Independent School Entrance (ISEB Pre-Test and 11+ CEM style) · Numerical Reasoning

Multi-step number problems

20 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 20 questions

  1. A cinema sells adult tickets at £9.50 and child tickets at £6.25. A family ticket for 2 adults and 2 children costs £28. What is the cheapest way for 2 adults and 4 children to buy tickets?
  2. Sound travels at about 340 m/s. A clap of thunder is heard 6 seconds after the lightning flash. How far away is the lightning, in kilometres?
  3. A school trip has 168 pupils and 12 staff. Each coach seats 52 people. What is the smallest number of coaches needed?
  4. Eve spends 2/5 of her money on a book, and then 1/3 of what is left on lunch. She has £12 left. How much money did she start with?
  5. A tap fills a bucket at 15 litres per minute. Each bucket holds 9 litres. How many seconds does it take to fill 5 buckets?
  6. A paint is mixed from blue and yellow in the ratio 2 : 3. A decorator uses 4.5 litres of blue. How much yellow does she use?
  7. A train 150 m long travels at a steady 20 m/s. How long does it take, from the moment the front enters a 250 m tunnel until the back has left it?
  8. A town has a population of 8,000. It grows by 5% each year for two years. What is the population after two years?
  9. The mean of a pupil's first four test scores is 72. After a fifth test the mean of all five scores is 75. What did the pupil score in the fifth test?
  10. 3 apples and 2 pears weigh 600 g in total. 2 apples and 3 pears weigh 650 g in total. All apples weigh the same and all pears weigh the same. How much does one pear weigh?
  11. A runner takes 1 minute 20 seconds to run one lap of a track. How many complete laps can she run in 10 minutes?
  12. Square tiles are placed in a row, each touching the next along a whole side. One tile has a perimeter of 4 units, two tiles have a perimeter of 6 units, and three tiles have a perimeter of 8 units. Wh…
  13. One square needs 4 matchsticks. Two squares in a row sharing a side need 7 matchsticks, and three squares in a row need 10. How many matchsticks are needed for a row of 20 squares?
  14. Paint covers 12 m² per litre. A wall is 4.5 m long and 2.8 m high and needs two coats. How many litres of paint are needed?
  15. A television costs £480. A customer pays a deposit of 15% and then pays the rest in 12 equal monthly payments. How much is each payment?
  16. A shop mixes 400 g of nuts costing £1.20 per 100 g with 600 g of raisins costing £0.70 per 100 g. What is the cost of the mixture per 100 g?
  17. A recipe for 8 people uses 3/4 of a cup of sugar. How much sugar is needed for 20 people?
  18. A watch loses 4 minutes every 24 hours. It is set correctly at noon on Monday. What time does it show when the true time is 6 pm on Thursday?
  19. Red, blue and green marbles in a bag are in the ratio 3 : 4 : 5. There are 24 blue marbles. How many marbles are in the bag altogether?
  20. A cyclist rides 27 km in 1 hour 30 minutes. At the same speed, how far does she ride in 3 hours 20 minutes?

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