This post was syndicated from: The Hacker Factor Blog and was written by: The Hacker Factor Blog. Original post: at The Hacker Factor Blog
It must be that time of the year… I’ve been hearing those dreaded three-letter initials over and over in the news: SAT, ACT, GRE.
Back when I took the SAT (OMG, has it really been 25 years???), those tests were promoted as a massive sign of stress. “Make good scores or you won’t get into college!” “Bad scores mean a low-paying job!” “We won’t think any less of you if you don’t do well.”
Of course back then, there was a small but vocal minority of complaints. That the test did not test knowledge, was racially biased, was gender biased, did not evaluate college readiness, and more. And each year the groups that run the tests say that they would address these issues.
Since I took those exams, there have been some changes. The ACT is now an accepted alternative to the SAT. (It might have been around back in the 1980s, but I do not recall it being an option for me.) They also added an essay section and claim to have made other changes to refocus the test.
However, I just looked at the online sample tests for the SAT and ACT and I really think nothing significant has changed. These are not tests that measures knowledge; they measure your ability to take a test.
Important for the wrong reasons
There’s a lot of emphasis on the test results. Colleges require good scores for admission. Summer programs use them to filter who gets into special activities. And as Our Lady of Infinite Loops noted, low scores can really damage a child’s self-esteem. “Try to convince kids that they’re smart after they bomb the SAT, though, and good luck.” A lot of self-doubt can continue for years.
I believe these standardized tests are important, but I do not believe they are important for evaluating the student’s knowledge level or subject proficiency. For example, the SAT still uses a bell-curve scoring from 200 to 800 on each section. 800 is a perfect score and you get 200 for writing your name. 500 is “average”. For me, I received 720 on math and 430 on English. (The test is so stressful that you are likely to remember your score decades later.) My scores say that I do no speak English. (I found it ironic since most of the math problems are word problems; if you cannot understand English, then you probably won’t break 550.) Ironically, when I took the GRE after 4 years of college, I ended up getting 760 on math, 780 on analytics, and 430 (again!) on English.
Since then, this non-English speaker has written three books, numerous articles and white-papers (some public, some just for customers), and I have this ongoing blog that is read by more than 12 people. While readers may debate the technical accuracy of this blog, the grammar and sentence structure is generally excellent. (And I haven’t taken any classes to improve my writing since college.)
I actually think that I failed the English sections because I over-thought every problem. The test does not measure depth of thought or your thinking process; it only counts correct marks. I certainly cannot give any tips about the reading section. However, I know exactly why I got such high scores on the math and analytics, and it had very little to do with being good at math and logic.
Hacking a standardized test
Back when I was in high school, there were 3 different teachers named “Mr. Clark”. One taught math, one covered English, and one did history. It was the English teacher who taught a class on “mass media” that I still think was one of the best courses I have ever taken. (How to spot good/bad reporting, the different parts of a paper, how advertisements work, etc.) He also gave a three-day after-school talk on how to take the SAT. His extracurricular talk changed everything for me.
The SAT, ACT, GRE, PSAT, LSAT, etc. are not about knowledge. They are about “how to take a test”. And since you will be tested over and over in life, these tests are a wonderful introduction. These tests won’t help you get a good job — I’ve never had an employer ask for my scores — and they don’t tell anything about how smart you are. (Dumb people can get high scores.) Their content won’t prepare you for college and beyond.
Colleges may require these tests, but there’s lots of stupid requirements in life — just go with it. This is what I really got out of Mr. Clark’s seminar: if you don’t like the system, don’t fight it. Instead, game the system. Find the flaws and exploit them. Take what you are given and apply it differently. That is the definition of ‘hacking’.
There are really just three rules that you need to remember:
- Time. The first rule is unbreakable. Like gravity or dividing by zero, ignoring it is a fatal mistake: these are timed tests. When the time is up, you are done. Time management is your single most important task.
- Correct answers. You only get positive points for correct answers. There may be a hundred questions for you to answer. Some questions may be harder than others, but all scoring is unweighted; a point is a point, regardless of the problem’s difficulty. For the best score based on the given time, do the easy questions first. Skip the hard ones and go back to them if you have time.
- Guessing. Some tests penalize for wrong answers. (When I took the SAT, it was a 1/4 point deduction for every wrong answer.) This does not mean that you should not guess. Instead, it means that you should optimize your guessing!
I cannot give you tips to extend the time limit — the duration is fixed and you cannot change it. What I can do is give you a couple of simple tips to best manage your time and improve the number of correct answers.
Tip #1: Minimize work
These tests have a lot of questions to answer and very little time per question. If there are 100 questions and only 50 minutes, then you cannot spend more than 30 seconds per question. What you want to do is find shortcuts so you can answer questions in under 30 seconds. If you can answer 10 questions in 10 seconds each, then you can saved up 290 seconds (nearly 5 minutes) that you can spend on harder questions later.
Don’t bother tracking your time. (“I saved 10 seconds here.” “I saved another 3 seconds there.”) It takes time to track time and the test is tracking the time for you. (You will stop when it is over.) Just go as fast as you can.
You are allowed to write notes in the test booklet (but not on the answer sheet!!!). You can use this to help your time management. For example, make small marks so it will be easier to go back. If I guessed or skipped a question, then I circled the question number. And if I didn’t understand the question or knew it was a type of problem that I was slow at solving, then I circled it twice. If I had time at the end, I would go back and focus on the circled questions. And if I still had time, I would try the double-circle questions.
Since all points are equal, you want to do the easy problems first. These circles save time by identifying the harder problems as I go back for a second pass.
Similarly, if I knew one of the multiple-choice answers was incorrect, I would cross out the letter so I could ignore it if I went back to that question. And no matter what, I always circled the correct letter in the booklet. This way, if time permitted, I could go back and double-check my answers without wasting time looking up my response on the answer sheet.
Tip #2: Short circuit
In computer programming, there is an algorithmic concept called a “short circuit“. Let A, B, C, and D be complex conditions that need to be evaluated. If you are given a test condition like “if (A or B or C or D) then …”, then you may not need to test every complex condition. Instead, you just test A. If A is true, then you can ignore B, C and D and enter the body of the condition. If A is false, then test B. It should be rare for you to need to test all four conditions. (The same short-circuit concept works with “and” conditions; the first failure stops the evaluation.)
This same idea works with standardized tests for math and analytics. In these tests, there are a fixed number of answers. You can use the short-circuit concept to reduce the number of options. If there is only one option left, then stop reading the question since you know the answer. For example, this question comes from the ACT online sample test:
A car averages 27 miles per gallon. If gas costs $4.04 per gallon, which of the following is closest to how much the gas would cost for this car to travel 2,727 typical miles?
A. $ 44.44
There’s a couple of ways to solve this problem. The first option is to brute-force solve it. 2,727 miles divided by 27 miles per gallon is 101 gallons. 101 gallons costs $4.04 per gallon, so that is $408.04. The answer is “D”.
The short-circuit approach would be a little simpler. We have one division and one multiplication and we just need to solve that first, hundredths digit. “7″ (from 27mpg) goes into “7″ (from the last digit of 2727) once. 1×4 (the last 4 in 4.04) is 4. This means that the last digit must be a “4″. We can immediately rule out B, C, and E since they do not end with a “4″. That leaves two options. At this point, we can easily guess “D” because 2727 (miles) is 2 decimal places larger than 27 (mpg); the value from “A” is too small. We would guess “D” and we be correct.
Solving one digit is much faster than solving the entire problem. And if A and D were closer together, then we could try solving for another digit.
This type of shortcut is also great for logic puzzles, where they list a bunch of conditions. Take each condition as you read it and test the answers. If the first condition does not work for “D”, then scratch off “D” as an answer. If the next condition does not work for “A”, then scratch off “A”. When there is only one answer left, you know the correct answer. You don’t have to solve the puzzle; you just have to find an answer that solves the puzzle. For example, this question comes from “Free SAT Math Questions“:
The table above shows the temperatures, in degrees Fahrenheit, in a city in Hawaii over a one-week period. If m represents the median temperature, f represents the temperature that occurs most often, and a represents the average (arithmetic mean) of the seven temperatures, which of the following is the correct order of m, f, and a?
(A) a < m < f
(B) a < f < m
(C) m < a < f
(D) m < f < a
(E) a = m < f
Identifying the average (a=73.29) is hard and time consuming because you have to add every number and then divide by the total. Even computing the median (m=75) is slow because it requires sorting the values and finding the one in the middle. But finding the value that occurs most often (f=78) is fast. 78 is also the highest value, so we can immediately rule out B and D. That leaves determining the relationship between a and m. At this point, I would solve m by sorting the values. I would find a by doing a rough average: (highest + lowest) / 2 = (78+66)/2 = 72. The rough average shows that a is likely < m. So I would guess “A” (and I would be correct).
That’s right: I said “guess”. It’s not worth my time to solve the problem. It’s better time management to rule out unlikely options and go with whatever is left.
Tip #3: Fitness
Rather than using the question to derive the answer, just see if each answer fits the question. For example, “Free SAT Math Questions” has a question that says:
If k is divisible by 2, 3, and 15, which of the following is also divisible by these numbers?
(A) k + 5
(B) k + 15
(C) k + 20
(D) k + 30
(E) k + 45
Rather than thinking about how to simplify the problem, I’d just go down the numbers. Is “5″ divisible by 2? No, so scratch “A”. 15 is not divisible by 2, so scratch “B”. 20 is not divisible by 3, so scratch “C”. 30 works for 2, 3, and 15. Stop there — “D” is the correct answer. I would not even look at “E”; evaluating “E” is a waste of time, and time is the most important factor to this test.
Tip #4: Trick
All of these questions may first look intimidating, but they all have a trick. If you recognize the trick, then you can solve it fast. If you don’t see the trick, then circle the question and move on.
Tricks are usually in the form of specially chosen numbers or key words in paragraphs. For example, the trick in the gas mileage problem were the numbers: 27 into 2727 (see the 27 repeated?) is 101 and 4.04 is 4×1.01. See how “101″ keeps appearing? That’s the trick. 101 is a special number because you can multiple any number from 0 to 99 without a value carried between the units and hundreds columns. (In other words, they expect it to be easy enough to do in your head.) If you noticed the trick, then you know that the value must end with “.04″ — there’s only one answer that works. You may also notice that $408.04 is the only palindromic answer with a relationship to 101 (another palidrome). If you noticed the repetition of 101, then you could solve the problem without ever knowing what they were asking.
Similarly with the divisor problem, the trick is that 3 is a divisor of 15, so you can ignore it. You really just need to check for multiples of 2 and 15. “2″ is special because it means every answer must be even (that rules out A, B, and E). You may also recognize that the lowest common denominator is 30 (only D works). Again: you can find the answer fast if you saw either of these tricks. And every problem has some kind of trick.
Tip #5: Guess!
With the SAT that I took, there was a 1/4 point (25%) deduction for every incorrect answer. With five answers, random guessing means that I will guess correctly 20% of the time. Or if we look at it another way: on average, 1 out of every 5 guesses will be correct. So 1 point for the correct answer and 4×-0.25=-1 for the wrong answers. As points go, guessing is a wash and doesn’t hurt.
However, if I can rule out just one bad answer from the five possible answers, then I can guess at a profit. If I can exclude just one answer then, on average, 1 out of every 4 guesses will be correct. That’s 1 point for being correct – 0.75 points for 3 wrong answers yields a positive difference of 0.25. That’s much better than the alternative of not guessing and getting zero points.
If you can rule out 2 of 5 answers, then guessing gives you an overall positive score of 0.5 (+1 for the correct and -0.25×2 for the two wrong guesses). And if you can narrow it down to two possible answers, then it’s not just a 50/50 chance of guessing correctly, it’s a net guessing total of 0.75 positive points (+1 – 0.25). That’s like playing roulette in Las Vegas when 3/4ths of the wheel are black! (With those kinds of odds, why would you ever bet on red? Or in this case, why would you ever not guess?)
And of course, if there is no penalty for guessing, then absolutely guess! But still, see if you can narrow down the choices in order to increase the likelihood of guessing correctly.
Tip #6: Practice! Practice! Practice!
There are lots of sample tests online. There are books you can get that have sample exams. (Try the used bookstores first.) There’s even classes you can take that will issue a sample test. Try doing a sample test every few days in the months before the actual test. If you run out of sample test material, then retake some of the earlier tests. If your friends have sample tests that are different from your samples, then trade with them.
Remember: these exams are not about knowledge. If the test was measuring your knowledge on the topic, then taking practice exams would not improve your score. These tests do not teach you anything about math or analytics or even English. They will not expand your understanding of the subject.
Instead, these tests measure your ability to take a standardized test. With practice, you will spot the tricks faster and gain experience in managing your time. Just the act of sitting and focusing on the exam for hours can be exhausting — both physically and mentally. Practice will build up your tolerance. Repeated practice will improve your score.
One other thing to remember: the score is based on a bell curve. You’re score is compared against everyone else who takes that test. A lot of people won’t practice — assume that they will be at the low end of the bell curve because they are not used to taking this type of exam. Just by repeatedly practicing with sample tests, you can move to the middle or upper end of the test range.
In my opinion, this is the real reason that colleges like these tests. The scores show that you can focus on a subject for extended periods and that you are willing to put in some effort. If you look at college entrance requirements, you’ll see that they do not require perfect scores. They just want people who are better than average. The people who are not willing to put in the effort are going to be below average.
These tests are not completely bogus. They do check for a basic knowledge of math. You must know how to read a math problem, how to do very basic algebra and maybe a little geometry. You need to know the definitions for words like “arithmetic mean” and “hypotenuse”. You need to know basic math principles, like how to find the perimeter or area of an object, and the difference between obtuse and acute angles.
However, these tests never actually check your baseline knowledge of these basic concepts. Did you miss the ‘hypotenuse’ question because you didn’t know the word, or because you added a number wrong?
Standardized tests really just check to see if you can answer problems quickly and (mostly) accurately. They do not determine if you actually know how to apply math or if you have a deeper understanding of the concepts. These exams only check if you know how to take a test when the set of possible answers are known. In the real world, you usually don’t know all of the possible outcomes ahead of time. (And if you do, then the test is probably rigged.)
However, I did end up taking away some life lessons from the experience. For example, do the best you can with the time you have. An educated guess is usually better than not answering. If it looks hard then there is probably a trick to it. Regardless of what you do, you can improve with practice. And most importantly: knowing the requirements and how success is measured allows you to hack the system.