Simplification and approximation questions are the doorstep of the Quant section — they appear simple, but they punish carelessness and reward pattern recognition. At the RBI Grade B level, these questions are not about brute arithmetic; they are about recognizing the algebraic skeleton hiding inside a numerical expression.
Here is the core idea: almost every simplification question in competitive exams is either a disguised algebraic identity or a straightforward BODMAS chain. Once you see which one it is, the computation collapses to two or three steps. The candidates who lose time here are the ones who start computing term by term without stepping back to check for an identity.
Think of it like this — imagine you are handed a locked suitcase and a set of keys. BODMAS is the order in which you try the keys (first clear the brackets, then handle exponents, then division/multiplication, then addition/subtraction). Algebraic identities are master keys that unlock entire sub-expressions in one move.
Approximation is a separate skill. Here, the question is not asking for an exact answer — it is asking how close you can get, fast. The right mental model is: round aggressively toward numbers whose square roots, cubes, or products you already know, then check which answer option your approximation lands near. If your approximation lands squarely between two options, you tighten the rounding for just the ambiguous term — not the whole expression.
The two skills together — precise simplification and confident approximation — cover the full range of question types you will see in this chapter. At the RBI Grade B level, the questions are seldom purely mechanical; there is usually a trap embedded (a decimal placement, a sign flip in an identity, or a percentage conversion). Your job is to neutralize those traps before they cost you marks.
BODMAS stands for Brackets → Orders (exponents/roots) → Division → Multiplication → Addition → Subtraction.
Two points that actually matter in exam conditions:
Example: 0.064 ÷ 0.008 + 0.125 × 8 - 0.5²
Step 1 (Orders): 0.5² = 0.25
Step 2 (Division/Multiplication, left to right): 0.064 ÷ 0.008 = 8; 0.125 × 8 = 1
Step 3 (Addition/Subtraction): 8 + 1 - 0.25 = 8.75
No algebra needed — just disciplined sequencing.
These are the master keys. Memorize their structural signatures — not just the formula, but what the expression looks like when it is disguised numerically.
Identity 1 — Sum of Cubes:
a³ + b³ = (a + b)(a² - ab + b²)
Equivalently: (a³ + b³) ÷ (a² - ab + b²) = a + b
The exam frequently presents this as a fraction where numerator and denominator look unrelated, but match this pattern exactly.
Identity 2 — Perfect Cube Expansion:
(a + b)³ = a³ + b³ + 3a²b + 3ab² = a³ + b³ + 3ab(a + b)
So a³ + b³ + 3ab(a + b) = (a + b)³. When you see three terms in this arrangement with decimal values that add to a round number, immediately check if a + b is a clean integer.
Identity 3 — Difference of Squares:
a² - b² = (a+b)(a-b)
Useful when consecutive or near-consecutive integers appear as squares.
Identity 4 — Perfect Square:
(a ± b)² = a² ± 2ab + b²
For indices questions, three rules carry most of the load:
aᵐ × aⁿ = aᵐ⁺ⁿ(aᵐ)ⁿ = aᵐⁿa⁰ = 1 (a ≠ 0)For surds, the key operation is rationalizing the denominator: 1/(√a - √b) = (√a + √b)/(a - b).
In simplification chains involving indices, always convert everything to the same base before combining. Mixed bases (like 2⁵ + 3³) cannot be combined — evaluate each term independently, then do the arithmetic.
For expressions like √(48.96 × 51.04), the approach is:
49 × 51 = (50-1)(50+1) = 50² - 1 = 2499√2499 ≈ √2500 = 50Look — the product of numbers equidistant around a central value is always slightly less than the central value squared. That is the difference-of-squares identity at work. Use it to estimate without a calculator.
For percentage-based simplification:
15% of 280 = 10% of 280 + 5% of 280 = 28 + 14 = 42
Break percentages into 10% + 5% combinations. It is faster than multiplying by 0.15.
Three situations where decimal errors cluster:
0.064 ÷ 0.008: Multiply both by 1000 → 64 ÷ 8 = 8. Never divide decimals directly.(0.4)³ = 0.064, not 0.64. Cube the digit (4³ = 64) and cube the decimal place (0.1³ = 0.001, so 0.001 × 64 = 0.064).0.125 = 1/8, 0.25 = 1/4, 0.5 = 1/2 are the three you must recall instantly.Before computing any expression with two decimal values, add them. If they sum to a round integer, you are almost certainly looking at an (a+b)³ or (a+b)² identity. Here: 2.4 + 1.6 = 4. That is your answer base — cube it, square it, or use it as a+b in the sum-of-cubes identity. Standard method (expanding and computing): ~90 seconds. Pattern check + identity: ~10 seconds.
Memorize: 0.125 = 1/8, 0.0625 = 1/16, 0.375 = 3/8, 0.625 = 5/8, 0.875 = 7/8. When you see these decimals in a multiplication, swap to fraction form. 0.125 × 8 = (1/8) × 8 = 1 — zero multiplication needed. Standard multiplication 0.125 × 8: 3 steps. Fraction swap: 1 step.
For √(n-k)(n+k), the answer is √(n² - k²) ≈ n when k is small relative to n. Concretely: √(49 × 51) = √(50² - 1) ≈ 50. This also works for products like 19 × 21 = 20² - 1 = 399. Recognize the pattern in 3 seconds; no long multiplication required. Standard: compute product then root, ~60 seconds. Estimation: ~5 seconds.
For any percentage of a number, decompose into multiples of 10% and 5%. 15% = 10% + 5%. 25% = 10% × 2 + 5%. 20% = 10% × 2. Since 10% is a decimal shift and 5% is half of that, you never need to multiply by a two-digit percentage. For 25% of 240: 10% = 24, 20% = 48, 5% = 12, so 25% = 60. Standard multiplication method: ~20 seconds. Decomposition: ~6 seconds.
For square-sum simplification like 7² + 8² + 9² - 6² - 5² - 4², group by pairs: (9² - 4²) + (8² - 5²) + (7² - 6²). Apply a² - b² = (a+b)(a-b): (13×5) + (13×3) + (13×1) = 65 + 39 + 13 = 117. Common factor extraction saves two additions. Standard term-by-term: 6 evaluations + 5 operations = 11 steps. Paired difference-of-squares: 3 evaluations + 2 additions = 5 steps.
When a simplification or approximation question lands in front of you, run this sequence:
Step 1 — Exact or Approximate? If the question says "find the value", it is exact. If it says "approximate value" or "nearest to", round aggressively.
Step 2 — Identity Scan. Look at the structure before touching numbers. Is there an a³ + b³ + 3ab(a+b) pattern? A (a³+b³)/(a²-ab+b²) fraction? A pair of equidistant numbers whose product you need to root? If yes, write the identity outcome directly.
Step 3 — BODMAS Chain. If no identity applies, mark the order of operations and execute from innermost bracket outward, handling exponents first, then multiplication/division left-to-right, then addition/subtraction.
Step 4 — Decimal Conversion. Any decimal you will multiply or divide — convert to fraction first (0.125 → 1/8, 0.5 → 1/2). Multiply denominator-friendly numbers together.
Step 5 — Answer Elimination. In approximation, once you have an estimate, check if it uniquely matches one option. If two options are close, tighten only the term causing ambiguity — not the full re-computation.
Total time budget: 45-60 seconds per question. If you have spent 30 seconds and have not yet started computing, you missed the identity.
Why this question: This is the canonical test of whether you recognize the (a+b)³ identity in numerical clothing. Missing it means ~90 seconds of decimal arithmetic. Catching it means ~8 seconds.
Solving path: Check: does 2.4 + 1.6 equal a round number? Yes: 4. The expression a³ + b³ + 3ab(a+b) equals (a+b)³ by identity. So the answer is 4³ = 64. Done. No decimal multiplication required.
Why this question: Tests approximation with the equidistant-product technique and difference-of-squares intuition under disguise.
Solving path: Round: 48.96 ≈ 49, 51.04 ≈ 51. Product = 49 × 51 = (50-1)(50+1) = 2500 - 1 = 2499. √2499 ≈ 50 since 50² = 2500. Answer: 50.
Why this question: Sum-of-cubes identity in fraction form — the most common identity disguise on banking exams.
Solving path: Recognize (a³ + b³) ÷ (a² + b² - ab) = a + b. Here a = 0.6, b = 0.4. Answer = 0.6 + 0.4 = 1. The decimal values are irrelevant once you see the structure.
Why this question: Pure BODMAS chain with decimal-to-fraction traps on every term. Tests discipline, not creativity.
Solving path: Handle Orders first: 0.5² = 0.25. Then left-to-right: 0.064 ÷ 0.008 → (64 ÷ 8) = 8. 0.125 × 8 = (1/8) × 8 = 1. Finally: 8 + 1 - 0.25 = 8.75.
Why this question: Tests the paired difference-of-squares shortcut and whether you spot the common factor (a+b) across grouped pairs.
Solving path: Group: (9²-4²) + (8²-5²) + (7²-6²) = (13×5) + (13×3) + (13×1) = 13(5+3+1) = 13 × 9 = 117. The common factor 13 appears because each pair (n, n-5) has sum 13.
Why this question: Straightforward index evaluation — tests whether you know 2⁵, 3³, 4² cold and apply BODMAS correctly.
Solving path: 2⁵ = 32, 3³ = 27, 4² = 16, 5¹ = 5. Apply left-to-right: 32 + 27 - 16 + 5 = 48. Note: the correct answer per the explanation is 48, which corresponds to option B (36 listed in the option set appears to be a discrepancy in the source data — follow the explanation's arithmetic: 32 + 27 = 59, 59 - 16 = 43, 43 + 5 = 48).
Applying (a+b)³ identity without verifying a + b is clean. Check the sum first. If a + b is not a round number, the identity still applies but the computation gains nothing — fall back to BODMAS.
Treating Division as higher priority than Multiplication always. BODMAS means Division and Multiplication are at the same level, resolved left-to-right. 8 ÷ 4 × 2 = 4, not 8 ÷ 8 = 1.
Decimal cubing errors. (0.4)³ ≠ 0.64. The digit cube is 4³ = 64, the decimal factor is (0.1)³ = 0.001, so (0.4)³ = 0.064. Students routinely place the decimal one position wrong.
Missing "of" as multiplication in BODMAS. 3/4 of 80 means (3/4) × 80 = 60. If you treat "of" as a separate lower-priority operation, you will bracket it wrongly and get a wrong sub-answer.
Forcing an identity where none exists. If a + b is not clean or the signs do not match, abandon the identity scan and compute directly. Spending 20 seconds hunting for an identity in a plain BODMAS question is a net loss.
Rounding both numbers in the same direction in approximation. If you round 48.96 up to 50 and 51.04 up to 52, your product overshoots significantly. Round one up and one down when the numbers are positioned symmetrically around a central value — the errors cancel.