Arithmetic Shortcuts & Estimation

Why Estimation Beats Brute-Force Calculation

The GRE's on-screen calculator handles arithmetic, but typing every number in wastes time and invites entry errors. Many Quant questions are designed so that a quick estimate immediately eliminates 3 of the 5 answer choices, leaving only a fast final check between the two that remain.

GRE-এর অন-স্ক্রিন ক্যালকুলেটর গণনা করে, কিন্তু প্রতিটি সংখ্যা টাইপ করা সময় নষ্ট করে। দ্রুত আনুমানিক হিসাব প্রায়ই ৫টির মধ্যে ৩টি বিকল্প বাদ দিতে পারে।

The core method: round each number to the nearest "friendly" value (nearest 10, nearest benchmark fraction), estimate the answer, then use the calculator only for the final precise step between remaining close choices.

মূল পদ্ধতি: প্রতিটি সংখ্যা সহজ মানে রাউন্ড করুন, আনুমানিক হিসাব করুন, তারপর প্রয়োজনে চূড়ান্ত নির্ভুল হিসাব করুন।

Benchmark Fractions & Percents

Memorizing these equivalents lets you convert between fractions, decimals, and percents instantly. এই সমতুল্যগুলো মুখস্থ করলে ভগ্নাংশ, দশমিক ও শতাংশে দ্রুত রূপান্তর করা যায়।

FractionDecimalPercent
1/20.550%
1/30.333...≈33.3%
1/40.2525%
1/50.220%
1/60.1667≈16.7%
1/80.12512.5%
1/100.110%
2/30.667≈66.7%
3/40.7575%

Percent shortcut: to find 10% of any number, shift the decimal one place left. Use that as a building block: 5% = half of 10%; 20% = double 10%; 15% = 10% + 5%.

শতাংশ শর্টকাট: ১০% বের করতে দশমিক এক ঘর বামে সরান — এটি দিয়েই অন্য শতাংশ বের করা যায়।

Worked Examples

Example 1 — Percent Estimation

Estimate 39% of 82.

ESTIMATERound to 40% of 80. 10% of 80 = 8, so 40% = 8 × 4 = 32. The actual answer (31.98) is extremely close — enough to select the right answer choice without a full calculation.
Example 2 — Friendly Multiplication

Compute 125 × 88 without a calculator.

BREAK IT DOWNRewrite 88 as (90 − 2): 125 × 90 = 11,250. 125 × 2 = 250. Subtract: 11,250 − 250 = 11,000. Breaking numbers into round components is often faster than direct multiplication.

Common Mistakes

  • Over-relying on the calculator for simple estimates: typing in every number costs more time than a 5-second mental estimate that's precise enough to pick the answer.
  • Rounding both numbers in the same direction: if you round one number up and another down, errors can partially cancel out; rounding both up (or both down) compounds the error.
  • Forgetting percent increase/decrease compounds, not adds: a 20% increase followed by a 20% decrease does not return to the original value (it results in a 4% net decrease).
  • Confusing "percent of" with "percentage point change": going from 20% to 25% is a 5 percentage-point increase, but a 25% relative increase in the underlying rate.

Your Turn — Estimate First

Estimate each answer before computing exactly. সঠিক হিসাবের আগে আনুমানিক মান বের করুন।

1 Estimate 21% of 396.
Show the logic

Round to 20% of 400 = 80. Actual ≈ 83.2, close enough to identify the correct choice.

2 A population of 4,850 grows by approximately 1/3. Estimate the new population.
Show the logic

1/3 of 4,850 ≈ 1,617. New population ≈ 4,850 + 1,617 = ≈ 6,467.

3 Compute 99 × 47 using a friendly-number shortcut.
Show the logic

99 = 100 − 1. 100 × 47 = 4,700. Subtract 47: 4,700 − 47 = 4,653.

4 A price increases by 20% and then decreases by 20%. Is the final price higher, lower, or the same as the original?
Show the logic

Start with 100: after +20% → 120; after −20% of 120 → 120 × 0.8 = 96. Lower than the original — percent changes compound, they don't cancel.

5 Estimate 7/8 of 240.
Show the logic

7/8 = 1 − 1/8. 1/8 of 240 = 30. 240 − 30 = 210.

Next guide: Algebra Strategies. Apply this skill on Quant Practice Test 2.

পরের গাইড: বীজগণিত কৌশল।