Nate Burke is a Content Developer at Knewton, specializing in GMAT prep.
In Part I of this series, I talked about approaching wordy GMAT questions as a businessperson would–by carefully reading these questions the first time around in order to absorb all information. The following GMAT problem has inspired me to expand this approach questions to include the actual process of decision-making:
A square countertop has a square tile inlay in the center, leaving an untiled strip of uniform width around the tile. If the ratio of the tiled area to the untiled area is 25 to 39, which of the following could be the width, in inches, of the strip?
a. I only
b. II only
c. I and II only
d. I and III only
e. I, II, and III
In case you haven’t figured out the answer, the strip could be any width. Answer choice E is correct. How do we arrive at this answer?
The problem-solving version of this question is taken from p. 85 of the GMAT Quantitative Review, 1st Edition. The solution given is computational; the basic steps are:
Let [pmath]t^2[/pmath] = area of the square tile inlay
Let [pmath]s^2[/pmath] = area of the entire countertop
Then [pmath](t^2)/(s^2 – t^2) = 25/39[/pmath], so that [pmath](t^2)/(s^2) = 25/(25 + 39) = 25/64[/pmath].
Taking the square root of both sides, we see that t/s = 5/8, which means that the length of the side of the square tile inlay is 5/8 the length of the side of the entire square countertop. At this point, the solution in the QR proceeds to write an expression for the width of the strip, w, in terms of these two variables: w = (s – t)/2, and then substitute an expression for t in terms of s to obtain an expression for w in terms of one variable, s:
[pmath]t/s = 5/8[/pmath] –> [pmath]t = (5/8)s[/pmath]. Then [pmath]w = (s – (5/8)s)/2 = (3/16)s[/pmath].
Presumably, you need to be able to write w = ks for some constant k, in order to see that w can take on any positive value. This is a lot of computation, and it will surely put you beyond the scant average of 2 minutes per question that you should allow. Is there a better way?
Imagine that this problem was posed as a data sufficiency question. It could look something like this:
A square countertop has a square tile inlay in the center, leaving an untiled strip of uniform width around the tile. What is the width, in inches, of the strip?
1. The ratio of the tiled area to the untiled area is 25 to 39.
2. The ratio of the tiled area to the total area of the countertop is 25 to 64.
Granted, this version of the question is slightly easier, because statement II gives you a clue to what your first step should be. But the same insight is necessary to solve this, and I maintain that it does not require computation. From either statement, you can reach the point reached in the solution given above: t = (5/8)s. Instead of plowing ahead with more computation, take a step back and use your imagination. The only constraint given by the problem is a proportion relating the length of a side of the tiled area to the length of a side of the table. FURTHERMORE, the question asks for width of the strip IN INCHES. This is slightly peculiar, given that the only other information about the table (a ratio of areas) does not mention ANY UNITS OF MEASUREMENT. What if the question had said “in feet.” Or “in millimeters.” Or “in miles.” Any one of these is possible given the information in the statements. The fact is that there is no way to determine absolute length measurements in terms of a specific unit if only proportions are known. A simpler question might look like this:
If a red spherical balloon contains twice the volume of a blue spherical balloon, which of the following can be the surface area of the red balloon, in square meters?
ANY of these numbers could be the surface area.
GMAT questions force the test-taker to make decisions about quantitative matters as quickly and as accurately as possible–very often without having to make calculations. The key behind these questions is to realize that computation is not necessary–a sense of what CAN be computed, however is indispensable.It makes sense that questions like these are on the GMAT. Very often in world of business, folks with an MBA are faced with the following decision: Should we spend all this time to do this computational task?
In the world of management, understanding when to ask this question can often be the difference between money wasted and money well-spent. On the GMAT, understanding this question will raise your score.