Cheat codes / Math
Pick your own numbers
When a problem has letters but no numbers, I put in easy numbers of my own and test the options.
How I think about it
The code in steps
- 1Choose easy numbers: 100 for percent, 10 for totals, 2 or 3 for x.
- 2Avoid 0, 1 and equal values for different letters.
- 3Calculate the question with your numbers and write the target.
- 4Put the same numbers in all four options.
- 5Pick the option that matches. If two match, try another number.
Learn it
1. What it is
Some Math questions hide the numbers. They say 'x', or 'a certain number', or 'a store raised its price by 20 percent'. The code is to put in numbers you choose, do the calculation with them, and then put the same numbers in each option. The option that gives the same result is the answer.
This works because if an algebra statement is true for all numbers, it is true for the numbers you pick.
2. The steps
1. Choose easy numbers. For percent, use 100. For a total in a ratio, use 10 or 100. For an expression with x, use x = 2 or x = 3.
2. Calculate the question with your numbers and write the target number.
3. Put the same numbers into every option.
4. The option that gives your target is the answer. Test all four options, because sometimes two options match one number.
5. If two options match, pick another number and test only those two.
3. Which numbers to avoid
Do not use 0 or 1 when you are testing expressions. With 0 and 1, many different expressions give the same result, so you cannot tell which option is right. Example: with x = 0, every term that has an x disappears, so only the last number is left.
Do not pick the same number for two different letters (x = 3 and y = 3). Then an option that mixes them looks right for the wrong reason.
Do not pick a number that makes a denominator 0. Do not pick a number the question forbids, such as 'x not equal to 3'.
Choose small, different, whole numbers such as 2, 3 or 5.
4. A tiny drill
Which expression is equal to 2(x + 3)? Options: 2x + 3, 2x + 6, x + 6, 2x + 5. Pick x = 2. Target: 2(5) = 10. Options give: 7, 10, 8, 9. Only 2x + 6 gives 10.
Now try the unlucky pick x = 0. Target: 6. Options give: 3, 6, 6, 5. Two match, so x = 0 would not decide. This is why we avoid 0.
5. How to know when to use it
Use it for questions that ask 'which expression is equivalent', for percent-change questions with no real starting amount, for ratio questions with unknown totals, and for geometry questions that compare shapes with letters such as r and h.
Do not use it when the problem already has numbers you can use, or when the question asks for the value of a letter.
Why it works
The SAT writes expression and percent questions so that they are true for every number, which means any allowed number you choose gives the right answer. Calculating with a small number such as 2 or 100 is much easier than doing algebra with letters, and four short calculations are fast. Every Math question has four options and only one is correct, so testing all four finds it. The code also gives you a way to check an answer you got from algebra.
Watch out: A bad pick can make two options give the same value, and then you have to try again. Never pick 0 or 1 for expressions. Also, you must test all four options, not just the first match, and you must not pick a number that the question does not allow. The code does not work for questions that ask for a particular value, such as 'what is x'.
See it work on real questions
Try each question your usual way first. Then open the box to see the code at work.
Equivalent expressions · question 4
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Equivalent expressions · question 5
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Percentages · question 7
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Area and volume · question 8
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Linear functions · question 8
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Percentages · question 5
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Do not just believe me. Test it.
Find 6 questions that ask about expressions, percent change or ratios. Do 3 with the usual algebra and 3 by choosing your own numbers. For each one, write down the time and if the choice of numbers worked the first time. If two options matched your number, count that as one failed pick. After that, compare the time and the failed picks.