Hi All,
Roman Numeral questions are relatively rare on the GMAT - you will likely see just one in the Quant section. In addition, they are often built with a 'shortcut' so that you don't actually have to do all of the work to get the correct answer. To take advantage of that potential shortcut when it's available, you have to pay attention to how the answer choices are organized.
Here, we're told that A and B are INTEGERS and that they are DISTINCT (meaning different) factors of 30. We're asked which of the three Roman Numerals CANNOT be a factor of 30 (which really means 'cannot ever be a factor of 30 no matter how many different examples we can come up with..."). The word DISTINCT is important here - in Quant questions, that means the variables are DIFFERENT numbers. If we can prove - even if it's just with one example - that an option CAN be a factor of 30, then we can eliminate that option from the answers.
To start, let's list out the factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
I. A^2 + B^2
Can you pick two DIFFERENT numbers from that list for A and B here that creates another value from that list?
IF....
A=1 and B= 2, then A^2 + B^2 = 5
Thus, Roman Numeral I COULD be a factor of 30.
Eliminate Answers A, D and E.
From the remaining answer choices, we know that one of the Roman Numerals CAN be a factor of 30 and the other CANNOT, so let's deal with the easier option first....
III. A + B
Can you pick two DIFFERENT numbers from that list for A and B here that creates another value from that list?
IF....
A=1 and B= 2, then A + B = 3
Thus, Roman Numeral III COULD be a factor of 30.
Eliminate Answer C
There's only one answer left...
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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