Maths: Number & Percentages

A coat priced at £84 is reduced by 35% in a sale. How much is taken off the price?

• A£33.60
• B£25.20
• C£29.40✓
• D£54.60

Answer: 35% of £84 is 0.35 × 84 = £29.40. The other figures are 30% of £84 (£25.20), 40% of £84 (£33.60) and the sale price itself after the reduction (£54.60).

A rent of £640 a month increases by 15%. What is the new monthly rent?

• A£696
• B£742
• C£755
• D£736✓

Answer: A 15% increase is a multiplier of 1.15, so 640 × 1.15 = £736. Adding 15% of £640 (£96) gives the same result; the alternatives come from adding 10% (£56 → £696) or miscalculating the percentage.

Which of these is equal to three eighths?

• A0.38
• B0.35
• C0.375✓
• D0.325

Answer: Three eighths is 3 ÷ 8 = 0.375 exactly. 0.38 is a rounded value rather than an equal one, and 0.35 and 0.325 are 7/20 and 13/40 respectively.

Write 0.000 062 in standard form.

• A6.2 × 10⁻⁵✓
• B62 × 10⁻⁶
• C6.2 × 10⁵
• D6.2 × 10⁻⁴

Answer: Standard form needs a number between 1 and 10 multiplied by a power of ten. Moving the decimal point five places to the right turns 0.000 062 into 6.2, so the power is 10⁻⁵. 62 × 10⁻⁶ has the right value but is not in standard form, and the others have the wrong power.

Which of these is the prime factorisation of 120?

• A2³ × 3 × 5²
• B2² × 3 × 5
• C2 × 3² × 5
• D2³ × 3 × 5✓

Answer: 120 = 2 × 60 = 2 × 2 × 30 = 2 × 2 × 2 × 15 = 2 × 2 × 2 × 3 × 5, which is 2³ × 3 × 5. The other products give 60, 600 and 90.

£1,200 is invested at 3% compound interest per year. How much is in the account after 2 years, to the nearest penny?

• A£1,308.00
• B£1,236.00
• C£1,273.08✓
• D£1,272.00

Answer: Compound interest multiplies by 1.03 each year: 1,200 × 1.03 × 1.03 = 1,200 × 1.0609 = £1,273.08. £1,272 is what simple interest would give (£36 a year for two years), £1,236 is after one year only, and £1,308 is three years of simple interest.

A student scores 45 out of 60 in a test. What is this as a percentage?

• A75%✓
• B70%
• C80%
• D65%

Answer: Divide the score by the total and multiply by 100: 45 ÷ 60 = 0.75, which is 75%. Simplifying the fraction first (45/60 = 3/4) gives the same answer.

Round 0.04567 to two significant figures.

• A0.05
• B0.0457
• C0.046✓
• D0.046 7

Answer: Significant figures are counted from the first non-zero digit: 4 and 5 are the first two, and the next digit (6) rounds the 5 up to 6, giving 0.046. Rounding to two decimal places would give 0.05, which is a different instruction.

Which of these is equal to 2⁵?

• A32✓
• B10
• C25
• D64

Answer: 2⁵ means 2 × 2 × 2 × 2 × 2 = 32. Multiplying the base by the power gives 10, 25 is 5², and 64 is 2⁶.

The price of a laptop falls by 28% to £540. What was the original price?

• A£750✓
• B£608
• C£691.20
• D£768

Answer: After a 28% fall the price is 72% of the original, so the original is 540 ÷ 0.72 = £750. Adding 28% back onto £540 gives £691.20, which is the common reverse-percentage error.

What is the highest common factor of 180 and 300?

• A30
• B60✓
• C900
• D20

Answer: 180 = 2² × 3² × 5 and 300 = 2² × 3 × 5². The common factors are 2² × 3 × 5 = 60. 900 is the lowest common multiple, not the highest common factor.

Estimate the value of 4.8 × 21.3 ÷ 0.51 by rounding each number to one significant figure.

• A100
• B2,000
• C20
• D200✓

Answer: Rounding to one significant figure gives 5 × 20 ÷ 0.5 = 100 ÷ 0.5 = 200. Dividing by 0.5 doubles a number rather than halving it, which is where 100 and 20 come from.