Fast Multiplication and Calculation Tricks

The candidate who clears the Numerical sectional timing is rarely the one who knows more formulas — it is the one who calculates faster. A handful of multiplication tricks shave five to ten seconds off every DI cell, and across 35 questions that saving is the whole difference between finishing the section and running out of time with easy marks still on the screen.

Trick 1: Multiply by 5, 25, 50 and 125

Powers of ten hidden inside these multipliers make them almost free. Replace the multiplier with a multiply-and-divide pair and the arithmetic becomes a single mental step.

• × 5 → × 10 then ÷ 2 (46 × 5 = 460 ÷ 2 = 230)
• × 25 → × 100 then ÷ 4 (68 × 25 = 6800 ÷ 4 = 1700)
• × 50 → × 100 then ÷ 2
• × 125 → × 1000 then ÷ 8

Trick 2: Multiplying Two Numbers Near 100

Base 100, deviations d1 and d2 → answer = (a + d2) written as hundreds, then (d1 × d2)

Take 96 × 97, with deviations −4 and −3 from 100. Compute (96 − 3) = 93 for the left part and (−4)(−3) = 12 for the right, giving 9312. This base method is a lifesaver in approximation and in any DI cell where both figures sit close to a round hundred.

Trick 3: Squaring Any Two-Digit Number

Split the number into a round part plus a small remainder and expand with (a + b)². For 43² write 43 = 40 + 3, so (40 + 3)² = 1600 + 240 + 9 = 1849. You can also step up from a known square: since 55² = 3025, 56² = 3025 + 55 + 56 = 3136.

Trick 4: The Digit-Sum Check

After any multiplication, verify with digit sums. For 96 × 97 the digit sums are 6 and 7, and 6 × 7 = 42 → 6. The answer 9312 has digit sum 9 + 3 + 1 + 2 = 15 → 6. They match, so the answer is internally consistent. This one-second check quietly kills the careless slips that cost otherwise strong candidates two or three marks a paper.

Solved Examples

Example 1: 84 × 25 = 8400 ÷ 4 = 2100.

Example 2: 98 × 94: (98 − 6) = 92 and (−2)(−6) = 12 → 9212.

Example 3: 46² = (46)² = 2000 + 116 + ... simpler as (45 + 1)²... use 45² = 2025, then 46² = 2025 + 45 + 46 = 2116.

✗ 68 × 25 by long multiplication  |  ✓ 6800 ÷ 4 = 1700 in one step