Hi All,
This question is an example of a "symbolism" question. You'll typically see 1 or 2 on Test Day and they almost always involve some type of simple arithmetic or algebra. The real "work" that you have to do is really about paying attention to what you're told about the symbol and how the symbol "works." You'll then be asked to perform a calculation using the symbol.
Here, we're told that for all integers X> 1, <X> = 2X + (2X-1) + (2X-2)+....+2 + 1
At first, this might look a little complicated, but symbolism questions usually DON'T involve complicated math, so we just have to figure out what this *really* means. Before I read another word of this question, I'm going to "play around" with this symbol a bit by TESTing VALUES....
Let's say X = 3....According to this symbol:
<X> = 2X + (2X-1) + (2X-2)....2 + 1
<3> = 2(3) + (6-1) + (6-2) +....+2 +1...
So....
<3> = 6 + 5 + 4 + 3 + 2 + 1 = 21
This isn't very hard at all; whatever number is inside the symbol, we just have to add it to the sum of every positive integer LESS than that number all the way down to 1.
From here, the rest of the work isn't that hard (both Bunuel and ravitejar have worked through those steps, so I won't rehash any of that here). Remember to stay calm and organized on Symbolism questions on Test Day - while relatively rare, they're usually some of the easiest points to pick up in the Quant section.
GMAT assassins aren't born, they're made,
Rich
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