Amelia is 9 years old. Her brother Kavi is 4 years older than her. How old is Kavi?
(Total for Question 1 is 1 mark)
2
Priya has 3 £1 coins and 4 50p coins. How much money does she have in total? Give your answer in pounds.
(Total for Question 2 is 2 marks)
3
Look at the sequence: 2, 5, 8, 11, 14, ... What is the 8th term of this sequence?
(Total for Question 3 is 2 marks)
4
Which number continues the sequence? 1, 4, 9, 16, 25, ...
A) 30
B) 36
C) 32
D) 28
(Total for Question 4 is 1 mark)
5
Ben buys 3 notebooks costing £1.20 each and 2 pens costing 45p each. He pays with a £10 note. How much change does he receive?
(Total for Question 5 is 3 marks)
6
All squares are rectangles. Some rectangles are red. Which statement must be true?
A) All squares are red.
B) Some squares are red.
C) All rectangles are squares.
D) It cannot be determined whether any squares are red.
(Total for Question 6 is 1 mark)
7
Four friends - Freya, Oscar, Mia and Leo - each have a different pet: a rabbit, a hamster, a cat and a dog. - Freya does not have the cat or the dog. - Oscar has the dog. - Mia does not have the rabbit. - Leo has the hamster. Work out which pet each friend has.
(Total for Question 7 is 4 marks)
8
Sam is twice as old as his sister Ella. In 6 years' time, Sam will be 26. How old is Ella now?
(Total for Question 8 is 3 marks)
9
A piggy bank contains only 20p and 10p coins. There are 15 coins in total, worth £2.20. How many 20p coins are there?
(Total for Question 9 is 3 marks)
10
Three friends - Noah, Zara and Priya - each own a different number of pets: 1, 2 or 3. - Noah owns more pets than Zara. - Priya does not own the most pets. Who owns the most pets?
A) Noah
B) Zara
C) Priya
D) Cannot be determined
(Total for Question 10 is 2 marks)
11
A train leaves London at 09:47 and arrives in Bristol at 11:15. The journey was delayed by 12 minutes due to signalling. What was the scheduled journey time, in minutes, before the delay?
(Total for Question 11 is 3 marks)
12
The nth term of a sequence is given by 3n + 2. What is the sum of the 4th term and the 10th term?
(Total for Question 12 is 3 marks)
13
A fruit squash is made by mixing orange concentrate and water in the ratio 2:5. How much orange concentrate is needed to make 700 ml of squash?
(Total for Question 13 is 3 marks)
14
A car travels at a constant speed of 60 km/h. How many minutes does it take to travel 45 km?
(Total for Question 14 is 2 marks)
15
A bag contains 4 red counters, 3 blue counters and 5 green counters, and nothing else. One counter is taken out at random. What is the probability that it is NOT blue?
A) 3/12
B) 9/12
C) 4/12
D) 5/12
(Total for Question 15 is 2 marks)
16
Four houses stand in a row, numbered 1 to 4 from left to right. Each house is a different colour: red, blue, green or yellow. - The blue house is somewhere to the left of the yellow house. - The green house is next to the red house. - House 1 is not red and not blue. - House 4 is yellow. Work out the colour of each house.
(Total for Question 16 is 4 marks)
17
A sequence starts 3, 7, 15, 31, 63, ... Describe the rule connecting one term to the next, and use it to find the next term in the sequence.
(Total for Question 17 is 3 marks)
18
Priya thinks of a number. She doubles it, then subtracts 7. She then divides the result by 3, and gets an answer of 9. What number did Priya start with?
(Total for Question 18 is 3 marks)
19
The ratio of Tom's age to his father's age is 2:7. In 5 years' time, the ratio of their ages will be 1:3. How old is Tom now?
(Total for Question 19 is 4 marks)
20
Jack has a number of coins made up only of 50p coins and £2 coins. He has 4 more 50p coins than £2 coins. The total value of his coins is £17. How many £2 coins does he have?
(Total for Question 20 is 4 marks)
21
Five children - Aisha, Ben, Chloe, Dev and Freya - take part in a running race. There are no ties. - Chloe finished immediately before Dev. - Aisha finished before Ben but after Freya. - Dev did not finish first. - Ben finished third. Work out the finishing order, from 1st to 5th.
(Total for Question 21 is 4 marks)
22
In a number pyramid, each block is found by adding together the two blocks directly below it. The bottom row (left to right) is: 5, x, 9, 4 The top block of the pyramid is 54. Find the value of x.
(Total for Question 22 is 4 marks)
23
A fruit salad recipe uses apples, grapes and strawberries in the ratio 3:4:5. A large batch is made using 600 g of strawberries. 15% of the total mass of fruit salad is then removed to make a smaller portion for a child. What mass of fruit salad, in grams, remains after the child's portion is removed?
(Total for Question 23 is 5 marks)
24
At a school fete, adult raffle tickets cost £3 each and child tickets cost £1.50 each. On Saturday, three times as many child tickets were sold as adult tickets, and the total raised was £90. On Sunday, half as many adult tickets were sold as on Saturday, but the same number of child tickets were sold as on Saturday. How much was raised in total on Sunday?
(Total for Question 24 is 5 marks)
Mark scheme · EP.M32 Problem Solving and Logic Set C
Question 1
B1 13 cao
Answer: 13
Question 2
M1 3 x 1 + 4 x 0.5 oe
A1 £5 cao
Answer: £5
Question 3
M1 identifies the common difference of 3 and extends the sequence, or uses 3n - 1 oe
A1 23 cao
Answer: 23
Question 4
B1 B (36) cao
Answer: B) 36
Question 5
M1 3 x 1.20 = £3.60
M1 2 x 0.45 = £0.90 (or total cost £4.50 seen)
A1 £5.50 cao
Answer: £5.50
Question 6
B1 D cao
Answer: D) It cannot be determined whether any squares are red.
Question 7
B1 Oscar - dog cao
B1 Leo - hamster cao
B1 Freya - rabbit cao (deduced by elimination)
B1 Mia - cat cao (deduced by elimination)
Answer: Oscar - dog, Leo - hamster, Freya - rabbit, Mia - cat
Question 8
M1 Sam's age now = 26 - 6 = 20
M1 Ella's age = 20 / 2 oe
A1 10 cao
Answer: 10
Question 9
M1 sets up x + y = 15 and 20x + 10y = 220 oe
M1 correct elimination step, e.g. 2x + y = 22, so x = 7 oe
A1 7 cao
Answer: 7
Question 10
M1 eliminates Zara (fewer than Noah) and Priya (not the most) from owning the most
A1 A (Noah) cao
Answer: A) Noah
Question 11
M1 finds the actual journey time = 1 hour 28 minutes (88 minutes)
M1 subtracts the delay, 88 - 12 oe
A1 76 minutes cao
Answer: 76 minutes
Question 12
M1 4th term = 3(4) + 2 = 14
M1 10th term = 3(10) + 2 = 32
A1 46 cao
Answer: 46
Question 13
M1 total parts = 2 + 5 = 7
M1 700 / 7 = 100 ml per part
A1 200 ml cao
Answer: 200 ml
Question 14
M1 time = 45 / 60 hours oe
A1 45 minutes cao
Answer: 45 minutes
Question 15
M1 total counters = 12 and not-blue counters = 12 - 3 = 9
A1 B (9/12) cao, accept equivalent fraction 3/4
Answer: B) 9/12 (= 3/4)
Question 16
B1 House 1 - green cao (deduced from clue 3, since house 4 is already yellow)
B1 House 2 - red cao (deduced, green must be next to red)
B1 House 3 - blue cao (remaining colour, consistent with blue left of yellow)
B1 House 4 - yellow cao (given)
Answer: House 1 - green, House 2 - red, House 3 - blue, House 4 - yellow
Question 17
B1 correctly states the rule: double the previous term and add 1 oe
M1 applies the rule to 63: 63 x 2 + 1
A1 127 cao
Answer: 127
Question 18
M1 reverses the final step: 9 x 3 = 27
M1 reverses the subtraction: 27 + 7 = 34
A1 17 cao (34 / 2)
Answer: 17
Question 19
M1 sets Tom's age = 2x and father's age = 7x
M1 forms (2x + 5)/(7x + 5) = 1/3 oe, e.g. 3(2x + 5) = 7x + 5
dM1 solves to x = 10 (dependent on previous M1)
A1 20 cao
Answer: 20
Question 20
M1 lets the number of £2 coins = x, so the number of 50p coins = x + 4
M1 forms the equation 2x + 0.5(x + 4) = 17 oe
dM1 simplifies to 2.5x = 15 (dependent on previous M1)
A1 6 cao
Answer: 6
Question 21
M1 deduces Freya and Aisha must occupy positions 1 and 2, since both finish before Ben in 3rd, with Freya before Aisha
B1 Freya - 1st and Aisha - 2nd cao
B1 Chloe - 4th and Dev - 5th cao, from the adjacency clue applied to the two remaining positions
A1 complete correct order: Freya, Aisha, Ben, Chloe, Dev