Simplification and Approximation Tricks for SSC, RRB and Bank Exams

There is a question you have seen in every mock: a long line of decimals, fractions, roots and percentages, with a question mark at the end. Nothing in it is conceptually hard. It is just long. You know how to do each step and you still lose ninety seconds, then get it wrong because you slipped at the third decimal.

Simplification and approximation are the least glamorous part of quant, and they are also the part where marks are most reliably won. No formula to derive, no clever insight. It is handling numbers so smoothly that the question stops feeling long. This post covers the working habits that get you there: the order of operations traps, a small set of identities worth memorising, a fraction-percent table, and the rules for rounding without going wrong.

Every example below was calculated and checked, so the answers you see are right, and where a shortcut gives only an approximate value I show the exact one next to it.

Where these questions actually appear

Exact counts change from year to year, and the notification is the final word, but broadly:

• IBPS PO and Clerk prelims: the quant section usually opens with a simplification or approximation block, often 5 to 10 questions. These are the cheapest marks in the section.
• SBI PO and Clerk prelims: same idea, often the first block in the numerical ability section.
• SSC CGL, CHSL and MTS: simplification is folded into the general quant section. Expect a couple of questions that are straightforward BODMAS, decimals, surds or fractions rather than a separate block.
• RRB NTPC and Group D: simplification, fractions, decimals and percentage-based number questions are a regular part of the maths section, and Group D leans on the school-level basics heavily.

If you are preparing for a bank exam, approximation is a full skill, and sets of ten questions in a few minutes are not unusual. If you are preparing for SSC or RRB, the same skill saves time for the harder questions in the paper.

Simplification and approximation are not the same thing

Simplification wants an exact answer. Approximation wants a close answer, and the options are spread widely enough that a close answer will do. Most people learn only one style and apply it to both. That is the leak.

• If the question says "find the value of" or has a missing number that must be an exact integer, treat it as simplification.
• If the question says "approximately" or "what should come in place of the question mark (?) in the following question" with options that are far apart and the numbers have awkward decimals like 39.8 or 7.98, treat it as approximation.

On the exam interface, you often see the phrase "(Note: you are not expected to calculate the exact value)". That is your permission to round.

Step zero: BODMAS, and the trap that costs marks every year

The order is brackets, orders (powers and roots), division and multiplication, addition and subtraction. The trap is that division and multiplication have the same rank, and you work left to right. The same goes for addition and subtraction.

Example: 48 ÷ 6 × 2 + 3² − 4.

• Powers first: 3² = 9.
• Then left to right on division and multiplication: 48 ÷ 6 = 8, then 8 × 2 = 16.
• Then addition and subtraction: 16 + 9 − 4 = 21.

The common mistake is to multiply 6 × 2 first, getting 48 ÷ 12 = 4, and ending at 4 + 9 − 4 = 9. That would have been right only if the expression had brackets around 6 × 2. Correct answer is 21.

Where does this bite in practice? In long fraction expressions with "of" in them. "Of" means multiply, and it acts immediately, like a bracket: 3/5 of 250 is done before you look at whatever is added to it.

Work through: 3/5 of 250 + 2/7 of 343 − 15% of 400.

• 3/5 of 250 = 150.
• 2/7 of 343 = 98 (343 ÷ 7 = 49, and 49 × 2 = 98).
• 15% of 400 = 60.
• Total: 150 + 98 − 60 = 188.

Another with three terms: 3/4 of 640 − 5/8 of 400 + 1/5 of 250 = 480 − 250 + 50 = 280.

Squares, cubes and the numbers that keep showing up

You do not need to memorise a table up to 100. What you need is:

• Squares up to 30, cold.
• Cubes up to 12 (12³ = 1728, 15³ = 3375 are worth knowing too).
• A handful of perfect squares that appear inside roots: 1521 = 39², 2116 = 46², 3025 = 55², 6084 = 78², 7569 = 87². I verified each of these. You will not memorise them all, but recognising that 6084 is a perfect square with last digit 4 (so the root ends in 2 or 8) helps you get it.

Squares of numbers ending in 5

Take the tens part n, compute n × (n + 1), then append 25.

• 35²: 3 × 4 = 12, append 25, giving 1225.
• 65²: 6 × 7 = 42, so 4225.
• 85²: 8 × 9 = 72, so 7225.

For a number like 18.5, treat it as 18.5² = 18 × 19 + 0.25 = 342 + 0.25 = 342.25. Same idea, and it is exact.

Squares near a base

Near 100: (100 − 2)² = 10000 − 400 + 4 = 9604 for 98². And 103² = 10000 + 600 + 9 = 10609.

Near 50: 47² = 2500 − 300 + 9 = 2209.

Formulas behind these are just (a ± b)² = a² ± 2ab + b², nothing more. The point is to pick the nearest round number.

The difference of squares

a² − b² = (a + b)(a − b). This one identity does an enormous amount of work.

Example: (47.5² − 2.5²) ÷ 45. Instead of squaring 47.5, note the numerator is (47.5 + 2.5)(47.5 − 2.5) = 50 × 45. Divide by 45 to get 50. It cancels neatly, and that neatness is your signal that you are using the right identity.

Another: 15.02² − 14.98² = (15.02 + 14.98)(15.02 − 14.98) = 30 × 0.04 = 1.2. Doing that by squaring two 4-digit decimals would take a minute and you would probably slip.

A third: 8.4² − 1.6² divided by 6.8. The numerator is (8.4 + 1.6)(8.4 − 1.6) = 10 × 6.8 = 68. Divide by 6.8 and you get 10.

Any time you see two squares subtracted, stop and check for this.

Multiplication shortcuts worth having

Situation	Method	Example
Multiply by 25	divide by 4, then ×100	48 × 25 = 12 × 100 = 1200
Multiply by 125	divide by 8, then ×1000	88 × 125 = 11 × 1000 = 11000
Multiply by 99, 999	multiply by 100 or 1000 and subtract	999 × 17 = 17000 − 17 = 16983
Two numbers equally far from a base	base² − gap²	96 × 104 = 100² − 4² = 9984
Multiply by 15	×10 plus half of that	4.8 × 15 = 48 + 24 = 72
Multiply by 12.5	divide by 8, ×100	12.5 × 3.2 = 40

Nothing exotic. What matters is that you notice the numbers in the question and have a shortcut waiting.

Checking with digit sums (a very underused trick)

When you have options that look alike, use the digit-sum check (the remainder mod 9) or the last-digit check to eliminate wrong ones quickly.

Example: 137 × 43. Last digit is 7 × 3 = 21, so it ends in 1. Digit sums: 137 gives 1 + 3 + 7 = 11, then 2. 43 gives 7. Their product is 14, which gives 5. The answer must have digit sum 5 and end in 1. The correct answer is 5891, whose digits add up to 23, then 5. It ends in 1. Check passed.

Say the options were 5871, 5891, 5981 and 5991. All end in 1, so the last digit does nothing. Digit sums do: 5871 gives 21, then 3, so it is out. 5991 gives 24, then 6, out. That leaves 5891 and 5981, which both give 5. Digit sums cannot separate them, because they are the same digits in a different order. That is the limit of the method: it catches most arithmetic slips but not transposed digits. Use it as a filter, not a proof.

The fraction-percent table (yes, again)

Memorise this once and you will use it in simplification, DI, profit and loss and percentages.

Fraction	Value	Fraction	Value
1/2	50%	1/9	11.11%
1/3	33.33%	1/10	10%
1/4	25%	1/11	9.09%
1/5	20%	1/12	8.33%
1/6	16.67%	1/13	7.69%
1/7	14.28%	1/14	7.14%
1/8	12.5%	1/16	6.25%

And a few multiples: 3/8 is 37.5%, 5/12 is 41.67%, 7/16 is 43.75%, 5/6 is 83.33%.

The use is more than converting. It lets you replace percentages with fractions and then cancel. For instance, 37.5% of 640: 37.5% is 3/8, and 640 ÷ 8 = 80, times 3 is 240. Or 12.5% of 640 is 80, which is a one-liner. Or 15% of 360 + 36% of 150: 15% of 360 is 54, and 36% of 150 is 54 too. Total 108.

Decimals, and the place-value slip

Most decimal errors are counting-zeros errors. Two habits help.

1. Count decimal places in the question, multiply as whole numbers, then place the decimal in the answer at the sum of places. For 2.5 × 0.04: 25 × 4 = 100, with 1 + 2 = 3 decimal places gives 0.100, which is 0.1.
2. For division, shift both numbers by the same power of ten until the divisor is a whole number. 1.2 ÷ 0.04 becomes 120 ÷ 4 = 30.

A longer example: (2.5 × 0.04) ÷ (0.05 × 10). Numerator = 0.1. Denominator = 0.5. Result = 0.2. Do it like this instead of expanding everything.

For squares of decimals, 0.7² = 0.49, 0.07 × 0.7 = 0.049, 1.1² = 1.21, and 0.99² = 0.9801. Get comfortable with these; they turn up inside roots.

Surds and roots

Square roots in simplification are almost always perfect squares hidden in decimals or fractions. √0.0169 = 0.13 (because 13² = 169, and 0.13² = 0.0169). √1.44 = 1.2. √2.25 = 1.5. The rule is that the number of decimal places in the root is half those in the number.

For non-perfect squares, use the nearest perfect square. √3599 is a hair under √3600 = 60. Actual value is 59.99. √624.8 is just under √625 = 25. Actual is 24.996. In approximation questions, that is all you need.

Estimating a root: for √n where n is between two known squares, interpolate. √150 is between 12 (144) and 13 (169). 150 is 6 above 144, and the gap to 169 is 25, so it is about 12 + 6/25 = 12.24. The exact value is 12.247. That is close enough to pick from options.

Approximation: the actual method

The rounding rules students often are not told:

Rule 1: Round to numbers that make the operation easy, not to the nearest whole number.

For 7.98 × 24.03, replace 7.98 with 8 and 24.03 with 24. Product is 192. The exact answer is 191.76. Error below 0.15%.

Rule 2: Errors accumulate. If you round three numbers, check that they do not all round in the same direction.

Consider 4789 ÷ 39.8 + 21.02². Round 4789 to 4800 (up) and 39.8 to 40 (up). Dividing, these errors partly cancel: 4800/40 = 120. The exact value of the first term is 120.33. Then 21.02² becomes 21² = 441. Sum is about 561. Exact value is 562.17. If the options are 540, 560, 580, 600, then 560 is your answer with room to spare.

Rule 3: Look at the spacing of the options. If the options are 5 or 10 percent apart, be aggressive. If two options are within 1 to 2 percent, round less, or compute.

Rule 4: Powers amplify error. 8.01³ is 513.92 exactly, whereas 8³ = 512. A 0.125% error in the base becomes about 0.375% after cubing. Still fine for wide options, but this is the one place where sloppy rounding shows.

Rule 5: Subtraction of near-equal numbers is where estimates fall apart. Look at 15.02² − 14.98². If you round each to 15², the difference becomes zero, but the real answer is 1.2. Whenever you subtract two close numbers, do not round first. Use the identity.

Worked approximations

1. 25% of 1199.8 + 12.5% of 800.4. Round to 1200 and 800. 25% of 1200 = 300, 12.5% of 800 = 100. Total 400. Exact is 399.99 or so, that is 299.95 + 100.05 = 400.0. Fine.

2. 5.2 × 19.8. Treat 19.8 as 20 − 0.2. So 5.2 × 20 = 104, less 5.2 × 0.2 = 1.04, giving 102.96. That is exact, not approximate, and it took about ten seconds.

3. 729 ÷ 26.9. Since 27 × 27 = 729, the quotient is 27.1 or so (exactly 27.10). Recognising 729 = 27² pays.

4. 44.9 ÷ 3.05. Round to 45 ÷ 3 = 15. Actual is 14.72, which is nearly 2% below. If the options include 14.7 and 15.2, the estimate would push you toward 15.2 wrongly, or make you unsure. Here you must compute more carefully, or round 3.05 to 3.05 and 44.9 to 45 and do 45/3.05 = 14.75. It shows how ratios magnify the error from the denominator. The denominator was rounded down by 1.6% (3.05 to 3), which raised the answer. So if you round the denominator, be careful.

5. 3.9² ÷ 1.3: recognise 3.9 = 3 × 1.3. So (3 × 1.3)² ÷ 1.3 = 9 × 1.3 = 11.7. Exact.

Notice that half of these "approximations" turned out to be exact once you saw the structure. Look for structure first.

Missing-number simplification

Typical shape: (? ÷ 45) = 15. Then ? = 45 × 15 = 675.

Or a cleaner one: 8.5² = ?. Use (8 + 0.5)² = 64 + 8 + 0.25 = 72.25.

The habit for missing-number questions is to work backwards from the answer choices when the operation chain is long. Plug in an option, check in one step. It sometimes beats solving forward.

Comparing fractions without a calculator

Cross-multiplication. Compare 3/7 and 5/12: 3 × 12 = 36, 5 × 7 = 35. Since 36 > 35, 3/7 is larger. Decimal check: 0.4286 against 0.4167. Correct.

In quantity comparison questions (Quantity I and Quantity II, common in bank mains and prelims), you often need the greater of two fractions, and cross-multiplying is almost always quicker than converting.

Common mistakes I see again and again

• Doing "of" after adding. "Of" belongs to its term, and it happens before the addition.
• Treating percent as a plain number in the middle of a calculation and forgetting to divide by 100.
• Rounding numerators and denominators in opposite directions so both errors add up.
• Squaring a decimal and miscounting places. 0.03² is 0.0009, not 0.009.
• Reaching for the calculator habit. In the real exam the calculator, when it exists, is slow. In many exams it does not exist.
• Approximating when the options are close. The scale of the answer choices should decide how much you round.
• Starting from the left and grinding the entire expression before looking for structure. Take five seconds to see if anything cancels.

A practice plan for four weeks

This is a rough plan; adjust it to your time.

Week 1: Foundations. Learn squares to 30, cubes to 12, the fraction-percent table and (a ± b)² and a² − b². Twenty minutes a day. Do not time yourself yet. The aim is recognition.

Week 2: Simplification blocks. Ten questions a day, exact answers, no calculator. Write down the shortcut you used in each. If you could not see one, note that too.

Week 3: Approximation. Ten a day, timed to about 40 seconds each. After each set, compute the exact values of two questions to see how much error your rounding created.

Week 4: Mixed timed sets. Sets of 10 in about 7 minutes, then trim. Add missing-number and quantity-comparison questions. Review every wrong answer and classify it: rounding, BODMAS, decimal place or careless.

In Pareeksha's free sectional practice you can pull quant sets and time yourself; the mock tests give you a section-level breakdown afterwards, so you can see whether your losses in the quant section come from simplification or from harder topics. That split matters. If you are losing marks in simplification, extra hours on geometry will not fix it.

Where this fits with the rest of quant

Simplification is the base for everything else. Percentages (percentage tricks), profit and loss, and data interpretation all depend on how fast you handle basic numbers. When you improve here, you get faster everywhere.

If you are deciding how many hours simplification deserves against other chapters, maths chapter weightage lays out the picture for SSC and RRB. Bank aspirants should think of it differently: the prelims quant is short and speed-heavy, and simplification-style questions can be the difference between a comfortable sectional cutoff and a scramble. See clearing banking sectional cutoffs for that side.

What to do this week

Pick ten simplification questions from any previous paper or mock you have already given. Redo each in under 45 seconds, and for every one, write the shortcut in a single line. If you cannot write it, you solved it the long way. Keep a running list of the shortcuts you use most; that list becomes your revision sheet before the exam.

FAQ

Do I need to memorise squares up to 50? Up to 30 is enough for most people, plus squares of numbers ending in 5 by the n(n+1) rule. Beyond 30 use the near-a-base method.

Is the on-screen calculator allowed in bank exams? It has been provided in some IBPS sections, but do not rely on it, since it slows you down and the notification is the final word. Practise without one.

How close should an approximation be? Within about 1 to 2 percent is comfortable when the options are spread by 5 percent or more. Check the spacing between the options before deciding how far to round.

Can I use these tricks in SSC exams too? Yes. Simplification in SSC is generally exact rather than approximate, but the identities, fraction-percent conversions and multiplication shortcuts all apply.

Should I do simplification first in the paper? In bank prelims, usually yes, since they are quick marks. In SSC, where sections are attempted in the order you choose within Quant, do the short questions first and leave long ones for the end.

Are the examples from real papers? No. They are practice examples built for this post, and every calculation was checked. Real papers are on the official sites.