UCAT Quantitative Reasoning quick facts

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• 1/8 as a percentage12.5%
• 3/8 as a percentage37.5%
• 5/8 as a percentage62.5%
• 7/8 as a percentage87.5%
• 1/3 and 2/3 as percentages33.3% and 66.7% (to 1 decimal place)
• 1/6 as a percentage16.7% (to 1 decimal place)
• 1/7 as a percentage14.3% (to 1 decimal place)
• 1/9 as a percentage11.1% (to 1 decimal place)
• 1/11 as a percentage9.1% (to 1 decimal place)
• 1/12 as a percentage8.3% (to 1 decimal place)
• 1/16 as a percentage6.25%
• Raise a price by 20%, then cut it by 20%. Net change?4% lower: 1.2 × 0.8 = 0.96.
• A price rose 25% to £150. What was it before?£120 (150 ÷ 1.25)
• £96 includes VAT at 20%. Price before VAT?£80 (96 ÷ 1.2)
• 30% of 40% as a percentage12% (0.3 × 0.4 = 0.12)
• A rate goes from 10% to 12%. Change in percentage points and in percent?2 percentage points, which is a 20% increase.
• Multiplier for a 15% decrease0.85
• 5% compound growth for 3 years: the multiplier1.05³ ≈ 1.158, so about 15.8% in total.
• Simple interest on £P at r% a year for t yearsP × r × t ÷ 100
• Average speed for a whole journeyTotal distance ÷ total time (not the mean of the speeds).
• Convert m/s to km/hMultiply by 3.6.
• 72 km/h in m/s20 m/s (72 ÷ 3.6)
• Seconds in an hour3,600
• 0.4 hours in minutes24 minutes
• 1.75 hours in hours and minutes1 hour 45 minutes
• 1 litre in millilitres and cm³1,000 ml, which is 1,000 cm³.
• 1 m³ in litres1,000 litres
• 1 m² in cm²10,000 cm²
• 1 tonne in kilograms1,000 kg
• Share £60 in the ratio 3:2£36 and £24 (5 parts of £12).
• The mean of 4 numbers is 15. A fifth number makes the mean 16. What is it?20 (5 × 16 − 4 × 15 = 80 − 60).
• Median of an even-sized ordered listThe mean of the two middle values.
• Area scale factor when lengths are multiplied by kk²; volumes scale by k³.