Simplification and approximation for IBPS PO

Simplification and approximation questions are the closest thing IBPS PO has to free marks. There is no concept to understand and no trap in the wording; the question is only whether you can calculate accurately in under 30 seconds. A candidate with sharp mental arithmetic can finish a set of five in two to three minutes and bank marks that others spend six minutes on.

That speed does not come from a list of tricks. It comes from a handful of facts you know by heart (squares, cubes, fraction–percentage pairs) and a few habits you practise daily. This guide covers both.

How the questions are asked

• Simplification: an exact expression with one missing value, shown as "?". You work out the number exactly.
• Approximation: the numbers are deliberately untidy (29.97%, 601.2, 14.02). You round them and pick the nearest option.
• In recent prelims papers these have often come as a set of about five, though some shifts replace them with other types. The instructions tell you which kind it is; read them, because "find the approximate value" changes how you should work.

BODMAS, with the traps

The order is Brackets, Orders (powers, roots, and "of"), Division and Multiplication from left to right, Addition and Subtraction from left to right.

• "Of" before division. In 80 ÷ 1/4 of 20, work out "of" first: 1/4 of 20 = 5, so the answer is 80 ÷ 5 = 16. Reading it as (80 ÷ 1/4) × 20 gives 6,400, which is wrong.
• Division and multiplication are equal in rank. 48 ÷ 6 × 2 = 8 × 2 = 16, not 48 ÷ 12 = 4. Go left to right.
• Negative signs inside brackets. 5 − (3 − 8) = 5 − (−5) = 10, not 0.

Percentage and fraction shortcuts

• Swap trick: x% of y = y% of x. Why: both equal xy/100. So 48% of 25 = 25% of 48 = 12, which is much easier.
• Split trick: 35% = 25% + 10%. So 35% of 280 = 70 + 28 = 98. Why: percentages add, and 25% and 10% are both easy.
• Fraction trick: 37.5% of 640 = 3/8 × 640 = 240.

Squares, roots and cubes

Learn squares to 50 and cubes to 20 by heart. Then use these methods for the rest.

Squares near 50: (50 + k)² = 2,500 + 100k + k². So 57² = 2,500 + 700 + 49 = 3,249. Why: it is (a + b)² with a = 50.

Squares near 100: (100 + k)² = 10,000 + 200k + k². So 104² = 10,000 + 800 + 16 = 10,816.

Square roots of perfect squares. Take √7,056.

• 80² = 6,400 and 90² = 8,100, so the root is between 80 and 90.
• The number ends in 6, and only numbers ending in 4 or 6 have squares ending in 6. So the root is 84 or 86.
• 85² = 7,225, which is more than 7,056, so the root is below 85: 84.

Cube roots of perfect cubes. The last digit of a cube fixes the last digit of its root: 0→0, 1→1, 2→8, 3→7, 4→4, 5→5, 6→6, 7→3, 8→2, 9→9. Take ∛42,875.

• It ends in 5, so the root ends in 5.
• Drop the last three digits: 42. Since 3³ = 27 ≤ 42 < 64 = 4³, the tens digit is 3.
• The root is 35. Check: 35³ = 42,875.

Difference of squares: a² − b² = (a − b)(a + b). So 15² − 12² = 3 × 27 = 81.

Approximation rules

1. Look at the options first. If they are far apart (for example 320, 360, 400), rough rounding is safe. If they are close (318, 320, 322), round more carefully.
2. Round to friendly numbers: 29.97% → 30%, 601.2 → 600, 14.02 → 14, 9.98 → 10.
3. Round in opposite directions where you can. If you round one factor of a product up, round the other down, so the errors partly cancel.
4. Keep roots honest. √1,225.4 ≈ √1,225 = 35. Do not round 1,225.4 to 1,200, because √1,200 is not a whole number.

Six worked examples

Example 1: 45% of 640 + 3/4 of 256 = ?

• 45% of 640: 10% is 64, so 40% is 256, and 5% is 32. Total 288.
• 3/4 of 256 = 192.
• Answer: 288 + 192 = 480.

Example 2: √1,764 + 17² = ?

• √1,764 = 42 (40² = 1,600; ends in 4, so 42 or 48; 45² = 2,025 is too big, so 42).
• 17² = 289.
• Answer: 331.

Example 3 (approximation): 29.97% of 601.2 + 14.02 × 9.98 ≈ ?

• ≈ 30% of 600 + 14 × 10 = 180 + 140 = 320.
• The exact value is about 320.1, so the rounding lost almost nothing.

Example 4 (missing value): √? × 14 = 25% of 1,176

• 25% of 1,176 = 294.
• √? = 294 ÷ 14 = 21.
• ? = 21² = 441.

Example 5 (fractions): 3¼ + 2⅔ − 1⅚ = ?

• Whole numbers: 3 + 2 − 1 = 4.
• Fractions: 1/4 + 2/3 − 5/6 = 3/12 + 8/12 − 10/12 = 1/12.
• Answer: 4 1/12.

Example 6 (approximation with a root): √1,225.4 × 7.98 − 24.97% of 399.8 ≈ ?

• ≈ 35 × 8 − 25% of 400 = 280 − 100 = 180.
• The exact value is about 179.5.

Checking with digit sums

To check a multiplication, add the digits of each number until one digit remains, multiply those, and reduce again. The answer's digit sum must match.

• 23 × 14 = 322. Digit sums: 2 + 3 = 5 and 1 + 4 = 5; 5 × 5 = 25, and 2 + 5 = 7. The answer: 3 + 2 + 2 = 7. The check passes.

Why it works: every number leaves the same remainder on division by 9 as its digit sum does, and remainders multiply. The check misses some errors, such as swapped digits, but catches most slips in a few seconds.

Common mistakes

• Doing division before "of".
• Rounding everything up, so the errors pile up in one direction.
• Confusing squares and square roots under time pressure. Read the symbol twice.
• Working out an approximation exactly. If the options are 40 apart, a rough answer is enough.
• Forgetting that ? may be squared or under a root in missing-value questions.

A daily 10-minute drill

Practice set

1. 35% of 280 + 2/5 of 150 = ?
2. √2,025 + 12² = ?
3. Approximate: 49.9% of 801 + 19.97 × 5.02
4. ? ÷ 8 = 15% of 480
5. 48% of 125 + 12.5% of 480 = ?
6. (?)² = 18² + 24²
7. Approximate: 1,199.8 ÷ 24.03 + 7.02 × 15.98
8. 4½ × 2⅔ ÷ 1⅓ = ?

Answers:

1. 158. 35% of 280 = 70 + 28 = 98; 2/5 of 150 = 60.
2. 189. √2,025 = 45; 12² = 144.
3. About 500. ≈ 50% of 800 + 20 × 5 = 400 + 100.
4. 576. 15% of 480 = 72, and 72 × 8 = 576.
5. 120. Swap: 48% of 125 = 125% of 48 = 60; 12.5% of 480 = 480 ÷ 8 = 60.
6. 30. 324 + 576 = 900, and √900 = 30.
7. About 162. ≈ 1,200 ÷ 24 + 7 × 16 = 50 + 112.
8. 9. 9/2 × 8/3 = 12, and 12 ÷ 4/3 = 12 × 3/4 = 9.

What to do next

• Learn squares to 50 and cubes to 20 this week, ten a day.
• Do the 10-minute drill daily for a month.
• Take one 5-question simplification set with a 2.5-minute timer every day.
• Then move on to number series, the next fastest block, and see the full quant plan.