For this question, you have two variables. The number of marbles, and the er, 'filledness' of the bowl (excuse my made-up word). You need a way to link the two variables together at least, for the answer to be somewhat possible. So (1) alone is not sufficient, because we are only talking about proportions of marbles and proportion of the bowl filled, regardless of what the actual fractions are. There's no way to work out the number of marbles in this case. We need to have at least a specific number of marbles corresponding to a proportion, somewhere, to maybe figure it out. (2) specifies a number of marbles, but doesn't correlate this to a particular proportion. So no, (2) is not sufficient either.

Then, if we have both... so from (1), we can figure out that 1/2 of the capacity of the bowl is equal to 3/4th the number of marbles initially there. If that's the case, then at the original number of marbles must be the reciprocal of 3/4 * 1/2, so 4/6 (or rather, 2/3) of the bowl was initially filled with marbles. We can work this backwards to be sure: if the bowl was 2/3 filled, and we took out 1/4th of the marbles, then we have 2/3 * 3/4 = 6/12, or 1/2. Now, knowing how much of the bowl was initially filled, we know from (2) that adding 100 marbles fill up the bowl, so in this case 100 marbles = 1/3rd of the bowl, and thus 2/3rd of the bowl would be filled with 200 marbles, which is also the starting number of marbles.

Tada! I hope. Not a math expert, but that's my two cents. Answer is C.

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Not a professional entity or a quant/verbal expert or anything. So take my answers with a grain of salt.