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Unofficial Guide 2016 PS 162

I’m going to do a number of these posts. You can think of them as commentary on the 2016Official Guide for GMAT Review. I’m going to use the abbreviations OG, PS, DS, RC, CR, and SC for Official Guide, Problems Solving, Data Sufficiency, Reading Comprehension, Critical Reasoning, and Sentence Correction, respectively. Sometimes I’ll present alternative solutions, more detailed solutions, and, occasionally an example problem.

I can’t reproduce the problem here, so if you don’t have your official guide handy, now would be the time to break it out – page 175

The authors of the OG solve the problem in a traditional frontal-assault manner. They manipulate two equations with two variables to produce a quadratic equation.

\(t^2 + 4t – 672 = 0\)

Based on their solution, the average student should know that \(672 = {28}\times{24}\). Not exactly a fact that the average student has at her firgertips. Don’t get me wrong, math facts are your friends, but this is a bit extreme.

Unfortunately, most of my students end up with that equation, and I might write a post about how to solve it if I run out of beer and useful things to do at the same time, but first we should evaluate how we got into this predicament from a strategic point of view.

Usually, our friend Don gets paid \(r\) dollars per hour and he estimates that a repair job will take \(t\) hours with a total cost of $336. Of course the job actually takes \(t + 4\) hours, and because he can’t change his estimate, he ends up being paid \(r – 2\) dollars per hour. So, we’ve got the following two equations:

\(rt = 336\)
\((t + 4)(r – 2) = 336\)

Hopefully, you recognize that this is going to turn into a quadratic. The archetype for this problem goes like this: If the perimeter of a rectangle is \(x\), and the area is \(y\), what are the dimensions of the rectangle? Everybody did at least one of these in high school… but this isn’t high school. So, what now?

  • STOP!
  • THINK!

Do you really want to solve that system of equations? Of course not. You’re too tired, too annoyed, and you’ve got to solve even more problems, and then there’s the Verbal Section… Before you walk out of the testing center or use your OG to get the grill going

Check your answers! Start with B or D (if you are a “pick C” person, I beg you to reconsider).

I’ll start with D for illustrative purposes.

If Don estimated 14 hours, then his rate would be

\(\Large\frac{336}{14}\) \( = \)\(\Large\frac{336}{(2)(7)}\)\( = \) \(\Large\frac{168}{7}\)… Seven goes into 16 two times, remainder 2,.. 28, seven goes into 28 four times…24!!!

So if Don really worked \(14 + 4 = 18\) and was actually paid \(24 – 2 = 22\) dollars per hour, then his estimate was

\({18}\times{22} = (20 – 2)(20 + 2) = 400 – 4 = 396\)

Nope. Too big – more hours, smaller wage, so check B.

It works!!!

See, that wasn’t too bad.

In sum, stop and think before you charge ahead into a thicket of nasty equations. There’s probably a better way to solve the problem.

Take a look at problem 208 on page 182. It’s essentially the same problem.