Categorizing Your Mistakes
Note: This is the third entry of a series on preventing careless mistakes. ¬†To start at the beginning, scroll down to the first entry, “Preventing Careless Mistakes”.
When you make a careless mistake, determine its nature so that you can be alert for it next time.
Careless mistakes come in a variety of forms, so it is important to identify the types that you are most susceptible to. Once you are aware of the things you fall for, you can maintain a heightened alertness for them. For instance, the first time I moved into an apartment with a door that locked automatically, I was constantly locking myself out of my apartment. Then I would have to sit in the hallway for hours, like an idiot, while I waited for the maintenance guy to come let me in. Yet these experiences, while terrible, did not seem to deter me from locking myself out of my apartment. It remained a regular part of my routine until I instituted a new rule: whenever I opened the door to go outside, I was not allowed to close it until I took my key out and held it in my hand. I don’t know if this is how most people prevent themselves from becoming locked out of their apartments, but it worked for me. You will find that similar workarounds can help prevent careless mistakes on math problems. Here are some common careless mistakes and tips for avoiding them:
1. Overlooking a key detail.
This kind of careless mistake occurs when you fail to incorporate an important detail from the given information into your solution. For example, consider the following problem:
If two distinct positive integers add to 38, what is the largest possible value for their product?
If you picked E. 361, you picked the sucker answer. The correct answer is D. 360. Someone who chooses ‘E’ most likely glossed over the word “distinct”. 19*19=361, but 19 and 19 are not distinct. The best you can do with two distinct¬†positive integers that add to 38 is 20*18=360.
Tip: If you find yourself making this kind of mistake repeatedly, slow down when you read the questions. Stop at each word and ask yourself how its presence will impact the solution.
2. Answering the wrong question.
This can happen if you assume you know what the question is going to be without ever actually verifying it. Here is a simple example:
If 2x-5=13, what is the value of 2x?
Here the sucker answer is ‘C’. In high school algebra, the goal of practically every single problem is to find the value of x. The GMAT is not so predictable. They like to throw things like this in to make sure that you are paying attention. People who pick ‘C’ are probably guilty of answering the wrong question, “What is x?” instead of the actual question, “What is 2x?” The correct answer, of course, is D. 18.
Tip: Before you submit an answer, always double check that you are answering the exact question that they asked.
3. Answering in the wrong units.
This is ¬†essentially the same as overlooking a key detail, but it comes up frequently enough that it deserves special attention. Here is a simple example of how it could come up:
How many minutes will it take David to drive 120 miles if he drives at an average speed of 40 miles per hour?
Here, the sucker answer is B. 3. It takes him 3 hours¬†to drive 120 miles, but the question is asking for the number of minutes. So the correct answer is E. 180.
I usually find that people who make a lot of mistakes with units don’t have a proper appreciation for how important units are. So, if you find yourself making these kinds of mistakes, take some time to think about how critical using proper units is to communicating information accurately. For example, let’s say that you and I have the following exchange:
You: How far is it to Lubbock, Texas from here?
You would be rightfully angry. What a stupid answer! Twenty-four what? Miles? Kilometers? Feet? Light-years? Maybe I’m even answering in hours. Clearly my answer is useless if I don’t include the units.
Also, try thinking about how changing the units of an answer can change an answer from plausible to ridiculous. 72 inches is a plausible height for a man. 72 feet is probably not. 3 hours is a reasonable amount of time to drive 120 miles. 3 minutes is probably not. Units are everything.
The point of all this is that sometimes there is a disconnect between how we perceive things in the real world and how we perceive them in a GMAT math problem. I don’t expect that any of you would ever, in the real world, make the mistake of saying that a man is 72 feet tall. However, people make mistakes like that on the GMAT without a second thought. GMAT problems tend to come across as artificial, like something that was isolated in a lab, lacking the nuances and messiness of real life. As a result, we let our guard down and don’t apply the same tests of plausibility that we would apply automatically in the real world. You must be vigilant about not letting this happen.
Tip: If you see any kind of unit in a GMAT math problem, keep your guard up. Make a special point to check that the answer you obtained is plausible in terms of the units given and that you handled all unit conversions properly.
4. Making an arithmetic error
Having to do arithmetic mentally or by hand on the GMAT can come as a rude awakening if you have come to rely on calculators. The arithmetic required is not very difficult, but if you’re out of practice it can slow you down significantly. It can also create terrific opportunities for careless mistakes. If you do feel rusty with arithmetic, here are a few things you can try.
First, stop using a calculator for arithmetic in your daily life unless it is absolutely necessary. If arithmetic doesn’t come up much in your daily life, look around for opportunities to practice. See how fast you can add up numbers that you see on license plates or in phone numbers. If something is on sale for 30% off, try to compute the sale price in your head. At the grocery store, try to compute the price per ounce of different products and see how close you can get. If arithmetic comes up that you have¬†to use a calculator for, try to guess a reasonable estimate for the answer first.
Second, find a simple arithmetic game to play online or find some free worksheets that you can print out. The games are easy to find by googling “timed arithmetic challenge”. Once you find one you like, play it repeatedly and see how high you can make your score. If you want to practice on paper, google “free arithmetic worksheets” and find some worksheets to print out.
Third, learn some mental math shortcuts. There are several shortcuts available that you can use to simplify certain calculations. For example, if you want to multiply a number by 15, just add half of that number to itself and multiply the result by 10. So, if you want to multiply 24 by 15, take half of 24(which is 12) and add it to 24 to get 36. Then multiply 36 by 10 to get 360. Thus, 24*15=360. There are plenty of other useful tricks like this that make arithmetic faster and easier. In the future, GMAT Math Pro will have a series of videos detailing the tricks. For now, try googling “mental math tricks” and try to find some that you think are useful.
Finally, when you do arithmetic mentally or on paper, it is important to be able to check if your answer is at least in the right ballpark. To do this, round the numbers you are working with to numbers that are close but more manageable. For example, suppose you are trying to determine what 53% of 612 is. 53% is close to 50% and 612 is close to 600. 50% of 600 is 300. Since the original numbers were slightly more than 50% and 600, we would expect the actual answer to be slightly higher than 300. So if you get something like 31 for your answer, you know you made a serious error. Of course, if you do¬†get an answer slightly higher than 300 it doesn’t necessarily mean you are correct. But you can use this technique to catch big mistakes like putting the decimal point in the wrong spot.
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