ANS: 6823
SOLUTION :
N=199*QUOTIENT= (200-1)*QUOTIENT:
Let abcd be the last 4 digits of the QUOTIENT.:
Then the QUOTIENT will be terminated xy00, xy resulting from multiplying cd by 2.
So the subtraction looks like:
xy00
abcd
________
7777
Therefore d=3 and c=2
x=2*d=6
y=2*C=4
and the quotient's last figures are 6823.

Please see Justin's solution(simple and beautiful) and Jer's and Charlie's verifications.)

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