Mental math practice for trading interviews
Trading firms test arithmetic speed in their first-round online tests. Below are representative questions with the shortcuts that make them fast: splitting products, rounding to tens, building percentages from 10% and 5%, and scaling fractions.
1What is 12 × 57?
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Answer: 684
Split 57 into 50 + 7: 12 × 50 = 600 and 12 × 7 = 84. Add them: 600 + 84 = 684.
2What is 5% of 120?
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Answer: 6
5% is half of 10%. 10% of 120 is 12, so 5% is 6.
3Write 7/8 as a decimal.
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Answer: 7/8
Scale the denominator to 1000: 7/8 = 875/1000 = 0.875.
4What is 14²?
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Answer: 196
Round to the nearest ten and correct: a² = (a − r)(a + r) + r². Here 14² = 10 × 18 + 16 = 180 + 16 = 196.
5What is 19 × 68?
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Answer: 1,292
Split 68 into 60 + 8: 19 × 60 = 1140 and 19 × 8 = 152. Add them: 1140 + 152 = 1292.
6What is 12% of 120?
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Answer: 72/5
Build it from easy pieces of 120: 10% is 12, 1% is 1.2. So 12% = 12 + 2 × 1.2 = 14.4.
7Write 11/16 as a decimal.
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Answer: 11/16 ≈ 0.6875
Start from the unit fraction: 1/16 = 0.0625. Then 11/16 = 11 × 0.0625 = 0.6875.
8What is 22²?
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Answer: 484
Round to the nearest ten and correct: a² = (a − r)(a + r) + r². Here 22² = 20 × 24 + 4 = 480 + 4 = 484.
9What is 26 × 68?
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Answer: 1,768
Split 68 into 60 + 8: 26 × 60 = 1560 and 26 × 8 = 208. Add them: 1560 + 208 = 1768.
10What is 15% of 80?
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Answer: 12
Build it from easy pieces of 80: 10% is 8, 5% is 4. So 15% = 8 + 4 = 12.
11Write 9/20 as a decimal.
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Answer: 9/20 ≈ 0.45
Scale the denominator to 100: 9/20 = 45/100 = 0.45.
12What is 29²?
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Answer: 841
Round to the nearest ten and correct: a² = (a − r)(a + r) + r². Here 29² = 30 × 28 + 1 = 840 + 1 = 841.
13What is 33 × 79?
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Answer: 2,607
Split 79 into 70 + 9: 33 × 70 = 2310 and 33 × 9 = 297. Add them: 2310 + 297 = 2607.
14What is 18% of 60?
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Answer: 54/5
Build it from easy pieces of 60: 10% is 6, 5% is 3, 1% is 0.6. So 18% = 6 + 3 + 3 × 0.6 = 10.8.
15Write 2/25 as a decimal.
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Answer: 2/25 ≈ 0.08
Scale the denominator to 100: 2/25 = 8/100 = 0.08.
16What is 36²?
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Answer: 1,296
Round to the nearest ten and correct: a² = (a − r)(a + r) + r². Here 36² = 40 × 32 + 16 = 1280 + 16 = 1296.
17What is 40 × 90?
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Answer: 3,600
40 × 90 = 40 × 9 × 10 = 360 × 10 = 3600.
18What is 25% of 60?
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Answer: 15
25% is a quarter: 60 × 1/4 = 15.
19Write 9/25 as a decimal.
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Answer: 9/25 ≈ 0.36
Scale the denominator to 100: 9/25 = 36/100 = 0.36.
20What is 44²?
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Answer: 1,936
Round to the nearest ten and correct: a² = (a − r)(a + r) + r². Here 44² = 40 × 48 + 16 = 1920 + 16 = 1936.
21What is 47 × 90?
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Answer: 4,230
47 × 90 = 47 × 9 × 10 = 423 × 10 = 4230.
22What is 35% of 40?
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Answer: 14
Build it from easy pieces of 40: 10% is 4, 5% is 2. So 35% = 3 × 4 + 2 = 14.
23Write 17/25 as a decimal.
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Answer: 17/25 ≈ 0.68
Scale the denominator to 100: 17/25 = 68/100 = 0.68.
24What is 51²?
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Answer: 2,601
Round to the nearest ten and correct: a² = (a − r)(a + r) + r². Here 51² = 50 × 52 + 1 = 2600 + 1 = 2601.
25What is 61 × 13?
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Answer: 793
Split 13 into 10 + 3: 61 × 10 = 610 and 61 × 3 = 183. Add them: 610 + 183 = 793.
26What is 35% of 720?
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Answer: 252
Build it from easy pieces of 720: 10% is 72, 5% is 36. So 35% = 3 × 72 + 36 = 252.
27Write 24/25 as a decimal.
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Answer: 24/25 ≈ 0.96
Scale the denominator to 100: 24/25 = 96/100 = 0.96.
28What is 59²?
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Answer: 3,481
Round to the nearest ten and correct: a² = (a − r)(a + r) + r². Here 59² = 60 × 58 + 1 = 3480 + 1 = 3481.
29What is 68 × 24?
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Answer: 1,632
Split 24 into 20 + 4: 68 × 20 = 1360 and 68 × 4 = 272. Add them: 1360 + 272 = 1632.
30What is 45% of 720?
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Answer: 324
Build it from easy pieces of 720: 10% is 72, 5% is 36. So 45% = 4 × 72 + 36 = 324.
31What is 66²?
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Answer: 4,356
Round to the nearest ten and correct: a² = (a − r)(a + r) + r². Here 66² = 70 × 62 + 16 = 4340 + 16 = 4356.
32Write 11/32 as a decimal.
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Answer: 11/32 ≈ 0.3438
Start from the unit fraction: 1/32 = 0.03125. Then 11/32 = 11 × 0.03125 = 0.34375.