Logic and Puzzle Problems: Practice Set 2 - Worksheets, Questions and Revision

23 original exam-style questions - 8 pages of questions with a full mark scheme - free printable PDF.

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11+ · Numerical Reasoning and Logical Problem-Solving

EP.M15B Logic and Puzzle Problems: Practice Set 2

GL ASSESSMENT GL11-MATHS-LOGIC · Calculators not allowed · about 90 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Look at the number sequence: 4, 9, 14, 19, ...
  • A) 23
  • B) 24
  • C) 25
  • D) 29
  • E) 20
(Total for Question 1 is 2 marks)
2
Look at this group of numbers: 14, 21, 28, 33, 42, 49
  • A) 14
  • B) 21
  • C) 33
  • D) 42
  • E) 49
(Total for Question 2 is 2 marks)
3
Freya is younger than Harun. Harun is younger than Isla. Which statement must be true?
  • A) Isla is younger than Freya
  • B) Freya is younger than Isla
  • C) Harun is the youngest
  • D) Freya and Isla are the same age
  • E) Not enough information to tell
(Total for Question 3 is 2 marks)
4
In a code, every letter is replaced by the letter 2 places earlier in the alphabet (so D becomes B and E becomes C), wrapping round so B becomes Z and A becomes Y. Using this code, what does the word BRAIN become?
  • A) DTCKP
  • B) XPYGL
  • C) ZPYGL
  • D) ZPWGL
  • E) ZPYGM
(Total for Question 4 is 2 marks)
5
In a hiking and cycling club with 40 members, 24 enjoy hiking, 19 enjoy cycling, and 9 enjoy both hiking and cycling.
(a)Find the number of members who enjoy hiking only, and the number who enjoy cycling only.(3)
(b)How many members enjoy neither hiking nor cycling?(2)
(Total for Question 5 is 5 marks)
6
Six friends - Beatrice, Mia, Connor, Deepak, Willow and Tariq - sit at a round table with six evenly spaced seats, numbered 1 to 6 clockwise. Seats directly opposite each other differ by 3 (for example, seat 1 is opposite seat 4). Use these clues: (1) Beatrice is directly opposite Deepak. (2) Willow sits immediately clockwise of Beatrice. (3) Connor sits immediately anticlockwise of Beatrice. (4) Tariq sits immediately clockwise of Deepak. (5) Mia is not seated immediately next to Connor.
(a)Complete the seating order, listing all six friends clockwise starting from Beatrice.(3)
(b)State who sits directly opposite Tariq.(1)
(c)State who sits immediately clockwise of Mia.(1)
(Total for Question 6 is 5 marks)
7
Four years ago, Malik was four times as old as his sister Yasmin. In six years' time, Malik will be twice as old as Yasmin. How old is Malik now?
  • A) 9
  • B) 15
  • C) 20
  • D) 24
  • E) 30
(Total for Question 7 is 4 marks)
8
A sequence is formed using the rule 'multiply by 2, then add 4', starting at 3: 3, 10, 24, ...
(a)Find the next two terms of the sequence.(2)
(b)Explain why every term from the second term onwards will always be an even number.(2)
(Total for Question 8 is 4 marks)
9
Four pupils - Zainab, Oscar, Priti and Callum - each play a different instrument: violin, piano, drums and flute. (1) Zainab does not play violin or piano. (2) Oscar plays the flute. (3) Priti's instrument is not drums. (4) Callum does not play violin. Which instrument does Callum play?
  • A) Violin
  • B) Piano
  • C) Drums
  • D) Flute
  • E) Cannot be determined
(Total for Question 9 is 4 marks)
10
A rule connects pairs of numbers: 4 is linked to 15, and 7 is linked to 27.
(a)Find the rule connecting the number n to its linked value, giving your answer in the form an+b.(2)
(b)Using your rule, find the value linked to 10.(1)
(c)Find the value of n whose linked value is 59.(2)
(Total for Question 10 is 5 marks)
11
I think of a number, double it, then add 7. The result is 31. What was my number?
  • A) 10
  • B) 11
  • C) 12
  • D) 13
  • E) 19
(Total for Question 11 is 2 marks)
12
In this 3 by 3 grid, every row and every column adds up to 30: Row 1: 7, 12, 11. Row 2: 14, a, 6. Row 3: 9, 8, b.
(a)Find the value of a.(2)
(b)Find the value of b.(2)
(Total for Question 12 is 4 marks)
13
If 3rd March 2027 falls on a Wednesday, what day of the week is 20th March 2027?
  • A) Thursday
  • B) Friday
  • C) Saturday
  • D) Sunday
  • E) Monday
(Total for Question 13 is 3 marks)
14
In a number code, a letter's value is found using 3n-2, where n is its position in the alphabet (A=1, B=2, ...). For example, the word BAD has value 4+1+10=15.
(a)Find the total code value of the word FIG.(2)
(b)A three-letter word has the form S _ N. Its first letter has value 55, its last letter has value 40, and the total code value of the whole word is 138. Find the missing middle letter.(3)
(Total for Question 14 is 5 marks)
15
Three sisters - Priya, Sana and Beth - have different amounts of pocket money: 5 pounds, 8 pounds and 12 pounds, though not necessarily in that order. (1) Priya has more than Sana. (2) Beth does not have the least amount. (3) Priya has less than Beth. How much money does Priya have?
  • A) 5 pounds
  • B) 8 pounds
  • C) 12 pounds
  • D) 10 pounds
  • E) 15 pounds
(Total for Question 15 is 2 marks)
16
The sum of two whole numbers is 34. One number is 6 more than the other. What is the smaller number?
  • A) 10
  • B) 14
  • C) 17
  • D) 20
  • E) 28
(Total for Question 16 is 2 marks)
17
A padlock has a 3-digit code using digits 1-5, and no digit may be repeated. How many different codes are possible?
  • A) 15
  • B) 20
  • C) 60
  • D) 125
  • E) 10
(Total for Question 17 is 2 marks)
18
Five pupils - Farah, Ben, Chidi, Diya and Ewan - each prefer a different drink: Tea, Coffee, Juice, Milk and Water. (1) Ben drinks Coffee. (2) Chidi drinks neither Tea nor Water. (3) Diya drinks Milk. (4) Farah does not drink Water. (5) Ewan does not drink Juice.
(Total for Question 18 is 4 marks)
19
Two whole numbers have a sum of 20 and a product of 91. What are the two numbers?
  • A) 10 and 10
  • B) 12 and 8
  • C) 13 and 7
  • D) 14 and 6
  • E) 15 and 5
(Total for Question 19 is 2 marks)
20
A drawer contains 6 red socks, 6 blue socks and 6 green socks, all mixed together and impossible to tell apart in the dark.
(a)What is the smallest number of socks you must take out to be certain of having a matching pair of the same colour?(2)
(b)What is the smallest number of socks you must take out to be certain of having a matching pair specifically of red socks?(3)
(Total for Question 20 is 5 marks)
21
Four parcels W, X, Y and Z each have a different weight, using the numbers 4, 8, 12 and 16 kilograms once each. (1) Parcel W is heavier than parcel Y. (2) The heaviest parcel is either X or Z. (3) Parcel X is lighter than parcel W. (4) Parcel Z is not the lightest. (5) Parcel Y is heavier than parcel X. What is the weight of parcel W?
  • A) 4 kg
  • B) 8 kg
  • C) 12 kg
  • D) 16 kg
  • E) 10 kg
(Total for Question 21 is 5 marks)
22
The value of a word is found by adding the alphabet positions of its letters, then subtracting twice the number of vowels (A, E, I, O, U) in the word. For example, the word BIRD has letters B=2, I=9, R=18, D=4, sum=33, and 1 vowel (I), so its value is 33-2x1=31.
(a)Find the value of the word STONE.(3)
(b)Which has the greater value: CLOUD or GRAPE? Show your working.(3)
(Total for Question 22 is 6 marks)
23
Three cousins, Ines, Jaden and Kwame, have a total of 96 marbles between them. Jaden has twice as many marbles as Ines. Kwame has 6 more marbles than Jaden.
(a)Form and solve an equation to find how many marbles each cousin has.(4)
(b)Jaden gives one third of his marbles to Kwame. How many marbles does each cousin have now, and who then has the most marbles?(3)
(Total for Question 23 is 7 marks)
Mark scheme · EP.M15B Logic and Puzzle Problems: Practice Set 2

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