Hi All,
Certain Quant questions are built around relatively simple short-cuts; this prompt has a great built-in logic shortcut that you can take advantage of (and avoid lots of unnecessary calculations). As such, instead of thinking of the 'level' of this question, you should try thinking in terms of whether you could have gotten it correct in a reasonable amount of time or not.
We're told that X and Y are POSITIVE. That is an important 'restriction' that impacts how the math 'works' and we can use it to our advantage. Next, we're told that X+Y = 1. With this information, we know that both X and Y will end up being positive fractions.
We're asked for what COULD be the value of 100X and 200Y.
To start, it helps to think about the 'extreme' possibilities.
IF.... X=1 and Y=0, then the sum would be 100(1) + 200(0) = 100
IF... X=0 and Y=1, then the sum would be 100(0) + 200(1) = 200
Now, neither of those is a possible outcome (remember that BOTH X and Y have to be positive, and 0 doesn't fit that restriction), but they do provide the limits to the possible sum.
If we made X really small, then the bulk of the total would be in Y (eg. X=0.01 and Y= 0.99), so the sum would be REALLY close to 200. In that same way, if we made Y really small, then the bulk of the total would in X (eg. X= 0.99 and Y=0.01), so the sum would be REALLY close to 100. Moving the values in tiny increments would give us every possible value between 100 and 200, but NOT 100 or 200. Thus, Roman Numerals II and III are possible, while Roman Numeral I is not.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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