Each question gives you two or more statements about people, animals or objects. Every statement must be treated as certainly true, however unusual it seems, and your answer must be based only on what the statements actually say, never on outside knowledge, guesswork or what seems likely. Some questions ask you to order people or things (for example by age, height, speed or cost); others give you a rule and ask what must logically follow from it. Read every statement carefully before choosing one option from A to E. Only pick 'cannot tell' if the statements truly do not give enough information to be certain; do not choose it just because working out the answer takes several steps.
Worked example. Aiden is taller than Bea. Bea is taller than Chidi. Who is the shortest?
A) Aiden
B) Bea
C) Chidi
D) Cannot tell
E) Aiden and Chidi are the same height Answer: C) Chidi. Combine the two statements into a single order: Aiden is taller than Bea, and Bea is taller than Chidi, so from tallest to shortest the order is Aiden, then Bea, then Chidi. Chidi is therefore the shortest. Because the chain is complete, 'cannot tell' is wrong, and no equal heights were mentioned, so option E is also wrong.
1
Amelia is heavier than Bilal. Bilal is heavier than Cody. Who is the lightest?
A) Cody
B) Amelia
C) Bilal
D) Cannot tell
E) Amelia and Cody weigh the same
(Total for Question 1 is 1 mark)
2
Dexter is younger than Ethan. Ethan is younger than Farah. Who is the oldest?
A) Dexter
B) Ethan
C) Farah
D) Cannot tell
E) Dexter and Farah are the same age
(Total for Question 2 is 1 mark)
3
Grace runs faster than Harun. Idris runs slower than Harun. Who runs the fastest?
A) Idris
B) Harun
C) Cannot tell
D) Harun and Grace run at the same speed
E) Grace
(Total for Question 3 is 1 mark)
4
The kettle costs more than the notebook. The candle costs less than the notebook. Which item is the cheapest?
A) Kettle
B) Notebook
C) Cannot tell
D) Candle
E) The notebook and candle cost the same
(Total for Question 4 is 1 mark)
5
Jayden is taller than Kiran. Kiran is taller than Lola. Who is neither the tallest nor the shortest?
A) Kiran
B) Jayden
C) Lola
D) Cannot tell
E) Jayden and Lola are the same height
(Total for Question 5 is 1 mark)
6
Mason is older than Noah. Noah is older than Omar. Omar is older than Poppy. Who is the second oldest?
A) Mason
B) Noah
C) Omar
D) Poppy
E) Cannot tell
(Total for Question 6 is 1 mark)
7
Quinn is taller than Reece. Saanvi is shorter than Theo. Theo is shorter than Reece. Who is the shortest?
A) Quinn
B) Reece
C) Theo
D) Saanvi
E) Cannot tell
(Total for Question 7 is 1 mark)
8
The lamp costs more than the vase. The mirror costs less than the lamp. The mirror costs more than the vase. Which item costs the most?
A) Lamp
B) Vase
C) Mirror
D) Cannot tell
E) The lamp and mirror cost the same
(Total for Question 8 is 1 mark)
9
In a queue, Umar is behind Vikram. Vikram is behind Willow. Willow is behind Xavier. Who is at the front of the queue?
A) Vikram
B) Willow
C) Umar
D) Xavier
E) Cannot tell
(Total for Question 9 is 1 mark)
10
Yasmin is faster than Zaid. Amelia is slower than Yasmin but faster than Bilal. Who is the slowest?
A) Yasmin
B) Zaid
C) Amelia
D) Bilal
E) Cannot tell for certain
(Total for Question 10 is 1 mark)
11
Cody is taller than Dexter. Ethan is taller than Cody. Dexter is not the shortest. Farah is the shortest. Who is the tallest?
A) Ethan
B) Dexter
C) Cody
D) Farah
E) Cannot tell
(Total for Question 11 is 1 mark)
12
Grace is older than Harun. Harun is the same age as Idris. Idris is older than Jayden. Who is the youngest?
A) Grace
B) Jayden
C) Harun
D) Idris
E) Cannot tell
(Total for Question 12 is 1 mark)
13
In a race, Kiran finished before Lola. Lola finished before Mason. Mason finished before Noah. Who finished last?
A) Kiran
B) Lola
C) Noah
D) Mason
E) Cannot tell
(Total for Question 13 is 1 mark)
14
Omar arrived before Poppy. Quinn arrived after Omar but before Reece. Poppy arrived after Reece. Who arrived first?
A) Quinn
B) Reece
C) Poppy
D) Omar
E) Cannot tell
(Total for Question 14 is 1 mark)
15
Statement 1: All the pupils in Year 6 wear blue jumpers. Statement 2: Noah wears a blue jumper. Which conclusion must be true?
A) Noah is in Year 6
B) Noah is not in Year 6
C) All blue-jumper wearers are in Year 6
D) No pupils outside Year 6 wear blue jumpers
E) Cannot tell whether Noah is in Year 6
(Total for Question 15 is 1 mark)
16
Statement 1: No reptiles can fly. Statement 2: A gecko is a reptile. Which conclusion must be true?
A) A gecko can fly
B) A gecko cannot fly
C) Some reptiles can fly
D) All animals that cannot fly are reptiles
E) Cannot tell whether a gecko can fly
(Total for Question 16 is 1 mark)
17
Statement 1: Every student who studies Latin also studies Greek. Statement 2: Poppy does not study Greek. Which conclusion must be true?
A) Poppy studies Latin
B) Poppy does not study Latin
C) Poppy studies Greek
D) Cannot tell whether Poppy studies Latin
E) All students study Greek
(Total for Question 17 is 1 mark)
18
Statement 1: Some of the counters in the jar are red. Statement 2: All red counters in the jar are plastic. Which conclusion must be true?
A) All counters in the jar are plastic
B) No counters in the jar are plastic
C) Some counters in the jar are plastic
D) All plastic counters in the jar are red
E) Cannot tell whether any counters in the jar are plastic
(Total for Question 18 is 1 mark)
19
Statement 1: If it is frosty, Quinn wears gloves. Statement 2: Quinn is wearing gloves. Which conclusion must be true?
A) It is frosty
B) It is not frosty
C) Quinn always wears gloves
D) Cannot tell whether it is frosty
E) Quinn wears gloves only when it is frosty
(Total for Question 19 is 1 mark)
20
Statement 1: If Reece wins the spelling bee, he receives a certificate. Statement 2: If Reece receives a certificate, his name is read out in assembly. Statement 3: Reece's name was not read out in assembly. Which conclusion must be true?
A) Reece won the spelling bee
B) Reece received a certificate
C) Cannot tell whether Reece won the spelling bee
D) Reece's name will never be read out in assembly
E) Reece did not win the spelling bee
(Total for Question 20 is 1 mark)
21
Saanvi is taller than Theo. Theo is taller than Umar. Umar is not the shortest. Vikram is shorter than Umar. Vikram is taller than Willow. Who is the shortest?
A) Willow
B) Saanvi
C) Theo
D) Umar
E) Vikram
(Total for Question 21 is 1 mark)
22
Xavier is older than Yasmin. Yasmin is older than Zaid. Zaid is older than Amelia. Amelia is older than Bilal. Who is the second youngest?
A) Xavier
B) Amelia
C) Yasmin
D) Zaid
E) Bilal
(Total for Question 22 is 1 mark)
23
Statement 1: Cody is older than Dexter. Statement 2: Dexter is the same age as Ethan. Statement 3: Ethan is older than Farah. Which conclusion must be true?
A) Farah is older than Cody
B) Cody is the same age as Ethan
C) Cody is older than Farah
D) Ethan is older than Cody
E) Cannot tell how Cody and Farah compare
(Total for Question 23 is 1 mark)
24
In a race, Grace finished before Harun. Harun finished before Idris. Idris finished before Jayden. Jayden finished before Kiran. Who finished first?
A) Harun
B) Idris
C) Kiran
D) Grace
E) Jayden
(Total for Question 24 is 1 mark)
25
Statement 1: No pupil who is in the drama club is in the debate club. Statement 2: Omar is in the debate club. Which conclusion must be true?
A) Omar is in drama club
B) Cannot tell whether Omar is in drama club
C) All debate club members are in drama club
D) Omar is in neither club
E) Omar is not in drama club
(Total for Question 25 is 1 mark)
26
Statement 1: If Saanvi is chosen for the orchestra, then Theo is not chosen. Statement 2: If Theo is not chosen, then Umar is chosen. Statement 3: Umar is not chosen. Which conclusion must be true?
A) Saanvi is not chosen for the orchestra
B) Saanvi is chosen for the orchestra
C) Umar is chosen for the orchestra
D) Cannot tell whether Saanvi is chosen
E) Theo is not chosen for the orchestra
(Total for Question 26 is 1 mark)
Mark scheme · EP.V21B Logic Deduction: Practice Set 2
Question 1
B1 A) Cody - the chain Amelia > Bilal > Cody puts Cody at the bottom
Answer: A) Cody
Question 2
B1 C) Farah - the chain Dexter < Ethan < Farah puts Farah at the top
Answer: C) Farah
Question 3
B1 E) Grace - the order Grace > Harun > Idris puts Grace at the top
Answer: E) Grace
Question 4
B1 D) Candle - the order kettle > notebook > candle puts the candle at the bottom
Answer: D) Candle
Question 5
B1 A) Kiran - the order Jayden > Kiran > Lola places Kiran in the middle
Answer: A) Kiran
Question 6
B1 B) Noah - the order Mason > Noah > Omar > Poppy places Noah second
Answer: B) Noah
Question 7
B1 D) Saanvi - the order Quinn > Reece > Theo > Saanvi places Saanvi last
Answer: D) Saanvi
Question 8
B1 A) Lamp - the order lamp > mirror > vase places the lamp highest
Answer: A) Lamp
Question 9
B1 D) Xavier - the order Xavier, Willow, Vikram, Umar (front to back) places Xavier first
Answer: D) Xavier
Question 10
B1 E) Cannot tell for certain - Zaid is never compared with Amelia or Bilal, so his position among them is unknown
Answer: E) Cannot tell for certain
Question 11
B1 A) Ethan - the order Ethan > Cody > Dexter > Farah places Ethan at the top
Answer: A) Ethan
Question 12
B1 B) Jayden - the order Grace > Harun = Idris > Jayden places Jayden last
Answer: B) Jayden
Question 13
B1 C) Noah - the order Kiran, Lola, Mason, Noah (first to last) places Noah last
Answer: C) Noah
Question 14
B1 D) Omar - the order Omar, Quinn, Reece, Poppy (earliest to latest) places Omar first
Answer: D) Omar
Question 15
B1 E) Cannot tell whether Noah is in Year 6 - wearing a blue jumper does not prove membership of Year 6
Answer: E) Cannot tell whether Noah is in Year 6
Question 16
B1 B) A gecko cannot fly - a valid deduction: no reptiles can fly, and a gecko is a reptile
Answer: B) A gecko cannot fly
Question 17
B1 B) Poppy does not study Latin - valid by contrapositive: not Greek means not Latin
Answer: B) Poppy does not study Latin
Question 18
B1 C) Some counters in the jar are plastic - the red counters that exist must be plastic, so at least some counters are plastic
Answer: C) Some counters in the jar are plastic
Question 19
B1 D) Cannot tell whether it is frosty - wearing gloves does not confirm the reason why
Answer: D) Cannot tell whether it is frosty
Question 20
B1 E) Reece did not win the spelling bee - chained contrapositive: no assembly mention means no certificate means no win
Answer: E) Reece did not win the spelling bee
Question 21
B1 A) Willow - the order Saanvi > Theo > Umar > Vikram > Willow places Willow last
Answer: A) Willow
Question 22
B1 B) Amelia - the order Xavier > Yasmin > Zaid > Amelia > Bilal places Amelia second from the bottom
Answer: B) Amelia
Question 23
B1 C) Cody is older than Farah - the chain Cody > Dexter = Ethan > Farah gives Cody > Farah
Answer: C) Cody is older than Farah
Question 24
B1 D) Grace - the finishing order Grace, Harun, Idris, Jayden, Kiran places Grace first
Answer: D) Grace
Question 25
B1 E) Omar is not in drama club - valid: no overlap between the clubs, and Omar is in debate club
Answer: E) Omar is not in drama club
Question 26
B1 A) Saanvi is not chosen for the orchestra - chained contrapositives show Theo is chosen, so Saanvi cannot be