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this is a great ratios problem, and if ratios & proportional thinking are not familiar to you, i strongly recommend watching the "intro to ratios" lesson video below. 

the revenue is divided in a 6 to 5 ratio. that means, doug gets 6 parts, and moira gets 5 parts. notice, right there, doug gets more than moira, because 6 > 5. if two people split something evenly, each gets half, but if they split it unevenly, the one with more always gets more than half and the one with less always gets less than half. doug gets more than half of the total, 6 parts of 11 parts, and moira gets less than half. 

whenever you see "more than half" or "less than half" pop up as conditions in a question, especially a qc, keep your antennae up for estimation possibilities, discussed in this gre blog, and if you want more information, also check out this gmat blog.  

what's half of $15,700? that would be $7,850, a simple calculator calculation. moira's share is less than half, that is, less than $7,850, which in turn is less than $7,900. therefore, column b is bigger. answer = b

you don't need to calculate the exact value of moira's share to answer the question, but if you are curious about how to do that, you create the fraction of her share by putting her "parts"—five parts—over the total number of "parts"—eleven parts.  moira gets of the whole.  × $15,700 = $7,136.36. knowing how to calculate that could be a valuable skill on a multiple choice question about proportional thinking, but on a quantitative comparison question like this, the estimation demonstrated above is definitely far more important to understand.