Numerical Estimation Techniques
Estimation is a powerful tool in numerical reasoning tests. When exact calculation is slow or unnecessary, a good estimate can give you the answer—or at least eliminate wrong options. Here's how to use it effectively.
When to Estimate
- "Approximately" or "closest to" – The question invites estimation. Round and calculate quickly.
- Options are far apart – If answers are 100, 500, 1000, 5000, a rough estimate can rule out several.
- Time pressure – When you're running low on time, estimation may be the only way to attempt more questions.
- Sanity check – After calculating, estimate to verify. If your answer is 847 and you estimated ~800, it's plausible. If you got 8470, something may be wrong.
Techniques
Round to friendly numbers – 47 × 23 ≈ 50 × 20 = 1000. 156 ÷ 7 ≈ 140 ÷ 7 = 20 (or 160 ÷ 8 = 20). Choose round numbers that make mental math easy.
Round consistently – If you round 47 up to 50, round 23 down to 20 to partially cancel error. Or round both in the same direction and note whether your estimate is high or low.
Percentage shortcuts – 10% of X = X ÷ 10. 5% of X = half of 10% = X ÷ 20. 15% of X = 10% + 5% = X ÷ 10 + X ÷ 20.
Order of magnitude – 47 × 23 is in the hundreds (40×20=800, 50×30=1500), so the answer is around 1000. Use this to eliminate options like 100 or 10000.
Practice
- Round first, then calculate – Get used to rounding before you compute. 3827 + 1943 ≈ 3800 + 1900 = 5700. Actual = 5770. Close enough for "approximately".
- Know your limits – Estimation works when options are spread out. When they're close (e.g. 24.5, 25.1, 25.8), you'll need to calculate more precisely.
- Use elimination – Even a rough estimate can rule out 2–3 options. That improves your odds if you have to guess.
Pitfalls
- Over-rounding – Rounding 47 to 50 and 23 to 20 gives 1000, but 47×23 = 1081. For "closest to", 1000 might still be correct among options 800, 950, 1081, 1200. But if options include 1050 and 1100, you need more precision.
- Wrong direction – If you round both numbers up, your estimate is high. If both down, it's low. Adjust your interpretation accordingly.
- Units – Don't forget to apply units. 50 × 20 = 1000, but if the values are in thousands, the answer might be 1,000,000.
Practice with numerical reasoning questions and the numerical reasoning test.
Frequently Asked Questions
How accurate does my estimate need to be?
It depends on the options. If they're 100, 500, 1000, 5000, an estimate of "around 1000" is enough. If they're 980, 1020, 1080, 1150, you need to be within about 50–100. Calculate more precisely in that case.
Can I use estimation for percentage change?
Yes. (New − Old) ÷ Old. Round New and Old to make the division easy. E.g. 107 − 95 ≈ 110 − 100. 10 ÷ 100 = 10%. Actual is 12.6%. For "approximately 10%" or options like 8%, 10%, 15%, 20%, your estimate may suffice.
What if the numbers have many digits?
Focus on the leading digits and order of magnitude. 47,382 × 0.23 ≈ 47,000 × 0.2 = 9,400. Or 47 × 0.23 ≈ 50 × 0.2 = 10. So the answer is around 10,000 (since 47,382 ≈ 50,000, and 50,000 × 0.2 = 10,000).