The 5 lb. Book: Regular Quant Problems with Translation
We’re very excited because our latest book, the 5 lb.Book of GRE Practice Problems, is about to hit shelves! The book contains more than 1,100 pages of practice problems (and solutions), so you can drill on anything and everything that might be giving you trouble.
Let’s try out one of the problems! This regular problem solving question asks us to pick one correct answer (other variations might ask us to select more than one answer or to type in our own answer). Give yourself approximately 2 minutes to finish (or guess). Afterwards, we’ll solve the problem and also discuss how to approach these in general
A taxi driver makes $50 an hour, but pays $100 in rent per day of use for his taxi and has other costs that amount to $0.50 per mile. If he works three 7-hour days and one 9-hour day and drives a total of 600 miles in one week, what is his profit?
(A) $700
(B) $800
(C) $1,100
(D) $1,200
(E) $1,500
© ManhattanPrep, 2013
Translation questions are the bane of most test-takers’ existence. (Don’t know the word bane? That’s a great GRE word “ go look it up!) First, we have to figure out how to re-write a paragraph in mathematical terms, and then we still have to do the actual math!
A number of techniques can help us with these tasks. We’re going to start with one discussed in our main Translations article: make it real. (Follow the link to the main, 2-part article, if you haven’t already read it.)
Make the story real
The problem no longer says taxi driver. Instead, your name is sitting there “ you’re the taxi driver. Now, what do you need to know in order to figure out how much money you get to keep at the end of the week?
Well, let’s see. First, I’d figure out how much I made, but then I’d have to subtract all of my costs. That’s how much I get to take home: my profit.
Revenue “ Cost = Profit
Now, calculate
I make $50/hr. For three days, I drove 7 hours a day, or 21 hours, and on a fourth day, I drove 9 hours, for a total of 30 hours that week. So I must have earned $50/h ´ 30h = $1,500. Great.
Now, what were my costs? I pay rent and I also have a per-mile usage cost.
I drove the taxi on 4 different days and I have to pay rent of $100 for each day that I used the taxi. That’s $400.
I also have to pay $0.50 per mile and I drove 600 miles, so I have costs of (0.5)(600) = $300. In total, my costs amount to $700.
Double-check: did you solve for the right thing?
$700 is an answer to this question “ but it’s a trap answer. The question asks for my profit, not for my costs. My profit is $1,500 “ 700 = $800. (Note that $1,500 is also among the answers!)
The correct answer is B.
We got through all of that while writing down only one real formula: R “ C = P. Many times, on story problems, we can get away with not setting up formal equations or official math. Instead, when we put ourselves into the story, we can use real-world common sense to work through each step.
Key Takeaways for Story Problems:
(1) Whenever possible, try to make the story real. Insert yourself into the story and ask yourself what you’d need to figure out if this were actually happening in the real world.
(2) Do write down your work “ but you don’t necessarily need to write out tons of formal equations. If the problem can be done using real-world common sense, that’s great!
(3) Aim for about 2 minutes, on average, for the more regular math problems. Quantitative Comparisons (which we’ll cover in another article) should be faster “ about 1 minute 15 seconds on average.
© ManhattanPrep, 2013