Quant Comp Guide page 29

[supswap27]

For the example on the top of Guide 6 on page 29, what does sentence: "Notice the Quantity B, 1/2+1/4+1/8, is less than 1/2+(1/4+1/4), and so must be less than 1. - - - where do you get the last part from..1/2+(1/4+1/4)?

[esledge]

The 1/2 +(1/4 + 1/4) is what I would call a "convenient hypothetical." If Quantity B were 1/2 + (1/4 + 1/4), it would be pretty easy to add (you might even do it in your head), getting a total of 1.

So the point of that sentence is that Quantity B must be less than 1, because the real last term 1/8 is less than the convenient hypothetical last term 1/4.

Using 1 as a benchmark value is smart here, not just because Quantity B can be shown to be <1 (per the above), but because we can do similar logic with Quantity A. It is the reciprocal of Quantity B, so Quantity A is >1.