Sometimes the Quant is the Verbal
The GMAT only has two sections that count towards your overall GMAT score: Quant and Verbal. On a surface level, these two sections might seem vastly different, but in many ways each is testing the same underlying skills. For example, in the Quant section, many Data Sufficiency questions use basic rules of math (most of which you already learned in middle or high school) to test, among other things, your working memory and logical thinking skills. In the Verbal section, meanwhile, those same skills are tested on Sentence Correction questions—the key difference is that in SC, the questions are built around the basic rules of English rather than math.
Similarly, both sections constantly test your reading skills. But to go a step further, I would argue that some Quant questions are only incidentally testing your quantitative ability and are primarily testing your reading skills. In these questions, the math itself is straightforward; the challenge lies in correctly comprehending a complex set of instructions or description of a multi-step process. In other words, sometimes the Quant is actually the Verbal. Today, I’d like to look at two good examples of problems that do this.
Here is a GMATPrep problem. Set your timer for 2 minutes and give it a go:
A certain library assesses fines for overdue books as follows. On the first day that a book is overdue, the total fine is $0.10. For each additional day that the book is overdue, the total fine is either increased by $0.30 or doubled, whichever results in the lesser amount. What is the total fine for a book on the fourth day it is overdue?
See what I mean? The only math we have to do here is some very basic addition and multiplication, but that doesn’t necessarily mean that this is an easy problem. When the math is this easy, then it’s not really a math question—it’s a reading question, and the GMAT has ways of making the reading difficult. So we have to be very careful about reading and setting up the problem accurately based on the given instructions.
In this case, we’re given instructions for how a library assesses fines for overdue books each day a book is overdue. First of all, this is a completely real-world problem. We’ve all borrowed books from the library, and most of us have occasionally had to pay an overdue fine. Or maybe you’ve gotten a speeding or parking ticket, and you had to look on the back of the ticket to figure out how much it was going to cost you.
The point is, think about this from a real world standpoint, not a ‘math problem’ standpoint—we call this strategy make it real.
Then, I strongly recommend organizing the given information in a systematic way and just taking it one step at a time. Here’s what my setup looked like:
I wrote columns for each of the 4 days the book was overdue (Day 1, Day 2, Day 3, and Day 4), rows for the two choices at each day (adding 30 cents or doubling, whichever is lesser), and the goal (the total fine on Day 4). Then I filled in the 10 cents fine on Day 1. All we have to do now is figure out the total fine on the subsequent days. Here goes:
Notice that each day, I did both calculations—adding 30 cents to the existing fine or doubling the fine—and I wrote them both down. Once I had them both down, it was easy to see which one would result in a lesser fine, and so I went with that option (and crossed out the costlier option). On Days 2 and 3, the lesser fine results from doubling the existing fine (10 cents to 20 cents, then 20 cents to 40 cents), but on Day 4, the lesser fine results from adding 30 cents (40 + 30 = 70). So that’s a grand total of 70 cents, and that’s the right answer.
Where might people go wrong on this? Misreading the question to calculate the total fine 4 days after the first day a book is overdue (for a total of 5 days overdue) would lead you to answer E, $1.00. Or simply doubling the fine every day for 4 days would get you C, $.80.
You might be thinking, “That was easy, though. I just did that in my head and I got it right.” Well, if that’s the case, then good for you. But I didn’t do it in my head, not because I can’t, but because I don’t do GMAT problems in my head; I always write them down. Because I know that sooner or later, I’m going to be faced with problems that I can’t do in my head, and it’s better to use the same good habits and approaches on easy problems that I use on hard problems.
So let’s try another one, also courtesy of GMATPrep. Two minutes, and go:
Rates for having a manuscript typed at a certain typing service are $5 per page for the first time a page is typed and $3 per page each time a page is revised. If a certain manuscript has 100 pages, of which 40 were revised only once, 10 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed?
Here was my setup:
Again, think about this from a real-world standpoint. How much would it cost to get some pages typed up and some revised once or twice? First, every one of the 100 pages has to be typed ($5 each) before anything can be revised, so that’s already $500—that eliminates $430 as an answer.
Of those 100 pages, 50 don’t need any revisions at all, so we’re done with those.
Of the other 50 pages, 40 need a single revision ($3 each), and 10 need double revisions ($3 each, but twice per page). So that’s $120 for the single revisions and $60 for the double revisions.
Sum it all up and we have $680, which is the right answer. Here’s what my page looked like:
To wrap up: These problems are pretty straightforward, but they’re also easy to get wrong if you’re not careful. Some students see the long, wordy setup to these problems and feel like they need to read quickly to stay on pace, but that’s exactly the wrong thing to do. When you see a question like this, slow down, read carefully, think about it from a real world standpoint, organize the information on your page, and solve the problem one step at a time.
Next time, we’ll take a look at the same phenomenon in reverse: Verbal problems that are really Quant problems in disguise.