Simplification and approximation questions are the quickest marks available in SBI PO Quant — and the quickest marks you can throw away by overthinking them. The distinction between the two is worth drawing clearly before you sit the exam.
Simplification means finding the exact value. The expression is designed so that every ugly decimal cancels out or every fraction reduces perfectly. You are not supposed to round — you are supposed to follow order of operations faithfully until the answer drops out cleanly.
Approximation means finding a value close enough to match one of the answer choices. The numbers are deliberately messy (18.97, 124.8, 23.8%) so that rounding them to the nearest integer or convenient number makes calculation trivially fast. The four options are spaced far enough apart that a well-rounded estimate will land on exactly one of them.
Think of it this way: simplification is arithmetic with a rulebook (BODMAS), and approximation is arithmetic with a compass — you don't need to be exact, you need to be pointed at the right answer.
The analogy that works in the classroom: simplification is like measuring a doorway with a tape measure to the millimetre before ordering a custom door. Approximation is like measuring it with your arm span before deciding whether to carry a sofa through it. Both are useful. The exam tests whether you know which tool to pick up and whether you can use it fast.
Here's the one thing that separates an 80-percentile from a 95-percentile candidate on these questions: the 95-percentile candidate never pulls out a long multiplication or division on an approximation question. They round first, every time, without guilt. Rounding is not sloppy — it is the method. The question is designed for it.
A few anchors to keep in your head:
48² and perfect cubes up to 20³ converts root questions from searches into instant recalls.BODMAS is not a trick, it is a convention. The order is:
The most common error candidates make is treating division as strictly higher priority than multiplication. They are co-equal and evaluated left to right. So 12 ÷ 4 × 3 = 3 × 3 = 9, not 12 ÷ 12 = 1.
A second common error is mishandling nested brackets. Work from the innermost bracket outward: 2 × [3 + {4 × (2 + 1)}] becomes 2 × [3 + {4 × 3}] → 2 × [3 + 12] → 2 × 15 = 30.
Not all rounding is equal. There are three levels of aggression you should apply based on how far apart the answer choices are.
Level 1 — Nearest Integer. Use this when answer choices differ by 4-6 units. Round 18.97 → 19, round 4.98 → 5, round 12.03 → 12. This level is standard for nearly all division/multiplication approximation questions.
Level 2 — Nearest Convenient Number. Use this when a number is close to a power of 2, a multiple of 25, or something that makes a calculation collapse. Round 124.8 → 125 (because 125 = 500/4, and you know 25 × 5 = 125 effortlessly). Round 98.7 → 100. Now the product is just 125 × 100 = 12,500.
Level 3 — Base Relationships. Use this when you notice a ratio hiding in the problem. Look at (7.98)³ ÷ (15.96)². Notice that 15.96 ≈ 2 × 7.98. Round both to 8 and 16. Now the problem is 8³ ÷ 16² = 512 ÷ 256 = 2. You never needed a calculator.
Percentage questions appear in approximation sets frequently. The fastest route is always:
For 23.8% of 847: round to 24% of 850. Now 24% = 6/25, so 850 × 6/25 = 34 × 6 = 204. That is close to 202. Done.
Percentages worth memorizing as fractions (these come up constantly):
| % | Fraction | |---|----------| | 12.5% | 1/8 | | 16.67% | 1/6 | | 33.33% | 1/3 | | 37.5% | 3/8 | | 62.5% | 5/8 | | 87.5% | 7/8 |
For root questions, you need two things: a table of perfect squares and cubes, and the ability to interpolate.
Perfect cubes to memorize: 10³=1000, 11³=1331, 12³=1728, 13³=2197, 14³=2744, 15³=3375, 16³=4096, 17³=4913, 18³=5832, 19³=6859, 20³=8000.
Perfect squares to memorize: at minimum, 1² through 48². The ones that come up in approximation: 37²=1369, 48²=2304 are exact values that appear in the PYQ set below.
When the number is not a perfect square/cube, bracket it: find the two perfect squares/cubes it falls between. Example: ∛6000 falls between 17³=4913 and 18³=5832... wait, 6000 > 5832, so between 18³=5832 and 19³=6859. Closer to 18 or 19? Midpoint is roughly 6346. Since 6000 < 6346, the answer is closer to 18. In an approximation context, ∛6000 ≈ 18.
When the expression has a numerator and denominator that are themselves expressions (like (156.7 + 243.2) ÷ (19.8 - 12.1)), round both independently before dividing. Do not cross-cancel before you round — that invites errors. Round numerator → 400, round denominator → 8, divide → 50. Check: closest option to 50 is 52. Done.
When you see an expression of the form A³ ÷ B², check immediately whether B ≈ 2A. If yes, substitute B = 2A mentally: A³ ÷ (2A)² = A³ ÷ 4A² = A/4. So 8³ ÷ 16² = 8/4 = 2. This collapses in 3 seconds. Standard approach (computing 512 ÷ 256) takes about 25 seconds with mental arithmetic.
When the percentage is within 1% of 12.5, 16.67, 25, 33.33, 37.5, or 62.5, switch to the fraction equivalent immediately. For 23.8% of 847: 23.8 ≈ 24 = 3/12.5... actually use 24% = 6/25. Round 847 → 850 (divisible by 25). 850 ÷ 25 = 34, 34 × 6 = 204. That is 3 multiplication steps. The decimal multiplication 0.238 × 847 takes 6-8 steps. Step-count difference: 5 fewer operations.
For expressions like (125 × 100) ÷ 125: recognize that 125 cancels completely. You get 100. No multiplication required at all. Train yourself to scan for cancellation before you compute. If the denominator divides the numerator cleanly (or nearly so), cancel first. Standard method: multiply then divide (two operations, ~20 seconds). Cancel-first method: one glance, ~3 seconds.
Before computing, look at the options. If they span a range of 20+ units (e.g., 48, 52, 56, 60), your rounding can be aggressive — off by ±3 is fine. If they span a range of 4 units (e.g., 46, 49, 52, 55), you need to be within ±1.5. This tells you how much rounding precision you need before you touch a number. Spending 5 seconds reading options saves you 15 seconds of over-precise calculation.
For perfect cubes, the unit digit of the cube root is unique: if the cube ends in 3, the root ends in 7; ends in 7, root ends in 3; ends in 2, root ends in 8; ends in 8, root ends in 2; all other digits (0,1,4,5,6,9) — the cube and root share the same unit digit. For ∛4913: ends in 3 → root ends in 7. Two-digit cube roots: 10³=1000, 20³=8000. Since 4913 < 8000 and > 1000, the root is between 10 and 20, and ends in 7. That gives 17 immediately. Time: 4 seconds vs. trial-and-error: 20+ seconds.
When you see a simplification/approximation question in the exam hall, run this decision path:
Step 1 — Exact or approximate? If all numbers are clean integers or simple fractions, it is a simplification — use BODMAS, do not round. If any number has a messy decimal (e.g., 18.97, 124.8), it is an approximation.
Step 2 — Scan for structure before computing. Look for: (a) cancellation between numerator and denominator, (b) a mirror ratio like B ≈ 2A, (c) a percentage close to a fraction anchor.
Step 3 — Check option spread. Wide spread (20+ units) → round aggressively to nearest 5 or 10. Tight spread (4-6 units) → round to nearest integer only.
Step 4 — Round, compute, compare. Do the arithmetic on the rounded numbers. Pick the closest option. If two options look equidistant from your estimate, you may have rounded too aggressively — redo with nearest integer instead of nearest 5.
Target time per question: 40-60 seconds. If you cross 75 seconds, mark your best guess and move on.
Why this question: Tests whether you spot the Level 2 rounding opportunity — 124.8 → 125 and 98.7 → 100 — and then notice the cancellation of 125 in numerator and denominator.
Solving path: Round 124.8 → 125, 98.7 → 100, 24.9 → 25, 4.97 → 5. Numerator: 125 × 100 = 12,500. Denominator: 25 × 5 = 125. Division: 12,500 ÷ 125 = 100. The answer is just below 100, so option 99. Confirm: the rounding pushed the numerator slightly up and the denominator slightly up, roughly cancelling. Answer: 99.
Why this question: Directly tests the Mirror Ratio Collapse trick. If you don't spot that 15.96 ≈ 2 × 7.98, you waste time computing 512 ÷ 256 from scratch.
Solving path: Round 7.98 → 8, 15.96 → 16. Notice 16 = 2 × 8. Apply pattern: 8³ ÷ (2×8)² = 8³ ÷ 4×8² = 8 ÷ 4 = 2. Answer: 2.
Why this question: Tests compound expression rounding — numerator and denominator must each be rounded independently before dividing.
Solving path: Numerator: 156.7 + 243.2 ≈ 157 + 243 = 400. Denominator: 19.8 - 12.1 ≈ 20 - 12 = 8. Division: 400 ÷ 8 = 50. Closest option is 52. Note: the denominator was rounded down (12.1 → 12) and up (19.8 → 20), which slightly understates the denominator from its true value of 7.7. True denominator is smaller than 8, so true quotient is slightly larger than 50. That pushes toward 52. Answer: 52.
Why this question: Straightforward nearest-integer rounding — no structural trick, just execution speed. If you over-think it, you lose time.
Solving path: 18.97 → 19, 12.03 → 12, 4.98 → 5. (19 × 12) ÷ 5 = 228 ÷ 5 = 45.6. Closest integer option: 46.
Why this question: Tests cube root by digit-ending pattern. Candidates who trial-and-error waste 20+ seconds. Candidates who use the unit-digit rule get it in under 5 seconds.
Solving path: 4913 ends in 3 → cube root ends in 7. The root is a two-digit number between 10 and 20. Only candidate ending in 7 in that range is 17. Verify mentally: 17² = 289, 289 × 17 = 4913. Answer: 17.
Why this question: Tests perfect-square recall for exact roots. √2304 and √1369 are both perfect squares — you should know 48² = 2304 and 37² = 1369 cold.
Solving path: √2304 = 48 (exact). √1369 = 37 (exact). 48 + 37 = 85. Answer: 85.
Applying approximation to a simplification question. If the numbers look messy but the question says "find the value" (not "approximate"), work it out exactly — the messiness is designed to cancel. Rounding here will give you a wrong answer that does not match any option exactly.
Treating division as higher priority than multiplication in BODMAS. 24 ÷ 6 × 2 is not 24 ÷ 12 = 2. It is 4 × 2 = 8. Division and multiplication are co-equal, evaluated left to right.
Rounding the denominator in the wrong direction. When you have A ÷ B and you round B down, your result goes up. When you round B up, your result goes down. In tight-option questions, be aware of which direction your rounding pushes the answer and use that to break ties between two adjacent options.
Using trial-and-error for cube roots instead of the digit-ending rule. This is a 20-second time sink per question. Learn the unit-digit mapping for cubes (3→7, 7→3, 2→8, 8→2, rest stay same) and cut that to 5 seconds.
Not scanning for cancellation before computing. Computing 125 × 100 ÷ 125 as two full operations instead of spotting the 125 cancellation immediately. Scan the full expression for shared factors before pressing any mental arithmetic button.
Over-precision on wide-spread options. If options are 48, 52, 56, 60, spending extra time to verify whether the answer is exactly 50 or exactly 52 is wasted. A rough estimate of "around 50" is enough to pick 52 as the only nearby option. Time spent beyond one rounding step yields zero additional accuracy for the answer you circle.