Number Puzzles and Logic Set D - Worksheets, Questions and Revision

24 original exam-style questions - 7 pages of questions with a full mark scheme - free printable PDF.

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11+ · Mathematics

EP.M71 Number Puzzles and Logic Set D

GL ASSESSMENT GL · Calculators not allowed · about 72 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
In a spelling test, Zainab scored higher than Tariq. Tariq scored higher than Yusuf. Write the three pupils in order from lowest score to highest score.
(Total for Question 1 is 2 marks)
2
Leon is 11 years old. His sister Nia is 5 years older than him. How old will Nia be in 8 years' time?
(Total for Question 2 is 2 marks)
3
Ravi has 5 twenty-pence coins and 2 fifty-pence coins in his money box. How much money does he have in total? Give your answer in pounds.
(Total for Question 3 is 2 marks)
4
A fruit squash is made by mixing orange concentrate and water in the ratio 3:7. If 300 ml of orange concentrate is used, how much water is needed?
(Total for Question 4 is 2 marks)
5
List all the two-digit numbers that can be made by choosing two different digits from 3, 6 and 9 (no digit repeated within a number).
(Total for Question 5 is 2 marks)
6
Look at this sequence: 2, 8, 14, 20, ... What is the next term?
(Total for Question 6 is 1 mark)
7
Four pupils - Amara, Callum, Diya and Jack - are queuing for the canteen.
1. Callum is directly behind Amara.
2. Jack is not first or last.
3. Diya is first.
Work out the order of the queue from first to last.
(Total for Question 7 is 3 marks)
8
In 5 years' time, Chidi will be twice as old as he was 3 years ago. How old is Chidi now?
(Total for Question 8 is 3 marks)
9
Meera has only 50p and GBP 1 coins in her purse. She has 12 coins in total, worth GBP 8.50 altogether. How many 50p coins and how many GBP 1 coins does she have?
(Total for Question 9 is 3 marks)
10
Paint mix A is made from blue and white paint in the ratio 3:2. Paint mix B is made from blue and white paint in the ratio 1:3. Sanjay mixes 500 ml of Paint A with 500 ml of Paint B. How much blue paint is there in total in the new mixture?
(Total for Question 10 is 3 marks)
11
How many three-digit numbers can be made using the digits 1, 3, 6 and 8, if each digit can be used only once per number and the number must be even?
(Total for Question 11 is 3 marks)
12
Look at this sequence: 2, 5, 10, 17, 26, ... What is the next term?
(Total for Question 12 is 3 marks)
13
Three friends - Freddie, Grace and Oliver - each have a favourite pizza topping (pepperoni, cheese or mushroom) and each wears a different colour T-shirt (red, blue or green).
1. Freddie's favourite topping is pepperoni.
2. The friend with a blue T-shirt has cheese as their favourite topping.
3. Grace does not have a red T-shirt.
4. Oliver has a green T-shirt.
Work out each friend's favourite topping and T-shirt colour.
(Total for Question 13 is 4 marks)
14
The sum of the ages of Isla, Josh and Kofi is 39. Josh is twice as old as Isla. Kofi is 4 years older than Josh. How old is each of them?
(Total for Question 14 is 4 marks)
15
A machine exchanges coins at no extra cost: every 3 ten-pence coins can be swapped for 1 twenty-pence coin and 2 five-pence coins (the same total value). Priya has a bag containing only ten-pence coins, worth GBP 5.00 in total. She exchanges as many groups of 3 ten-pence coins as she can. How many twenty-pence coins and how many five-pence coins does she receive, and what value is left over in ten-pence coins that could not be exchanged?
(Total for Question 15 is 4 marks)
16
A fruit drink is made by mixing juice and water in the ratio 5:9. Elena has 450 ml of juice and wants to use all of it. How much water must she add, and what is the total volume of the drink she makes?
(Total for Question 16 is 4 marks)
17
A code is made from one letter (A, B or C) followed by one digit (1, 2, 3 or 4). How many different codes are possible, and how many of these codes end in an even digit?
(Total for Question 17 is 4 marks)
18
A sequence is formed using the rule: multiply by 2, then add 5. The first term is 4. Find the first four terms of the sequence.
(Total for Question 18 is 3 marks)
19
Four friends - Aaron, Bella, Charlie and Deepa - each have a different favourite subject (Maths, Science, Art or History) and each travels to school a different way (car, bike, bus or on foot).
1. The friend who likes Science travels by bike.
2. Aaron does not like Art or History.
3. Charlie travels by bus.
4. Bella's favourite subject is History.
5. The friend who walks to school likes Art.
6. Deepa does not travel by bike.
Work out each friend's favourite subject and how they travel to school.
(Total for Question 19 is 4 marks)
20
In a family, the combined age of a grandmother, her daughter and her granddaughter is 100 years. The daughter's age is 4 more than 3 times the granddaughter's age. The grandmother's age is 2 less than twice the daughter's age. How old is each person?
(Total for Question 20 is 4 marks)
21
A 4-digit code is made using four different digits chosen from 2, 3, 7, 8 and 9 (each digit used at most once). How many such codes are even and greater than 7000?
(Total for Question 21 is 4 marks)
22
Exactly 50p is to be made using only 20p, 10p and 5p coins (any number of each coin, including zero, but at least one coin used in total). Explain why no more than 2 twenty-pence coins can be used, then find the total number of different ways to make exactly 50p.
(Total for Question 22 is 5 marks)
23
Five friends - Arun, Bea, Cody, Dana and Evan - each collected a different number of football stickers over one week: 3, 5, 7, 9 and 11 (one each, no ties).
1. Cody collected more stickers than Arun but fewer than Dana.
2. The difference between Bea's total and Evan's total is 8.
3. Evan collected the fewest stickers.
4. Dana did not collect the most.
5. Arun collected 5 stickers.
Work out how many stickers each friend collected, and state who collected the most.
(Total for Question 23 is 5 marks)
24
A sequence is generated by the rule: the nth term = n2 - n + 1. Find the first four terms of the sequence, and find the value of n for which the nth term equals 91.
(Total for Question 24 is 5 marks)
Mark scheme · EP.M71 Number Puzzles and Logic Set D

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24