How to Solve Approximation Problems Quickly
Solve approximation aptitude problems fast by rounding operands first, with a worked example and practice questions with answers.
Expected Interview Answer
Approximation problems ask for the closest whole number or round value to a complex arithmetic expression, solved by rounding each term to a convenient nearby value before computing, not by computing the exact answer and then rounding.
Round every number in the expression to the nearest value that makes mental computation easy — nearest ten, nearest hundred, or nearest simple fraction — while trying to round some values up and others down so the errors partially cancel rather than compound in one direction. For division and roots, round to the nearest perfect square, cube, or clean divisor so the operation resolves without a remainder. Multi-step expressions should be rounded and simplified using BODMAS order just like exact ones, only with rounded operands. Always sanity-check the approximate answer against the answer choices, since options are usually spread far enough apart that a rough estimate uniquely identifies the correct one.
- Rounding-first is dramatically faster than computing exact values
- Balanced up/down rounding keeps the estimate close to the true answer
- Answer choices are usually spread apart, so rough estimates suffice
AI Mentor Explanation
A commentator estimating a team’s final score rounds the current run rate and remaining overs to convenient numbers — 8.5 runs per over stays 8.5, roughly 10 overs remaining — rather than tracking every single run precisely. This quick mental rounding, done in directions that roughly cancel across the two factors, gives a close enough projection to compare against the target. Approximation problems reward exactly this: round first, then compute, rather than computing exactly and rounding after.
Worked example
Round terms
- 48.9% of 599 -> 49% of 600
- 29.7% of 401 -> 30% of 400
Compute rounded values
- 49% of 600 = 294
- 30% of 400 = 120
Approximate answer
- 294 + 120 = 414
Step-by-Step Explanation
Step 1
Round each operand
Round every number to the nearest value that is easy to compute mentally.
Step 2
Balance rounding direction
Round some values up and some down so errors partially cancel.
Step 3
Apply BODMAS to the rounded values
Simplify the rounded expression in the correct operator order.
Step 4
Match against answer choices
Compare the estimate to the options — they are usually spread apart enough to identify uniquely.
What Interviewer Expects
- Rounding operands before computing, not after
- Choosing rounding directions that balance the overall error
- Rounding roots/divisions to perfect squares or clean divisors
- Cross-checking the estimate against the given options
Common Mistakes
- Computing the exact value first and rounding only the final answer
- Rounding every number in the same direction, compounding the error
- Over-rounding to numbers so coarse the estimate misses the correct option
- Ignoring the answer choices when they could shortcut the amount of rounding needed
Best Answer (HR Friendly)
“For approximation problems I round each number to something easy to compute mentally, deliberately mixing rounding up and down so the errors cancel rather than pile up. I then apply the same BODMAS order to the rounded numbers and check the result against the given options, since the choices are usually spread far enough apart that a rough estimate is all that is needed.”
Follow-up Questions
- How close should a rounded estimate be to the exact value for typical answer-choice spacing?
- How do you approximate a square root that is not a perfect square?
- When should you round to the nearest ten versus the nearest whole percent?
- How would you approximate a three-term expression combining percentages and division?
MCQ Practice
1. Approximate value of 39.8% of 250.3 is closest to?
Round to 40% of 250 = 100.
2. Approximate value of 63.9 x 4.98 is closest to?
Round to 64 x 5 = 320.
3. Which approach is correct for approximation problems?
Approximation problems are solved fastest by rounding operands before computing, not after.
Flash Cards
Core approximation rule? — Round operands first, then compute — not the other way around.
Why mix rounding up and down? — Errors from over- and under-rounding partially cancel, keeping the estimate close.
How to approximate a division? — Round to the nearest clean divisor that removes the remainder.
How to finalize the answer? — Compare the rough estimate against the given options, which are usually spread apart.