Bank Exam Quant Tricks: Simplification, Series, Quadratic Equations

Open any bank prelims quant section and you will see the same shape: a block of simplification or approximation, a number series or two, a pair of quadratic equations, and a few quantity comparisons. None of it needs advanced maths. All of it needs speed. Aspirants who score well here are not smarter, they simply recognise the pattern in three seconds and avoid the long way round.

This guide gives you the method for each of these four topics, how to practise it, and 38 original worked examples. Every calculation has been checked step by step, so you can use the examples as a model for your own working. It also has a fractions-to-percentage table, squares up to 30, a list of common traps and a 30-day speed plan.

Percentage, profit and loss, time and work and data interpretation tricks are covered in other posts on this site, so we leave them out here.

Where these topics sit in a bank prelims

In IBPS PO prelims, the quantitative aptitude section has been 35 questions in 20 minutes, with a negative mark of one-fourth for each wrong answer. Other bank exams use similar sectional timing, but counts and timing change from year to year, so check the latest notification for the exam you are targeting.

Because each section has its own timer, you cannot borrow time from English or reasoning. That is why these four topics matter. They are quick if you know the method, and they let you bank easy marks before you touch the harder arithmetic and data sets.

• Simplification and approximation: usually a block of questions that rewards speed above everything else.
• Number series: one pattern per question, often with a missing term or a wrong term.
• Quadratic equations: two equations, find the relation between x and y.
• Quantity comparison: compare two quantities without fully solving both.

Simplification: BODMAS and the order that saves time

BODMAS means Brackets, Orders (powers and roots), Division and Multiplication, then Addition and Subtraction. Two points cause most errors.

• Division and multiplication have equal rank. Work from left to right. So 48 ÷ 6 × 2 is 8 × 2 = 16, not 48 ÷ 12 = 4.
• Addition and subtraction also have equal rank. Work from left to right.

Then use these habits to cut the calculation:

• Spot the easy partner before you multiply. Multiplying by 5, 25 or 125 is the same as multiplying by 10, 100 or 1000 and dividing by 2, 4 or 8.
• Convert percentages and decimals to fractions when the fraction is simpler: 12.5% is 1/8, 37.5% is 3/8, 16.67% is 1/6.
• Use identities: a² − b² = (a + b)(a − b), (a + b)² and (a − b)² expansions, and (100 − x)(100 + x) = 10000 − x².
• Cancel before you multiply when two or more fractions are being multiplied.

Square, cube and table shortcuts

• Squares ending in 5: take the tens digit n, multiply by (n + 1), and put 25 after it. 35² → 3 × 4 = 12, so 1225. 65² → 6 × 7 = 42, so 4225.
• Squares near 50: for 50 + d, the answer is (25 + d) followed by d² as two digits. 52² → 27 then 04, so 2704. For 50 − d, use (25 − d): 48² → 23 then 04, so 2304.
• Squares near 100: for 100 − d, the answer is (100 − 2d) followed by d² as two digits. 97² → 94 then 09, so 9409. For 100 + d, use (100 + 2d): 103² → 106 then 09, so 10609.
• Multiplying by 11: write the two ends and put the sum of the digits in the middle. 63 × 11 → 6, (6 + 3), 3 gives 693. If the middle sum is 10 or more, carry: 78 × 11 → 7, 15, 8 gives 858.
• Multiplying two numbers near a round number: 17 × 13 = 15² − 2² = 221.
• Cubes: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000 for 1 to 10; 11³ = 1331, 12³ = 1728, 13³ = 2197, 14³ = 2744, 15³ = 3375.

Worked examples: simplification

Example A1. Simplify: 125 × 16 ÷ 8 + 45. Left to right: 125 × 16 = 2000; 2000 ÷ 8 = 250; 250 + 45 = 295. Faster: 16 ÷ 8 = 2 first, then 125 × 2 = 250.

Example A2. Simplify: (84 ÷ 7) × 3 + 5² − 2³. Bracket: 84 ÷ 7 = 12. Then 12 × 3 = 36. Powers: 5² = 25, 2³ = 8. Total: 36 + 25 − 8 = 53.

Example A3. Simplify: 48 ÷ 6 × 2 + 3 × (10 − 4). Bracket: 10 − 4 = 6. Left to right: 48 ÷ 6 = 8, 8 × 2 = 16. Then 3 × 6 = 18. Total: 16 + 18 = 34. (Doing 6 × 2 first would give 4 + 18 = 22, which is wrong.)

Example A4. Find 3/8 of 640 + 5/6 of 288. 640 ÷ 8 = 80, so 3/8 is 240. 288 ÷ 6 = 48, so 5/6 is 240. Sum: 480.

Example A5. Find 0.25 × 360 + 12.5% of 480 − 1/6 of 120. 0.25 is 1/4, so 360 ÷ 4 = 90. 12.5% is 1/8, so 480 ÷ 8 = 60. 120 ÷ 6 = 20. Total: 90 + 60 − 20 = 130.

Example A6. Simplify: 98 × 102 + 37² − 36². 98 × 102 = (100 − 2)(100 + 2) = 10000 − 4 = 9996. 37² − 36² = (37 + 36)(37 − 36) = 73 × 1 = 73. Total: 9996 + 73 = 10069.

Example A7. Simplify: 15³ ÷ 25 + 4³. 15³ = 3375. 3375 ÷ 25 = 135 (since 3375 × 4 = 13500, and 13500 ÷ 100 = 135). 4³ = 64. Total: 135 + 64 = 199.

Example A8 (approximation). Find the approximate value of 39.97% of 849.8 + 14.9% of 600.2. Round to friendly values: 40% of 850 = 340; 15% of 600 = 90. Sum ≈ 430. The exact value is about 429.09, so 430 is the right choice when the options are spaced apart.

Example A9 (approximation). Find the approximate value of √624.9 × 11.98 ÷ 4.02. √624.9 ≈ √625 = 25; 11.98 ≈ 12; 4.02 ≈ 4. So 25 × 12 ÷ 4 = 25 × 3 = 75. The exact value is about 74.5, so look for the nearest option.

How to do approximation without going wrong

• Check the gap between options. If they differ by 1 or 2, round gently; if by 20 or more, you can round hard.
• Round each number to the nearest value that is easy to work with, not necessarily the nearest integer. 624.9 becomes 625 because 625 is a perfect square.

Reference tables: fractions to percentages, and squares up to 30

Learn these until you can recall them without thinking. A table you have read is not a table you know. Cover one column and test yourself.

Fractions to percentages

Fraction	Percentage	Fraction	Percentage
1/2	50%	1/11	9.09%
1/3	33.33%	1/12	8.33%
2/3	66.67%	1/13	7.69%
1/4	25%	1/14	7.14%
3/4	75%	1/15	6.67%
1/5	20%	1/16	6.25%
2/5, 3/5, 4/5	40%, 60%, 80%	1/17	5.88%
1/6	16.67%	1/18	5.56%
5/6	83.33%	1/19	5.26%
1/7	14.29%	1/20	5%
2/7	28.57%	1/8	12.5%
3/7	42.86%	3/8	37.5%
4/7	57.14%	5/8	62.5%
5/7	71.43%	7/8	87.5%
6/7	85.71%	1/9, 2/9	11.11%, 22.22%
1/10	10%	1/25	4%

Percentages are rounded to two decimal places where they do not end exactly. Any other fraction can be built from these: 5/9 is 5 × 11.11% = 55.56%, and 7/16 is 7 × 6.25% = 43.75%.

Squares from 1 to 30

n	n²	n	n²	n	n²
1	1	11	121	21	441
2	4	12	144	22	484
3	9	13	169	23	529
4	16	14	196	24	576
5	25	15	225	25	625
6	36	16	256	26	676
7	49	17	289	27	729
8	64	18	324	28	784
9	81	19	361	29	841
10	100	20	400	30	900

Squares are the backbone of series, quadratics and approximation. Knowing that 169 is 13² lets you spot a prime-square series. Knowing that 625 is 25² lets you round 624.9 safely.

Practice for simplification: do 10 mixed questions a day against a timer (about 40 seconds for plain simplification, 60 for approximation), note the shortcut you missed after each set, and spend 10 minutes daily on tables, squares and the fraction table in the first two weeks.

Number series: find the rule in under 30 seconds

Every series question is a search for one rule. Do the search in a fixed order so you never stare at the numbers.

1. Look at the size of the jumps. Small steady jumps mean a difference pattern. Terms that double or triple mean a ratio pattern.
2. Write the differences. If the differences are not constant, write the differences of the differences, or check whether they are squares, primes or a doubling sequence.
3. Check the ratios. Is each term a multiple of the previous one, or a multiple plus or minus a growing number (× 2 + 1, × 2 + 2, ...)?
4. Compare with squares and cubes. Terms like 9, 28, 65, 126 are one more than cubes. Terms like 4, 9, 25, 49 are squares of primes.
5. Check for two interleaved series. If terms alternate between small and large, or jump up and down, split the odd and even positions.
6. Try a sum rule. Each term may be the sum of the previous two.

For a missing term, find the rule from the terms that are clear, then fill the gap and check that the terms after it still fit. For a wrong number, find the rule from the first three or four terms, then spot where the series stops obeying it. The last terms often confirm the pattern.

Worked examples: number series

Example S1 (difference). 7, 12, 19, 28, 39, ? The differences are 5, 7, 9, 11, so the next difference is 13. Answer: 39 + 13 = 52.

Example S2 (ratio). 3, 6, 18, 72, 360, ? The multipliers are × 2, × 3, × 4, × 5, so the next is × 6. Answer: 360 × 6 = 2160.

Example S3 (squares of primes). 4, 9, 25, 49, 121, ? These are 2², 3², 5², 7², 11², so the next is 13². Answer: 169.

Example S4 (cubes). 9, 28, 65, 126, 217, ? These are 2³ + 1, 3³ + 1, 4³ + 1, 5³ + 1, 6³ + 1. Next: 7³ + 1 = 343 + 1 = 344.

Example S5 (alternating). 5, 3, 10, 6, 20, 12, 40, ? Odd positions: 5, 10, 20, 40 (× 2). Even positions: 3, 6, 12 (× 2). The missing term is the next even-position term: 12 × 2 = 24.

Example S6 (mixed). 4, 9, 20, 43, 90, ? Check: 4 × 2 + 1 = 9; 9 × 2 + 2 = 20; 20 × 2 + 3 = 43; 43 × 2 + 4 = 90. The next is 90 × 2 + 5 = 185.

Example S7 (missing term). 2, 5, 11, ?, 47, 95. Check the rule: 2 × 2 + 1 = 5; 5 × 2 + 1 = 11. So the missing term is 11 × 2 + 1 = 23. Confirm: 23 × 2 + 1 = 47, and 47 × 2 + 1 = 95. The rule fits all the way.

Example S8 (wrong number). 12, 14, 18, 26, 42, 75, 138. The differences are 2, 4, 8, 16, 33, 63. The doubling pattern says the differences should be 2, 4, 8, 16, 32, 64. So 42 + 32 = 74, and 74 + 64 = 138. The wrong number is 75; it should be 74.

Example S9 (differences of differences). 2, 3, 6, 11, 18, 27, ? The differences are 1, 3, 5, 7, 9, which increase by 2 each time. The next difference is 11. Answer: 27 + 11 = 38.

Example S10 (n(n + 1)). 2, 6, 12, 20, 30, 42, ? These are 1 × 2, 2 × 3, 3 × 4, 4 × 5, 5 × 6, 6 × 7. The next is 7 × 8 = 56. The differences (4, 6, 8, 10, 12) confirm it, since the next is 14 and 42 + 14 = 56.

Example S11 (sum of previous two). 4, 5, 9, 14, 23, 37, ? Check: 4 + 5 = 9; 5 + 9 = 14; 9 + 14 = 23; 14 + 23 = 37. Next: 23 + 37 = 60.

Example S12 (× n + n). 8, 9, 20, 63, 256, ? Check: 8 × 1 + 1 = 9; 9 × 2 + 2 = 20; 20 × 3 + 3 = 63; 63 × 4 + 4 = 256. Next: 256 × 5 + 5 = 1285.

How to practise number series

• Keep a pattern notebook. Each time a series stumps you, write the series and the rule on one line. Re-read the notebook every weekend.
• Practise the six-step order above until the first check becomes automatic.
• In the exam, if a series stays unclear after about 40 seconds, skip it. Wrong answers cost you a quarter mark; a lost minute costs more.

Quadratic equations: factorise, then compare

In the standard bank format you get two equations, one in x and one in y. You solve both and state the relation between x and y: x > y, x ≥ y, x < y, x ≤ y, x = y, or no relation (also called cannot be determined).

Method: splitting the middle term

1. Rearrange to the form ax² + bx + c = 0. If a is negative, multiply the whole equation by −1.
2. Multiply a and c. Find two numbers whose product is ac and whose sum is b.
3. Split the middle term using those two numbers, then factorise by grouping.
4. Set each bracket to zero to get the two roots.
5. Check: the sum of roots is −b/a and the product of roots is c/a.

Take 2x² − 7x + 6 = 0. Here ac = 12 and b = −7, so the two numbers are −3 and −4. Then 2x² − 4x − 3x + 6 = 2x(x − 2) − 3(x − 2) = (2x − 3)(x − 2). Roots: x = 3/2 and x = 2. Check: the sum is 3.5 and −b/a = 7/2 = 3.5; the product is 3 and c/a = 6/2 = 3.

Sign shortcut

For ax² + bx + c = 0 with a positive, you can tell the signs of the roots before you solve:

• c positive and b negative: both roots are positive.
• c positive and b positive: both roots are negative.
• c negative: one root is positive and one is negative. The larger root in absolute value takes the sign of −b.

This lets you pick the right pair of numbers faster. For x² + 9x + 20 you need two numbers with product 20 and sum 9, and both roots must be negative, so the roots are −4 and −5.

The comparison rules

Write the roots of x and the roots of y. Compare every root of x with every root of y, that is four comparisons for two roots each.

• If every x root is less than every y root, then x < y.
• If every x root is less than or equal to every y root (with at least one equality), then x ≤ y. The same logic holds for > and ≥.
• If all four comparisons come out equal, then x = y. This is rare and needs both equations to have the same repeated root.
• If the comparisons disagree (some say greater, some say less), then there is no relation.

A number line helps. Mark the x roots and the y roots. If the x points are all on one side of the y points, you have a relation. If they interleave or overlap beyond a single touching point, you do not.

Worked examples: quadratic equations

Example Q1. I: x² − 11x + 30 = 0. II: y² − 13y + 42 = 0. For I, product 30 and sum −11 give −5 and −6, so (x − 5)(x − 6) = 0 and x = 5, 6. For II, product 42 and sum −13 give −6 and −7, so y = 6, 7. Compare: 5 < 6, 5 < 7, 6 = 6, 6 < 7. Result: x ≤ y.

Example Q2. I: x² + 9x + 20 = 0. II: y² + 11y + 30 = 0. For I: (x + 4)(x + 5) = 0, so x = −4, −5. For II: (y + 5)(y + 6) = 0, so y = −5, −6. Compare: −4 > −5, −4 > −6, −5 = −5, −5 > −6. Result: x ≥ y.

Example Q3. I: x² − 7x + 12 = 0. II: y² − 5y + 4 = 0. For I: (x − 3)(x − 4) = 0, so x = 3, 4. For II: (y − 1)(y − 4) = 0, so y = 1, 4. Compare: 3 > 1 but 3 < 4. The results disagree, so no relation.

Example Q4. I: 2x² − 7x + 6 = 0. II: 2y² − 9y + 10 = 0. I gives x = 3/2, 2 as shown above. For II, ac = 20 and the numbers are −4 and −5: 2y² − 4y − 5y + 10 = 2y(y − 2) − 5(y − 2) = (2y − 5)(y − 2), so y = 5/2, 2. Compare: 1.5 < 2.5, 1.5 < 2, 2 < 2.5, 2 = 2. Result: x ≤ y.

Example Q5. I: x² − 16 = 0. II: y² − 9y + 20 = 0. I gives x = 4 or −4. II: (y − 4)(y − 5) = 0, so y = 4, 5. Compare: −4 < 4, −4 < 5, 4 = 4, 4 < 5. Result: x ≤ y.

Example Q6. I: 3x² + 11x + 10 = 0. II: 2y² + 7y + 6 = 0. For I, ac = 30 and the numbers are 5 and 6: 3x² + 6x + 5x + 10 = 3x(x + 2) + 5(x + 2) = (3x + 5)(x + 2), so x = −5/3, −2. For II, ac = 12 and the numbers are 3 and 4: 2y² + 4y + 3y + 6 = 2y(y + 2) + 3(y + 2) = (2y + 3)(y + 2), so y = −3/2, −2. Compare with decimals: x = −1.67, −2 and y = −1.5, −2. Then −1.67 < −1.5, but −1.67 > −2. The results disagree, so no relation.

Example Q7. I: x² − 5x − 14 = 0. II: y² − 3y − 10 = 0. For I: (x − 7)(x + 2) = 0, so x = 7, −2. For II: (y − 5)(y + 2) = 0, so y = 5, −2. Compare: 7 > 5, but −2 < 5. No relation.

Example Q8. I: x² − 17x + 72 = 0. II: y² − 11y + 28 = 0. For I: (x − 8)(x − 9) = 0, so x = 8, 9. For II: (y − 4)(y − 7) = 0, so y = 4, 7. Every x root (8, 9) is greater than every y root (4, 7). Result: x > y.

Example Q9. I: x² + 5x + 6 = 0. II: y² − y − 2 = 0. For I: (x + 2)(x + 3) = 0, so x = −2, −3. For II: (y − 2)(y + 1) = 0, so y = 2, −1. The largest x root is −2, which is less than the smallest y root, −1. Result: x < y.

Example Q10 (rearranged first). I: 2x² + 5x = 12. II: y² − 7y + 10 = 0. Rearrange I: 2x² + 5x − 12 = 0. Here ac = −24 and b = 5, so the numbers are 8 and −3: 2x² + 8x − 3x − 12 = 2x(x + 4) − 3(x + 4) = (2x − 3)(x + 4), so x = 3/2, −4. For II: (y − 2)(y − 5) = 0, so y = 2, 5. Largest x is 1.5, smaller than the smallest y, 2. Result: x < y.

How to practise quadratic equations

• First master factorisation. Take 20 equations with a = 1 and find the roots in your head. Then move to a ≠ 1.
• Do 10 equation pairs a day with a timer, aiming for 60 to 75 seconds per pair.
• Practise the comparison step separately: take pairs of root sets and name the relation within five seconds.

Quantity comparison: compare, do not calculate

In quantity comparison you get Quantity I and Quantity II and must decide which is greater, or whether they are equal or cannot be compared. The goal is to compare, not to compute both values to the last digit.

• Cross-multiply fractions: a/b versus c/d is the same as ad versus bc, for positive numbers.
• Use differences: if both quantities are close to the same number, compare how far each is from it.
• Use identities: the product of two unequal positive numbers is always smaller than the square of their average.
• Approximate: if one quantity is clearly larger by a wide margin, you need no more precision.
• Test values: when a variable is involved and the relation depends on its value, the answer is usually that it cannot be determined.

Worked examples: quantity comparison

Example C1. I: 17 × 13. II: 15². 17 × 13 = (15 + 2)(15 − 2) = 225 − 4 = 221. II is 225. Quantity II is greater.

Example C2. I: 5/9 of 198. II: 3/7 of 245. 198 ÷ 9 = 22, and 22 × 5 = 110. 245 ÷ 7 = 35, and 35 × 3 = 105. Quantity I is greater.

Example C3. I: the sum of the first 20 odd natural numbers. II: the sum of the first 19 even natural numbers. The sum of the first n odd numbers is n², so I = 400. The sum of the first n even numbers is n(n + 1), so II = 19 × 20 = 380. Quantity I is greater.

Example C4. I: the larger root of x² − 5x − 24 = 0. II: the HCF of 24 and 40. For I: (x − 8)(x + 3) = 0, so the roots are 8 and −3, and the larger is 8. For II: 24 = 2³ × 3 and 40 = 2³ × 5, so the HCF is 8. Both quantities are equal.

Example C5. I: 7/9. II: 5/7. Cross-multiply: 7 × 7 = 49 and 5 × 9 = 45. Since 49 > 45, the first fraction is larger. Quantity I is greater. Check with decimals: 0.778 versus 0.714.

Example C6. I: the value of x if 5x − 8 = 3x + 6. II: the value of y if 3(y − 2) = 2(y + 1). For I: 2x = 14, so x = 7. For II: 3y − 6 = 2y + 2, so y = 8. Quantity II is greater.

Example C7. I: the 7th term of 3, 6, 12, 24, ... II: the 6th term of 2, 6, 18, 54, ... For I, the terms follow 3 × 2^(n − 1), so the 7th is 3 × 2⁶ = 3 × 64 = 192. For II, the terms follow 2 × 3^(n − 1), so the 6th is 2 × 3⁵ = 2 × 243 = 486. Quantity II is greater.

Common traps

• Left-to-right slips: treating multiplication as stronger than division, or the reverse. They share a rank.
• Over-rounding in approximation: rounding hard when the options are close together. Look at the option gap first.
• Sign errors in quadratics: the factors (x − 5)(x − 6) give positive roots 5 and 6, not negative ones. Always set each factor to zero.
• Forgetting to rearrange: an equation like 2x² + 5x = 12 must be moved to one side before you factorise.
• Declaring a relation too early: checking only two of the four root pairs. Always check all four before you settle on a relation.
• Calling x = y when ≥ or ≤ fits: equality needs all four comparisons to match, which is rare. Most "equal" cases are ≤ or ≥.
• Quantity comparison over-calculation: computing two long values when a cross-multiplication would do.
• Skipping the unsure ones: guessing blindly costs a quarter mark each, but staying stuck for two minutes costs several easier questions.

A 30-day speed plan

Plan for about 60 to 90 minutes a day. The first two weeks build the toolkit; the last two weeks add timers and mixed sets. This is a planning suggestion, not a fixed rule, so shorten or lengthen it to suit your own starting point.

Days	Focus	Daily task
1 to 3	Tables, squares to 30, cubes to 15	10 minutes recall drill; 10 simplification questions with BODMAS only
4 to 6	Fraction-percentage table, fraction of a number	10 minutes recall drill; 15 questions mixing fractions and decimals
7 to 9	Simplification shortcuts (identities, near-100 squares, ×11)	20 simplification questions, record your time
10 to 12	Approximation and rounding rules	15 approximation questions; note where rounding changed the answer
13 to 15	Number series: difference, ratio, square and cube	15 series; maintain the pattern notebook
16 to 18	Number series: alternating, mixed, missing and wrong term	15 series with a 30-second limit each
19 to 21	Quadratic equations: factorisation with a = 1, then a ≠ 1	20 equations; find roots only
22 to 24	Quadratic comparisons and the no-relation cases	10 equation pairs with a 75-second limit each
25 to 26	Quantity comparison	10 comparisons; choose the method before calculating
27 to 28	Mixed sectional sets of all four topics	One 20-minute set a day; review every error
29	Full-length mock	Attempt the quant section first; log time per question type
30	Review and repair	Redo every wrong question from the month; revise both tables

Frequently asked questions

How many questions from these four topics can I expect in prelims? It varies by exam and shift. Check the latest notification and recent shift analyses for the exam you are taking, and prepare all four topics.

Should I memorise squares up to 30 or up to 50? Up to 30 is enough for most questions, along with the near-50 and near-100 shortcuts. Add 31 to 40 later if you have time.

Is it better to solve quadratics by factorisation or by the formula? Factorisation is usually faster for the equations set in bank-style practice, since the roots are typically whole numbers or simple fractions. Use the formula only if you cannot find the factors within about 20 seconds.

What does "no relation" mean? The roots of x and y overlap, so x is greater than y for some pairs and less for others.

How do I choose between approximation and exact calculation? Look at the options. If they are well spaced, approximate. If they differ by only one or two, calculate more precisely.

What if I cannot find the series pattern? Skip it after about 40 seconds and come back if time allows. A single series is not worth more than a full minute.

How much time should I give each topic in the 20-minute quant section? This is a suggestion, not a rule: roughly 6 to 8 minutes for the simplification and approximation block, 3 to 4 minutes for series, 3 to 4 minutes for quadratics, and the rest for the remaining questions. Adjust after your mocks.

How long before I see speed improving? It depends on where you start and how consistently you practise. Log your time per set and compare week to week.

Putting it into practice

These topics reward repetition, not cleverness. Learn the methods above, run the 30-day plan, and then test yourself under real conditions. Pareeksha has full-length mocks and sectional tests for bank exams, so you can time the quant section the way the exam will and see which of the four topics still slows you down.