Percentages via 10 percent
Ten percent of anything is a single decimal shift to the left. Ten percent of 340 is 34. This is the anchor for every percentage problem you will see on an aptitude test.
From there, all other percentages are combinations. Thirty-five percent of 80 is ten percent of 80 (which is 8) times three, plus half of 8, giving you 24 plus 4, which is 28. Done in under five seconds once you practice. Faster than long multiplication and far faster than setting up an equation.
Drill this with random three-digit numbers and random percentages between 5 and 95 for a week. The fluency builds faster than people expect.
Multiplication by 11
Multiply by 10 and add the original. Forty-seven times 11 is 470 plus 47, which is 517. No pencil, no scratch paper, no mental gymnastics.
The same trick works for numbers like 12 and 9. Times 12 is times 10 plus times 2. Times 9 is times 10 minus the original. These chains eliminate almost all hand arithmetic on the numerical sections of aptitude tests.
Multiplication by 5
Multiply by 10, then divide by 2. Sixty-eight times 5 is 680 divided by 2, which is 340.
This sounds obvious but many candidates still try to multiply 68 by 5 the long way. The shortcut is always faster because halving a number is easier than multiplying by 5 for most mental arithmetic.
Squaring numbers ending in 5
Take the tens digit, multiply by the next integer, then append 25. Thirty-five squared is 3 times 4 is 12, append 25, answer is 1225.
Forty-five squared is 4 times 5 is 20, append 25, answer is 2025. Eighty-five squared is 8 times 9 is 72, append 25, answer is 7225. This trick alone saves you from 20 seconds of hand multiplication on any squaring question.
Fraction-to-percent conversions worth memorizing
One third is 33.3 percent. One quarter is 25 percent. One sixth is 16.7 percent. One seventh is 14.3 percent. One eighth is 12.5 percent. One ninth is 11.1 percent.
These appear constantly on numerical reasoning questions disguised as word problems. Memorize all six. Multiples of one-eighth are especially common because 12.5, 37.5, 62.5, and 87.5 are so frequent as answer choices that the test writers basically cannot avoid them.
The difference of squares trick
A squared minus b squared equals (a plus b) times (a minus b). One hundred one squared minus 99 squared is 200 times 2, which is 400.
This pattern hides in disguise on many aptitude test questions. Whenever you see two squared numbers subtracted, try the difference-of-squares decomposition first. It usually collapses the arithmetic into something you can do in your head.
Rough estimation before precision
Before any calculation, estimate the order of magnitude of the answer. If the choices are 4, 40, 400, and 4000, and your estimate says the answer is close to 50, you have eliminated three options without doing any arithmetic.
This is not a shortcut as much as a selector. Use it on every numerical question. It prevents you from doing precise arithmetic when rough arithmetic is enough.
Double and halve
To multiply two numbers, double one and halve the other repeatedly until one of them is trivial. Twenty-five times 14 becomes 50 times 7, which is 350. Sixteen times 12.5 becomes 32 times 6.25 or 8 times 25, which is 200.
Double-and-halve is the secret weapon for ugly multiplication problems. It converts every nasty multiplication into a clean one.
Drill structure
Ten minutes a day for two weeks. Split into three blocks: percentages, multiplication shortcuts, and estimation. Use a random number generator so you do not memorize specific problems.
Track your per-problem time. The goal is not perfect accuracy on every shortcut. It is a 50 percent reduction in average arithmetic time compared to day one. That is the improvement that shows up on your cognitive test score.