The numerical tests do not contain hard sums. They contain easy sums with almost no time, which is a different problem and needs different techniques. Most school methods are built for accuracy on paper and are simply too slow here.
Round, then correct
The most useful habit in mental arithmetic. Move a number to something convenient, do the easy version, then adjust.
Worked example
48 × 7
- 50 × 7 = 350.
- You added 2 sevens too many, so subtract 14.
Answer: 336
Worked example
396 + 247
- 400 + 247 = 647.
- You added 4 too many, so subtract 4.
Answer: 643
Multiplying by the awkward numbers
- By 5: halve it and multiply by 10. 86 × 5 becomes 43 × 10, which is 430.
- By 9: multiply by 10 and subtract the number. 34 × 9 becomes 340 minus 34, which is 306.
- By 11 for two digits: split the digits and put their sum in the middle. 43 × 11 becomes 4, then 7, then 3, which is 473.
- By 25: divide by 4 and multiply by 100. 36 × 25 becomes 9 × 100, which is 900.
- By 15: multiply by 10, then add half of that. 24 × 15 becomes 240 plus 120, which is 360.
Percentages
Build everything from 10 percent, which is just moving the decimal point, then combine.
Worked example
35% of 240
- 10% is 24, so 30% is 72.
- 5% is half of 10%, which is 12.
- 72 + 12.
Answer: 84
One more worth knowing: percentages reverse freely. 16 percent of 25 is awkward, but 25 percent of 16 is a quarter of 16, which is 4. They are the same number. When a percentage question looks unpleasant, try it the other way round before doing anything else.
Division
Long division has no place in a timed test. Estimate the answer by multiplication instead, because you are usually choosing between options rather than producing a number from nothing.
Worked example
1,368 ÷ 24
- 24 × 50 = 1,200, so the answer is above 50.
- 24 × 60 = 1,440, so it is below 60.
- The remaining 168 divided by 24 is 7.
Answer: 57
The judgement that matters more than any of this
Knowing when to stop calculating. In a multiple choice test the options are information, and often they are far apart. A rough estimate then eliminates three of them in a couple of seconds, and doing the sum properly would have added nothing except time you did not have.
Glance at the options before you start working. If they are widely spread, estimate. If they are close together, calculate. That single habit is worth more than every trick above.
Where a test lets you type an answer rather than choose one, this does not apply and you have to be right. Know which kind you are sitting before you start.
Practise the right way
Always with a clock. Untimed arithmetic practice builds confidence and measures nothing, because every one of these questions is easy given as long as you like. If you are not slightly uncomfortable, you are not practising the thing being tested.