tens' digit

IMO 4

7^1-7
^2-49
^3-343
^4-2401
^5-16807
^6-....649
.
.
.
and so on... if you see the 4 appears in the pattern shown when it is squared to 2 and its multiples.. get a calculator and see for the first 10 numbers....

shibal wrote:IMO 4

7^1-7
^2-49
^3-343
^4-2401
^5-16807
^6-....649
.
.
.
and so on... if you see the 4 appears in the pattern shown when it is squared to 2 and its multiples.. get a calculator and see for the first 10 numbers....

please elaborate some more on ur solution..
thanks

Please check the pattern.

The tens digit follows a pattern of 0, 4, 4, 0 for first, second, third, fourth square powers of 7. This pattern is repeated.

so, 2002 = 2000/4 + 2.

So, after 2000 times, the tens digit will be 0.
after 2002 times, the tens digit will be 4.

Hope you got it.

thanks gmat_dest,
i got it!! missed something earlier..
thanks again..

I have found another way of solving the problem...but aint sure if the mechanism is alright:

7^2002 = (7^2)^1001 = 49^1001.

If we look closely, we can find that the last two digits of the result for 49^1001 will be 49, because 49 is being multiplied by 01 of 1001 while deriving the result.

So the answer is 4.

49 is NOT being multiplied by 01 of 1001. 1001 is the power not a co-efficient. One solution that I know of is the pattern-solution (someone already posted the solution).