11+ Entrance Mathematical Problem Solving Questions and Answers

Question 1

Aisha buys 3 magazines at £2.50 each and a book for £5.99. She pays with a £20 note. How much change does she receive?

Accepted Answer

£6.51

Answer

First, calculate the total cost of the magazines: 3 x £2.50 = £7.50. Next, add the cost of the book to find the total spending: £7.50 + £5.99 = £13.49. Finally, subtract the total cost from the amount paid to find the change: £20.00 - £13.49 = £6.51.

Question 2

A bus leaves a depot at 09:15 and arrives at the town centre at 10:05. It then waits for 7 minutes before continuing its journey to the park, which takes a further 22 minutes. At what time does the bus arrive at the park?

Accepted Answer

10:34

Answer

The bus arrives at the town centre at 10:05. It waits for 7 minutes, so its departure time from the town centre is 10:05 + 7 minutes = 10:12. The journey to the park takes another 22 minutes. Therefore, the arrival time at the park is 10:12 + 22 minutes = 10:34.

Question 3

A bag of flour weighs 1.5 kg. A baker uses 2/5 of the flour for a loaf of bread and then 20% of the *remaining* flour for some scones. How much flour is left in the bag, in grams?

Accepted Answer

720g

Answer

First, convert the total weight to grams: 1.5 kg = 1500g. The amount used for bread is (2/5) of 1500g, which is (1500 ÷ 5) × 2 = 600g. The remaining flour is 1500g - 600g = 900g. The amount used for scones is 20% of the remaining 900g, which is 0.20 × 900g = 180g. The final amount of flour left is 900g - 180g = 720g.

Question 4

A rectangular garden is 12 metres long and 8 metres wide. A square patio with sides of 3 metres is laid in one corner of the garden. What is the area of the lawn that remains?

Accepted Answer

87 m²

Answer

The area of the entire rectangular garden is calculated by multiplying its length and width: 12 m × 8 m = 96 m². The area of the square patio is calculated by squaring its side length: 3 m × 3 m = 9 m². To find the remaining area of the lawn, subtract the patio's area from the garden's total area: 96 m² - 9 m² = 87 m².

Question 5

A recipe for 12 cupcakes requires 150g of sugar. How much sugar is needed to make 30 cupcakes?

Accepted Answer

375g

Answer

To find the amount of sugar for one cupcake, divide the total sugar by the number of cupcakes: 150g ÷ 12 = 12.5g per cupcake. To make 30 cupcakes, multiply the amount per cupcake by 30: 12.5g × 30 = 375g. Alternatively, recognise that 30 is 2.5 times 12 (30 ÷ 12 = 2.5). Therefore, you need 2.5 times the amount of sugar: 150g × 2.5 = 375g.

11+ Practice Test

11+ Practice Test

11+ Entrance Mathematical Problem Solving Questions and Answers