Adv. Quant - WS 4 - #33 (suggestion)

[dudewheysmehemail]

Hello MGMAT team,

I'm working through the workout sets in the Advanced Quant guide and I don't agree with part of the explanation of #33 and wanted to share my thoughts and maybe in a future release of the book it can get adjusted.
(This is from Workout Set #4, Question #33. Question is on page 238 and the Explanation is on page 293.)

In my scratch work I added xy + xy to get 2xy, rephrasing the question to is "2xy < xy?". I then rephrased this to "is xy negative?".
I got to this rephrase because the only way 2xy could be less than xy is if xy was negative (for example, let -2 = xy).
Then 2xy would be 2(-2) = -4.
-4 < -2.

In the explanation, it says that the proper rephrase is from subtracting xy from both sides to get "is xy < 0?", and then goes on to say to be careful not to rephrase as 2xy < xy because "2 is definitely not less than 1, no matter what the statements say."

Just wanted to clarify that it still is possible to get to the correct rephrase through 2xy < xy and the logic behind it, and hopefully this will in turn increase the quality of this already great product!

Many thanks!
--Rishi

[StaceyKoprince]

Actually, it's saying not to rephrase through the multiple steps there that include dividing by variables when we don't know whether the variables are positive or negative. The mistake is in that step (as noted in the book), not in the first step.

So, yes, you can take just that first step that you took... and then take the next step the book describes as the right way, which is to subtract an xy from both sides and get "is xy < 0" = is xy negative. :)