Number and the Number System

At 6am the temperature inside a cold store was -2°C. A fault made it rise by 7°C, and engineers then cooled it by 11°C. What was the temperature once the engineers had finished?

• A6°C
• B-6°C✓
• C16°C
• D-20°C

Answer: Start at -2°C. Rising by 7°C gives -2 + 7 = 5°C. Cooling by 11°C then gives 5 - 11 = -6°C. The store ends up 6 degrees below freezing, so the answer is negative.

A freezer is at 4°C when it is switched on. Its temperature then falls by 3°C every hour for 6 hours. What is its temperature at the end of the 6 hours?

• A-22°C
• B-18°C
• C14°C
• D-14°C✓

Answer: The total fall is 6 × 3 = 18°C. Starting from 4°C, the temperature becomes 4 - 18 = -14°C. Forgetting the starting temperature gives -18°C, and starting from -4°C instead of 4°C gives -22°C.

A current account has a balance of -£126. The account holder pays in £45 at the end of each week and spends nothing. What is the balance after 4 weeks?

• A-£54
• B£306
• C£54✓
• D-£81

Answer: Over 4 weeks the payments total 4 × £45 = £180. The new balance is -£126 + £180 = £54. The account is back in credit because more has been paid in than was owed.

A square patio has an area of 30.25 m². Edging strip is sold in 1 m lengths. How many lengths are needed to go all the way round the edge of the patio?

• A11
• B31
• C24
• D22✓

Answer: The side of the square is √30.25 = 5.5 m. The perimeter is 4 × 5.5 = 22 m, so 22 one-metre lengths are needed. Rounding the side up to 6 m first would give 24, which buys more strip than is needed.

A spreadsheet cell contains the formula =3+2^3*5. The ^ sign means 'to the power of'. What value does the cell show?

• A33
• B43✓
• C1,003
• D55

Answer: Order of operations: powers first, so 2³ = 8. Then multiplication: 8 × 5 = 40. Addition comes last: 3 + 40 = 43. Adding 3 + 8 before multiplying gives 55, and reading 2³ as 2 × 3 gives 33.

An invoice for 48 trays of sandwiches at £21.75 per tray shows a total of £10,440. By rounding each number to one significant figure, which conclusion is correct?

• AThe estimate is £1,000, so the total is about ten times too big✓
• BThe estimate is £10,000, so the total on the invoice looks right
• CThe estimate is £800, so the total on the invoice is far too big
• DThe estimate is £1,100, so the total is only slightly too big

Answer: Rounded to one significant figure, 48 becomes 50 and £21.75 becomes £20. The estimate is 50 × £20 = £1,000. The invoice says £10,440, which is about ten times the estimate, so a place-value error is likely (the true total is £1,044).

A lottery rollover of £12.6 million is shared equally between 4 winners. How much does each winner receive?

• A£31,500,000
• B£3,015,000
• C£3,150,000✓
• D£315,000

Answer: £12.6 million is £12,600,000. Divided by 4: £12,600,000 ÷ 4 = £3,150,000, which is £3.15 million each. £315,000 and £31,500,000 have the digits in the wrong place-value columns.

Which is the best estimate for (398 × 5.1) ÷ 0.49?

• A4,000✓
• B40,000
• C400
• D1,000

Answer: Round each number: 398 ≈ 400, 5.1 ≈ 5 and 0.49 ≈ 0.5. Then 400 × 5 = 2,000, and 2,000 ÷ 0.5 = 4,000, because dividing by a half doubles the value. Multiplying by 0.5 instead of dividing gives 1,000.

A council's budget of £2.4 million is split so that 3/8 goes on roads and the rest is shared equally between 5 other services. How much does each of the other services receive?

• A£187,500
• B£480,000
• C£900,000
• D£300,000✓

Answer: Roads: 3/8 of £2,400,000 = £900,000. The rest is £2,400,000 - £900,000 = £1,500,000, and £1,500,000 ÷ 5 = £300,000 for each service. £480,000 shares the whole budget between 5 without taking the roads money out first.

A company made a loss of £1.35 million in 2024 and a profit of £0.8 million in 2025. By how much did its result improve from 2024 to 2025?

• A£2.05 million
• B£1.55 million
• C£2.15 million✓
• D£0.55 million

Answer: A loss of £1.35 million is -£1.35 million. The improvement is £0.8 million - (-£1.35 million) = £0.8 million + £1.35 million = £2.15 million. Subtracting the two sizes (1.35 - 0.8) gives £0.55 million, which ignores that one is a loss.