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tens' digit

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Source: — Problem Solving |
Master | Next Rank: 500 Posts
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by shibal » Tue Jul 21, 2009 5:15 pm
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....
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by ketkoag » Wed Jul 22, 2009 1:29 am
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
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by gmat_dest » Thu Jul 23, 2009 7:59 am
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.
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by ketkoag » Sat Jul 25, 2009 11:51 am
thanks gmat_dest,
i got it!! missed something earlier..
thanks again..
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by wanttobeat » Mon Jul 27, 2009 12:04 am
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.
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by gmat_2010 » Thu Jul 30, 2009 4:24 am
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).
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