+1)=16*8 i.e 128, so last 3 digits of 2988^687 is ....0000-128=872

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Smart  (10 years ago)

ans:872
period of 8 (8,4,2,6,8,4,2,6........) is 4,hence when 687 divide by 4 we will get 3 as remainder
hence for last 3 digit no we just have to calculate 88^3=(88*88)*88=44*88=872(last 3 digits)

Is this solution Helpfull? Yes (15) | No (7)  

satyam shivam  (10 years ago)

divide 687 by 4
then rem will be 3
so 8^3 is 512
that is ans.

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

vinay  (10 years ago)

592 must be the answer.

Is this solution Helpfull? Yes (6) | No (4)  

tauseef arbab  (10 years ago)

562 is the answer

Is this solution Helpfull? Yes (5) | No (11)  

Abhishek Chand  (10 years ago)

ans is 512

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

Rahul Singh  (10 years ago)

please explain the procedure....

Is this solution Helpfull? Yes (2) | No   

Chandan Kumar Nayak  (10 years ago)

Last 3 digit of the expression 2988^687 depends upon last 3 digit of 88^687. So last 3 digit of 88^687= (2*44)^687 -> = 2^687 * 44^687 -> = (2^10)^68 * 2^7 * (44^2)^343 * 44 -> = 76 * 28 * 16 * 44 -> = 1498112 .... So 112 will be the last 3 digit

Is this solution Helpfull? Yes (2) | No   

Sambit Panda  (10 years ago)

988=(990-2)^687
if we subtract last 3 digits of 2^687 from the last 3 digits of 990^687(which will be 000) then we get the last 3 digits of 2988^687

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

ankush vaishya  (10 years ago)

Unit Digit of any no. repeats after power 4n where n=0,1,2.....
Ex.:-7^1=7
7^2=9(Unit digit)
7^3=3(Unit digit)
7^4=1(Unit digit)
Unit Digit of 7^5=7 is same as 7^1=7.
i.e.in this question divide 687 by 4.then rem will be 3 so 8^3=512.

Is this solution Helpfull? Yes (1) | No (4)  

Chandan Kumar Nayak  (10 years ago)

(2^10)^68 * 2^7 * (44^2)^343 * 44
= 76 * 28 * 16 * 44(last two digits of each expression) = 1498112 ....

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

saradha devi  (9 years ago)

Take last three digits.
988^1=988
988^2=144
988^3=272
988^4=--6
last digit repeats for every 4 cycle, 687 % 4= remainder is 3
so 272 is the ans.

Is this solution Helpfull? Yes (1) | No   

simmi  (10 years ago)

91 is the answer

Is this solution Helpfull? Yes | No (12)  

Shashank Salaj  (10 years ago)

2888^687
dividing 687 by 4 gives a remainder 3.
no 8^3= 512
so last 3 digits of 2988^687 is 512

Is this solution Helpfull? Yes | No (13)  

abhijit gupta  (10 years ago)

192
check your windows calculator
go by options is what i can suggest
check last digit ie 2
then second last digit 88^7=92

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Sana  (10 years ago)

Answer is 984

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