How to Make Educated Guesses on Quant
Ive been getting lots of great article ideas from students lately, and this is one of them: how do we make educated guesses on quant problems? (Ill do a separate article about verbal in future.)
Note: if you requested a different topic, dont worry! I keep a list of all requests; I will get to your request eventually. Im generally choosing the order based upon the number of requests I get from different people about the same topic.
What is Educated Guessing?
Generally speaking, there are two kinds of guessing: random and educated. A random guess is one in which you really dont have any good idea how to choose among all five answer choices. An educated guess is simply one in which you have used good reasoning to eliminate a wrong answer or more before you make a random guess from among the remaining choices.
It is often the case that we can figure out some likely wrong answers even when we have no idea how to find the right answer. When we narrow our options in this way, we give ourselves a better chance of guessing correctly when we finally do guess. In order to narrow our options effectively, though, we actually have to have studied this in advance; this is not something that you just know how to do.
Everyone will have to guess at some point on the GMAT; theres no way around that. The test will give you things that you cant do. (Most people have to guess on between 4 and 7 questions in each section.)
When Should I Make an Educated Guess?
We need to average two minutes per question on quant. By the halfway mark, one minute, we have to be on track we know what the problem is asking, have a good idea of how to get to the answer, and have started setting up the calculations. If were not on track by the one minute mark, then this is when we should switch to educated guessing. Were not suddenly going to figure everything out and finish all of the work in the second minute. In addition, it can take 30 to 60 seconds to make an effective educated guess, and we dont want to lose time on an educated-guessing question.
Useful Techniques
There are many different techniques that we can use to make educated guesses. Some techniques can work on a large percentage of questions; some will work only on very specific types of questions. Ill discuss some of the most common below, but you should consider this just a starting point. As you study from now on, ask yourself: how can I eliminate wrong answers on this question? (Tip: its often easier to figure this out on questions you answered correctly; learn how to do it on questions you understand, then apply the technique to harder problems of the same type.)
Also, on Problem Solving questions, get into the habit of glancing at the answer choices before you start solving the problem. Certain characteristics can give you ideas about how to solve or how to make an educated guess and you want to notice those things right away.
You may be able to use the first three techniques to get to a single (correct!) answer; for these three, you may decide to use one right from the start on some problems.
Estimation (Problem Solving and sometimes Data Sufficiency)
Does the problem contain the word approximately or something similar? Are the numerical answer choices decently far apart? Is there a diagram, or could you draw one, that would allow you to estimate? Can you assess things in terms of more than half vs. less than half (this often works well on probability, sets, rates, work, fractions, percents)? Can you assess things in terms of positive vs. negative or greater than one vs. less than one (this often works well with number theory)?
If the answer to any of those question is yes, you can likely get rid of some answers by estimating. Practice when and how.
Try the Answers (Problem Solving)
Are the answers generally small, easy numbers? Try them in the problem! Start with B or D. After every choice, if that choice is wrong, try to determine whether you need a larger or smaller number. For example, lets say that we try B first. Its wrong and we can also tell that we need a larger number. A is smaller, so cross off A as well. Next, try D. Its wrong, too, but we can tell that we need a smaller number. Therefore, the answer is C. If you can tell whether you need a smaller or larger number, then you never need to try more than two choices (B and D) in order to get to the answer.
Pick Numbers (Problem Solving)
Are there variable expressions in the answers? Try picking your own easy numbers to find an answer that works. Even if you find that two answers work (which happens sometimes), at least youve narrowed down to two!
Know How DS Answers Work (Data Sufficiency)
If the two statements ultimately say exactly the same thing no more and no less then you know that the answer is either D or E. (Think about why.) If statement 2 includes exactly what statement 1 says plus some additional info, then the answer is neither A nor C. If statement 1 includes exactly what statement 2 says plus some additional info, then the answer is neither B nor C. (Again, think about why.) If its very obvious that using the two statements together will work (as in: a 14 year old could tell immediately that the two together will work), then the answer is probably A or B. If one statement is really complicated and looks like Greek guess that it works.
Eliminate the Odd One Out (Problem Solving)
In some problems (often rates, work, sets, fractions, percents), four of the answers are presented in pairs of two. For instance, if Johnny and Susie are 20 miles apart and walking towards each other, <blah detail numbers blah>. How far will Johnny have walked when they meet? Answers: 6, 8, 9, 11, 12. Which answer is the odd one out?
The pairs are based on the total distance walked: 20 miles. 8 and 12 add up to 20 and 9 and 11 add up to 20. The most common wrong answer will be based on solving for Susies distance (the other half of the pair) rather than Johnnys distance. Dont guess 6. (And take it even further: can you tell whether Johnny walked more or less than half of the distance? You cant from what I typed above, but you might be able to on a real problem. Now, youre down to just two answers!)
Your Turn!
Its up to you now to keep studying and find more of these. Talk to your friends. Ask your instructors. STUDY the problems youre doing from this point of view. What else can you do?
Also, Id like to invite some enterprising Beat the GMAT member to start a new thread in the Quant forum. Title it Educated Guessing or something similar. Link to this article and include whatever other strategies youve devised. Include a sample problem and your written-out reasoning of the educated guessing process for that problem. Then ask others to start listing other strategies, along with specific problem examples and written reasoning. Send a link to the thread via PM to the experts and ask them to contribute as well. Lets get a good list going that Beat The GMAT can make a permanent resource for everyone!