Mental maths for trading interviews: how to get faster

An arithmetic screen at a market maker gives you about six seconds a question. That is not enough time to multiply two two-digit numbers the way school taught you, carrying digits in your head, and it is not meant to be. What the screen rewards is a small set of rewrites, practised until you no longer choose them, and the discipline to leave a question alone when you are not sure. The formats themselves are described on our mental maths tests page. This article is about the technique.

Round, then correct

The most useful habit is to move one number to something round and pay back the difference. 49 × 38 is 50 × 38 − 38, which is 1900 − 38 = 1862. 198 × 7 is 1400 − 14 = 1386. The correction is always small and easy, and the round product is one you know.

The same move works for addition and subtraction. 373 + 57 is 373 + 60 − 3 = 430. 1000 − 287 is 713: subtract each digit from 9 and the last from 10. Doing these the long way costs little each time, but a test has eighty of them.

Split the number you multiply by

When neither number is near a round one, break the smaller into tens and units. 34 × 27 is 30 × 27 + 4 × 27, which is 810 + 108 = 918. Two easy products and one addition, held in your head without any carrying. Multiplying by 5 is halving and multiplying by 10: 48 × 5 = 240. Multiplying by 25 is dividing by 4 and multiplying by 100.

Percentages break the same way. 18% of 350 is 10% (35) plus 8% (28), which is 63. And a percentage can be swapped with its base: 8% of 25 is the same as 25% of 8, which is 2.

Squares, and products that are secretly squares

Learn the squares to 30 by heart, then use them for everything nearby. 47² is (50 − 3)², which is 2500 − 300 + 9 = 2209. A number ending in 5 squares by multiplying the tens digit by the next number up and writing 25 after it: 65² is 6 × 7 = 42, so 4225; 85² is 7225.

Two numbers the same distance either side of a round one multiply as a difference of squares. 53 × 47 is 50² − 3² = 2491. 98 × 102 is 9996. Interviewers like these because they look like hard multiplications and take two seconds once you see them.

Fractions you should not be working out

Most of the decimals and fractions in these tests are a few families, and memorising them is quicker than any method of division. The ones worth knowing cold:

Anything over 99 or 33 becomes a repeating decimal at a glance. 37/33 is 1 + 4/33, and 4/33 is 12/99, so the answer is 1.1212… An improper fraction is a whole number plus one of the families above: 17/8 is 2 + 1/8 = 2.125.

Divide by the factors, not the number

Long division in your head is slow because you have to hold the remainder. Dividing by factors avoids it. 3108 ÷ 12 is 3108 ÷ 4 ÷ 3, which is 777 ÷ 3 = 259. A missing-number question such as 66 × ? = 138.6 is a division in disguise: 138.6 ÷ 66 is 2.1, because 66 × 2 = 132 and the 6.6 left over is a tenth of 66.

Check without redoing the sum

In a multiple-choice test the options often differ by more than the likely error, so a rough check is enough. Check the size first: 0.37 × 0.42 is a bit under 0.4 × 0.4 = 0.16, so 0.1554 is plausible and 1.554 is not. Check the last digit: 34 × 27 must end in 8, because 4 × 7 does.

When two options share both, add up the digits. A number leaves the same remainder on division by 9 as the sum of its digits, and products keep those remainders. For 34 × 27: 3 + 4 = 7 and 2 + 7 = 9, so the product must be a multiple of 9. 918 is (9 + 1 + 8 = 18); 928 is not.

When to skip

Under +1 for a right answer and −1 for a wrong one, a guess that is right with probability p is worth p − (1 − p) = 2p − 1 points. That is positive only above one half. With four options, a blind guess costs half a point on average, and ruling out two options only brings you to zero. So guessing helps only when you have a real lean, typically from the size or the last digit, and the six seconds are better spent on the next question.

The same logic sets your pace. A question that has taken eight seconds without an answer is unlikely to come out in the next two. Candidates who score well are usually not the ones who answered most; they are the ones who did not throw away points on the questions they could not finish.

How to practise

Ten minutes a day for four weeks does more than an hour the night before, because the point is to stop choosing a method and simply see it. Three rules make the practice count:

• Accuracy first, speed after. Practise slowly until you rarely make mistakes, then push the pace. Speed built on errors is speed at losing points.
• Keep a log of what you get wrong. Errors cluster: fractions over 7, three-digit subtraction, decimals with two places. Drill the cluster, not the whole test.
• Practise in the real format. If the test is multiple choice, practise multiple choice; the skill of eliminating options is part of it. Practise tired, too, since many screens arrive at the end of a long day.

Our timed tests report accuracy and pace by question type, weakest first, which is the log built for you. For individual questions with worked answers, use the mental arithmetic bank.

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