Estimation and Approximation

Practice bank for UCAT Quantitative Reasoning questions where you must estimate the answer rather than calculate it exactly. These questions reward speed and number sense over precision.

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Quick-Reference: Estimation Strategies

Rounding Strategy

1. Round each number to 1 significant figure
2. Perform the simplified calculation
3. Match to the closest answer option

Useful Benchmarks

Value	Approximation
1/3	33% or 0.33
1/7	14% or 0.14
1/9	11% or 0.11
sqrt(2)	1.41
sqrt(3)	1.73
pi	3.14

Bounding Technique

When options are close together, calculate a rough lower bound and upper bound to narrow down the answer.

Order of Magnitude

Quickly determine whether the answer is in the ones, tens, hundreds, or thousands. This alone can eliminate 1-2 options.

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Strategy

• Always look at the answer options first to see how precise you need to be
• If options are far apart, round aggressively and estimate
• If options are close, you may need a more precise calculation
• Never spend more than 30 seconds on a pure estimation question
• Use compatible numbers (numbers that divide evenly) wherever possible

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Practice

Complete the 20 assessment questions. Each tests your ability to estimate quickly and accurately.