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GMATinsight I feel that the question would become more interesting (and I think also more realistic) if the answer choices are less dispersed. Maybe something you can think about.
there are 19 numbers containing atleast one seven from 100 to 200. The same will be true for the eight following hundreds sequences except the 700-800 sequence. The 700 - 800 sequence contains 100 numbers that has atleast one seven in it . So the total no of digits can be calculated as 8*19 + 100 = 252. Ans D