Calculation speed for AFCAT: shortcuts that work and why

AFCAT's numerical questions are set at Class 10 level, so the ideas are rarely hard. What costs marks is the arithmetic: a slow multiplication, a carried digit that goes missing, or three minutes spent on a sum that should take forty seconds. With about 72 seconds per question across the paper, calculation speed turns directly into extra questions attempted.

This guide covers what to memorise, a small set of shortcuts that come up again and again, the reason each one works (so you can trust it under pressure), and quick ways to check an answer against the options.

What to learn by heart

Memorised facts are the fastest calculation of all. Aim for these:

Learn them in both directions. Seeing 289 should make you think "17²" without effort, just as 17² should give you 289.

Shortcuts, and why each one works

Multiplying by 5, 25 and 125

• × 5 = × 10 ÷ 2. 48 × 5 = 480 ÷ 2 = 240.
• × 25 = × 100 ÷ 4. 36 × 25 = 3,600 ÷ 4 = 900.
• × 125 = × 1,000 ÷ 8. 56 × 125 = 56,000 ÷ 8 = 7,000.

These work because 5 = 10/2, 25 = 100/4 and 125 = 1,000/8. Halving and dividing by 4 or 8 is much easier than multiplying by 5 or 25.

Multiplying a two-digit number by 11

Write the two digits apart and put their sum in the middle: 43 × 11 = 4 | 7 | 3 = 473. If the sum is 10 or more, carry the 1: 76 × 11 = 7 | 13 | 6 → 836.

Why: a two-digit number is 10a + b, and (10a + b) × 11 = 100a + 10(a + b) + b. The middle digit is literally a + b.

Squares of numbers ending in 5

Multiply the tens digit by the next number, then write 25: 65² → 6 × 7 = 42, then 25 → 4,225.

Why: (10a + 5)² = 100a² + 100a + 25 = 100a(a + 1) + 25.

Squares near 50

(50 + a)² = 2,500 + 100a + a². So 53² = 2,500 + 300 + 9 = 2,809, and 47² = 2,500 − 300 + 9 = 2,209.

This is just (x + a)² = x² + 2xa + a² with x = 50, where 2 × 50 × a = 100a.

Numbers near 100 (the base method)

Find how far each number is from 100. Take one number minus the other's shortfall, then write the product of the shortfalls as the last two digits.

• 97 × 96: shortfalls 3 and 4. 97 − 4 = 93, and 3 × 4 = 12 → 9,312.
• 96 × 98: shortfalls 4 and 2. 96 − 2 = 94, and 4 × 2 = 08 → 9,408. The product must fill two places.
• 104 × 107: excesses 4 and 7. 104 + 7 = 111, and 4 × 7 = 28 → 11,128.

Why: (100 − x)(100 − y) = 100(100 − x − y) + xy. The first part gives the hundreds and the second gives the last two digits. If xy is 100 or more, carry: 88 × 89 → 77 | 132 → 7,700 + 132 = 7,832.

Difference of squares

When two numbers are equally spaced around a round number, use (a + b)(a − b) = a² − b².

• 43 × 37 = 40² − 3² = 1,600 − 9 = 1,591.
• 52 × 48 = 50² − 2² = 2,496.

Percentages by 10% and 1%

Break any percentage into 10%, 5% and 1% pieces. 17% of 640: 10% = 64, 5% = 32, 2% = 12.8, total 108.8.

Also remember that x% of y = y% of x. 24% of 75 is the same as 75% of 24, which is 18.

Checking answers against the options

Often you do not need the full answer. You only need enough to rule out three options.

• Last digit. The last digit of a product depends only on the last digits of the numbers.
• Digit sum (casting out nines). Add the digits until one digit remains. The digit sum of a product equals the digit sum of the product of the digit sums.
• Size. A rough estimate removes options that are far too big or small.
• Divisibility. If the answer must be a multiple of 3, 4 or 11, test the options.

Worked examples

Example 1. 48 × 25 = ?

• 48 ÷ 4 = 12, then × 100 = 1,200.

Example 2. 76 × 11 = ?

• 7 | (7 + 6 = 13) | 6. Carry the 1 into the 7: 836.

Example 3. 93 × 97 = ?

• Shortfalls 7 and 3. 93 − 3 = 90, and 7 × 3 = 21 → 9,021.

Example 4. 36% of 450 = ?

• 10% = 45, so 30% = 135. 1% = 4.5, so 6% = 27.
• Total = 135 + 27 = 162.

Example 5 (option check). 23 × 47 × 19 = ? Options: 20,539; 20,541; 20,543; 20,549.

• Last digits: 3 × 7 = 21, so 1; then 1 × 9 = 9. The answer ends in 9, which leaves 20,539 and 20,549.
• Digit sums: 23 → 5, 47 → 11 → 2, 19 → 10 → 1. So 5 × 2 × 1 = 10 → 1.
• 20,539 → 2 + 0 + 5 + 3 + 9 = 19 → 10 → 1. 20,549 → 20 → 2.
• Answer: 20,539, found without multiplying out. (Check: 23 × 47 = 1,081, and 1,081 × 19 = 20,539.)

A 10-minute daily drill

1. 3 minutes: 20 multiplications using the shortcut that fits each one.
2. 2 minutes: 10 squares and cubes, recalled both ways.
3. 2 minutes: 10 fraction–percentage conversions.
4. 3 minutes: 5 option-check questions, where you choose the answer without full calculation.

Keep a log of your time for the 20 multiplications. The number should fall steadily over three or four weeks. If it stops falling, go back to the tables and squares.

Practice set

1. 64 × 25
2. 72 × 11
3. 95²
4. 96 × 98
5. 58²
6. 103 × 108
7. 61 × 59
8. 125 × 56

Answers:

1. 1,600. 64 ÷ 4 = 16, then × 100.
2. 792. 7 | 9 | 2.
3. 9,025. 9 × 10 = 90, then 25.
4. 9,408. Shortfalls 4 and 2: 94 | 08.
5. 3,364. 2,500 + 800 + 64.
6. 11,124. Excesses 3 and 8: 111 | 24.
7. 3,599. 60² − 1² = 3,600 − 1.
8. 7,000. 56 ÷ 8 = 7, then × 1,000.

What to do next

• Finish the memory list: tables to 20, squares to 30, cubes to 15.
• Do the 10-minute drill daily for four weeks and log your times.
• Use approximation whenever the options are far apart.
• Apply the shortcuts inside real questions from percentage and other arithmetic topics, so they become automatic under exam pressure.