Recently, GMAC released two more official practice tests. Though the GMAT is not going to test completely new concepts – if the test changed from year to year, it wouldn’t really be standardized – we can get a sense of what types of questions are more likely to be emphasized by noting how official materials change over time. I thought it might be interesting to take these practice tests and break down down any conspicuous trends I detected.

In the Quant section of the first new test, there was one type of question that I’d rarely encountered in the past, but saw multiple times within a span of 20 problems. It involves unit conversions in two or three-dimensional shapes.

Like many GMAT topics, this concept isn’t difficult so much as it is tricky, lending itself to careless mistakes if we work too fast. If I were to draw a line that was one foot long, and I asked you how many inches it was, you wouldn’t have to think very hard to recognize that it would be 12 inches.

But what if I drew a box that had an area of 1 *square* foot, and I asked you how many *square* inches it was? If you’re on autopilot, you might think *that’s easy. It’s 12 square inches. *And you better believe that on the GMAT, that would be a trap answer. To see why it’s wrong, consider a picture of our square:

We see that each side is 1 foot in length. If each side is 1 foot in length, we can convert each side to 12 inches in length. Now we have the following:

Clearly, the area of this shape isn’t 12 square inches, it’s 144 square inches: 12 inches * 12 inches = 144 inches^2.

Another way to think about it is to put the unit conversion into equation form. We know that 1 foot = 12 inches, so if we wanted the unit conversion from feet^2 to inches^2, we’d have to square both sides of the equation in order to have the appropriate units. Now (1 foot)^2 = (12 inches)^2, or 1 foot^2 = 144 inches^2. So converting from square feet to square inches requires multiplying by a factor of 144, not 12.

Let’s see this concept in action. (I’m using an older official question to illustrate – I don’t want to rob anyone of the joy of encountering the recently released questions with a fresh pair of eyes.)

*If a rectangular room measures 10 meters by 6 meters by 4 meters, what is the volume of the room in cubic centimeters? (1 meter = 100 centimeters)*

*A) **24,000*

*B) **240,000*

*C) **2,400,000*

*D) **24,000,000*

*E) **240,000,000*

First, we can find the volume of the room by multiplying the dimensions together: 10*6*4 = 240 cubic meters. Now we want to avoid the trap of thinking, *“Okay, 100 centimeters is 1 meter, so 240 cubic meters is 240*100 = 24,000 cubic centimeters.” * Remember, the conversion ratio we’re given is for converting meters to centimeters – if we’re dealing with 240 *cubic* meters, or 240 meters^3, and we want to find the volume in *cubic* centimeters, we’ll need to adjust our conversion ratio accordingly.

If 1 meter = 100 centimeters, then (1 meter)^3 = (100 centimeters)^3, and 1 meter^3 = 1,000,000 centimeters^3. [100 = 10^2 and (10^2)^3 = 10^6, or 1,000,000.] So if 1 cubic meter = 1,000,000 cubic centimeters, then 240 cubic meters = 240*1,000,000 cubic centimeters, or 240,000,000 cubic centimeters, and our answer is E.

Alternatively, we can do all of our conversions when we’re given the initial dimensions. 10 meters = 1000 centimeters. 6 meters = 600 centimeters. 4 meters = 400 centimeters. 1000 cm * 600 cm * 400 cm = 240,000,000 cm^3. (Notice that when we multiply 1000*600*400, we can simply count the zeroes. There are 7 total, so we know there will be 7 zeroes in the correct answer, E.)

Takeaway: Make sure you’re able to do unit conversions fluently, and that if you’re dealing with two or three-dimensional space, that you adjust your conversion ratios accordingly.** If you’re dealing with a two-dimensional shape, you’ll need to square your initial ratio. If you’re dealing with a three-dimensional shape, you’ll need to cube your initial ratio. **The GMAT is just as much about learning what traps to avoid as it is about relearning the elementary math that we’ve long forgotten.

**GMATPrep question courtesy of the Graduate Management Admissions Council.*

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*By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles written by him here.*