Hi All,
We’re asked which of the following Roman Numerals can be written as an INTEGER.
While Roman Numeral questions can sometimes be time-consuming, this one is relatively straight-forward and is built on a couple of Number Property rules that can help you to avoid doing heavy calculations. You also do not need to consider all 3 Roman Numerals to answer it…
First, it’s worth noting that 82 is NOT a Perfect Square (if you know your Perfect Squares at this point, then you know that 9x9 = 81 and 10x10 = 100 are the two Squares just ‘below’ and ‘above’ 82, respectively).
I.
Adding any two identical terms together can be rewritten as 2(that term). For example, 3 + 3 = 2(3)…. X + X = 2(X)…. Etc.
Here, we’re adding root-82 to root-82, so that’s 2(root-82). Squaring that term would give us (2)(2)(82)… which is clearly an INTEGER (it’s 328, but you don’t actually have to do that math).
III.
Here, we are multiplying the same Square Root against itself – and any time you do that, you end up with the original integer. For example (root-4)(root-4) = (2)(2) = 4… (root-5)(root-5) = 5… Etc.
Thus, we would end up with 82 in the numerator and 82 in the denominator – and 82/82 = 1. This also is clearly an INTEGER.
Based on how the Answers are written, we can stop working.
Final Answer: E
GMAT Assassins aren’t born, they’re made,
Rich
