In each question you are given two or three statements. Treat every statement as TRUE, even if it seems unlikely, and use ONLY the information given (not outside knowledge or guesswork) to work out the answer. Some questions ask you to put people or things in order (for example, by height, age or speed); others give you a rule and ask what must follow from it. Read all the statements carefully before choosing your answer from options A to E. If the statements do not give enough information to be certain, choose the option that says so - do not pick the answer that merely seems likely.
Worked example. Ali is taller than Ben. Ben is taller than Cara. Who is the shortest?
A) Ali
B) Ben
C) Cara
D) Cannot tell
E) Ali and Cara are the same height Answer: C) Cara. The two statements give a complete chain: Ali is taller than Ben, and Ben is taller than Cara. Putting this in order from tallest to shortest gives Ali, then Ben, then Cara, so Cara must be the shortest. There is enough information to be certain, so 'cannot tell' is wrong, and no equality was stated, so option E is also wrong.
1
Tom is taller than Priya. Priya is taller than Josh. Who is the shortest?
A) Josh
B) Tom
C) Priya
D) Cannot tell
E) Tom and Josh are the same height
(Total for Question 1 is 1 mark)
2
Fatima is younger than Ben. Ben is younger than Isla. Who is the oldest?
A) Fatima
B) Isla
C) Ben
D) Cannot tell
E) Fatima and Isla are the same age
(Total for Question 2 is 1 mark)
3
Chen is older than Aisha. Ryan is younger than Aisha. Who is the youngest?
A) Chen
B) Aisha
C) Ryan
D) Cannot tell
E) Chen and Ryan are the same age
(Total for Question 3 is 1 mark)
4
The red pen costs more than the blue pen. The green pen costs less than the blue pen. Which pen is the cheapest?
A) Red pen
B) Blue pen
C) Cannot tell
D) Green pen
E) The blue and green pens cost the same
(Total for Question 4 is 1 mark)
5
Sophie runs faster than Kwame. Leo runs slower than Kwame. Who runs the fastest?
A) Leo
B) Kwame
C) Cannot tell
D) Kwame and Sophie run at the same speed
E) Sophie
(Total for Question 5 is 1 mark)
6
Zara is older than Amara. Amara is older than Oliver. Who is neither the oldest nor the youngest?
A) Amara
B) Zara
C) Oliver
D) Cannot tell
E) Zara and Oliver are the same age
(Total for Question 6 is 1 mark)
7
Maya is taller than Daniel. Daniel is taller than Ben. Ben is taller than Rhys. Who is the second tallest?
A) Maya
B) Daniel
C) Ben
D) Rhys
E) Cannot tell
(Total for Question 7 is 1 mark)
8
Yusuf is older than Nia. Callum is older than Yusuf. Nia is older than Freya. Who is the youngest?
A) Yusuf
B) Callum
C) Freya
D) Nia
E) Cannot tell
(Total for Question 8 is 1 mark)
9
The jacket costs more than the scarf. The hat costs less than the scarf. The jacket costs less than the coat. Which item costs the most?
A) Jacket
B) Scarf
C) Hat
D) Coat
E) Cannot tell
(Total for Question 9 is 1 mark)
10
Priya is faster than Tom. Josh is slower than Priya but faster than Fatima. Who is the slowest?
A) Priya
B) Tom
C) Josh
D) Fatima
E) Cannot tell for certain
(Total for Question 10 is 1 mark)
11
Rhys is taller than Isla. Callum is taller than Rhys. Isla is not the tallest. Freya is the shortest. Who is the tallest?
A) Callum
B) Isla
C) Rhys
D) Freya
E) Cannot tell
(Total for Question 11 is 1 mark)
12
Oliver is older than Maya. Maya is the same age as Daniel. Daniel is older than Ben. Who is the youngest?
A) Oliver
B) Ben
C) Maya
D) Daniel
E) Cannot tell
(Total for Question 12 is 1 mark)
13
In a queue, Ryan is in front of Chen. Chen is in front of Aisha. Aisha is in front of Sophie. Who is at the back of the queue?
A) Ryan
B) Chen
C) Sophie
D) Aisha
E) Cannot tell
(Total for Question 13 is 1 mark)
14
Amara arrived before Kwame. Leo arrived after Amara but before Zara. Kwame arrived after Zara. Who arrived first?
A) Leo
B) Zara
C) Kwame
D) Amara
E) Cannot tell
(Total for Question 14 is 1 mark)
15
Statement 1: All the pupils in Class 5 play the recorder. Statement 2: Priya plays the recorder. Which conclusion must be true?
A) Priya is in Class 5
B) Priya is not in Class 5
C) All recorder players are in Class 5
D) No pupils outside Class 5 play the recorder
E) Cannot tell whether Priya is in Class 5
(Total for Question 15 is 1 mark)
16
Statement 1: No fish can walk. Statement 2: A trout is a fish. Which conclusion must be true?
A) A trout cannot walk
B) A trout can walk
C) Some fish can walk
D) All animals that cannot walk are fish
E) Cannot tell whether a trout can walk
(Total for Question 16 is 1 mark)
17
Statement 1: Every student who studies French also studies Spanish. Statement 2: Ben does not study Spanish. Which conclusion must be true?
A) Ben studies French
B) Ben does not study French
C) Ben studies Spanish
D) Cannot tell whether Ben studies French
E) All students study Spanish
(Total for Question 17 is 1 mark)
18
Statement 1: Some of the shapes in the box are triangles. Statement 2: All triangles in the box are blue. Which conclusion must be true?
A) All shapes in the box are blue
B) No shapes in the box are blue
C) Some shapes in the box are blue
D) All blue shapes in the box are triangles
E) Cannot tell whether any shapes in the box are blue
(Total for Question 18 is 1 mark)
19
Statement 1: If it is raining, Oliver carries an umbrella. Statement 2: Oliver is carrying an umbrella. Which conclusion must be true?
A) It is raining
B) It is not raining
C) Oliver always carries an umbrella
D) Cannot tell whether it is raining
E) Oliver carries an umbrella only when it rains
(Total for Question 19 is 1 mark)
20
Statement 1: If Freya wins the race, she gets a gold medal. Statement 2: If Freya gets a gold medal, her name goes on the trophy. Statement 3: Freya's name is not on the trophy. Which conclusion must be true?
A) Freya won the race
B) Freya got a gold medal
C) Cannot tell whether Freya won the race
D) Freya's name will never go on the trophy
E) Freya did not win the race
(Total for Question 20 is 1 mark)
21
Aaliyah is taller than Jack. Jack is taller than Callum. Callum is not the shortest. Rhys is shorter than Callum. Rhys is taller than Zara. Who is the shortest?
A) Zara
B) Aaliyah
C) Jack
D) Callum
E) Rhys
(Total for Question 21 is 1 mark)
22
Maya is older than Ben. Ben is older than Sophie. Sophie is older than Leo. Leo is older than Daniel. Who is the second youngest?
A) Maya
B) Leo
C) Ben
D) Sophie
E) Daniel
(Total for Question 22 is 1 mark)
23
Statement 1: Chen is older than Priya. Statement 2: Priya is the same age as Fatima. Statement 3: Fatima is older than Josh. Which conclusion must be true?
A) Josh is older than Chen
B) Chen is the same age as Fatima
C) Chen is older than Josh
D) Fatima is older than Chen
E) Cannot tell how Chen and Josh compare
(Total for Question 23 is 1 mark)
24
In a race, Yusuf finished before Kwame. Kwame finished before Nia. Nia finished before Rhys. Rhys finished before Freya. Who finished first?
A) Kwame
B) Nia
C) Rhys
D) Yusuf
E) Freya
(Total for Question 24 is 1 mark)
25
Statement 1: No pupil who is in the chess club is in the football club. Statement 2: Callum is in the football club. Which conclusion must be true?
A) Callum is in chess club
B) Cannot tell whether Callum is in chess club
C) All football club members are in chess club
D) Callum is in neither club
E) Callum is not in chess club
(Total for Question 25 is 1 mark)
26
Statement 1: If Zara is picked for the team, then Isla is not picked. Statement 2: If Isla is not picked, then Ben is picked. Statement 3: Ben is not picked. Which conclusion must be true?
A) Zara is not picked for the team
B) Zara is picked for the team
C) Ben is picked for the team
D) Cannot tell whether Zara is picked
E) Isla is not picked for the team
(Total for Question 26 is 1 mark)
Mark scheme · EP.V21 Logic Deduction
Question 1
B1 A) Josh - the chain Tom > Priya > Josh puts Josh at the bottom
Answer: A) Josh
Question 2
B1 B) Isla - the chain Fatima < Ben < Isla puts Isla at the top
Answer: B) Isla
Question 3
B1 C) Ryan - the order Chen > Aisha > Ryan puts Ryan at the bottom
Answer: C) Ryan
Question 4
B1 D) Green pen - the order red > blue > green puts green at the bottom
Answer: D) Green pen
Question 5
B1 E) Sophie - the order Sophie > Kwame > Leo puts Sophie at the top
Answer: E) Sophie
Question 6
B1 A) Amara - the order Zara > Amara > Oliver places Amara in the middle
Answer: A) Amara
Question 7
B1 B) Daniel - the order Maya > Daniel > Ben > Rhys places Daniel second
Answer: B) Daniel
Question 8
B1 C) Freya - the order Callum > Yusuf > Nia > Freya places Freya last
Answer: C) Freya
Question 9
B1 D) Coat - the order hat < scarf < jacket < coat places the coat highest
Answer: D) Coat
Question 10
B1 E) Cannot tell for certain - Tom is never compared with Josh or Fatima, so his position among them is unknown
Answer: E) Cannot tell for certain
Question 11
B1 A) Callum - the order Callum > Rhys > Isla > Freya places Callum at the top
Answer: A) Callum
Question 12
B1 B) Ben - the order Oliver > Maya = Daniel > Ben places Ben last
Answer: B) Ben
Question 13
B1 C) Sophie - the order Ryan, Chen, Aisha, Sophie (front to back) places Sophie last
Answer: C) Sophie
Question 14
B1 D) Amara - the order Amara, Leo, Zara, Kwame (earliest to latest) places Amara first
Answer: D) Amara
Question 15
B1 E) Cannot tell whether Priya is in Class 5 - playing the recorder does not prove membership of Class 5
Answer: E) Cannot tell whether Priya is in Class 5
Question 16
B1 A) A trout cannot walk - a valid deduction: no fish can walk, and a trout is a fish
Answer: A) A trout cannot walk
Question 17
B1 B) Ben does not study French - valid by contrapositive: not Spanish means not French
Answer: B) Ben does not study French
Question 18
B1 C) Some shapes in the box are blue - the triangles that exist must be blue, so at least some shapes are blue
Answer: C) Some shapes in the box are blue
Question 19
B1 D) Cannot tell whether it is raining - carrying an umbrella does not confirm the reason why
Answer: D) Cannot tell whether it is raining
Question 20
B1 E) Freya did not win the race - chained contrapositive: no trophy means no medal means no win
Answer: E) Freya did not win the race
Question 21
B1 A) Zara - the order Aaliyah > Jack > Callum > Rhys > Zara places Zara last
Answer: A) Zara
Question 22
B1 B) Leo - the order Maya > Ben > Sophie > Leo > Daniel places Leo second from the bottom
Answer: B) Leo
Question 23
B1 C) Chen is older than Josh - the chain Chen > Priya = Fatima > Josh gives Chen > Josh
Answer: C) Chen is older than Josh
Question 24
B1 D) Yusuf - the finishing order Yusuf, Kwame, Nia, Rhys, Freya places Yusuf first
Answer: D) Yusuf
Question 25
B1 E) Callum is not in chess club - valid: no overlap between the clubs, and Callum is in football club
Answer: E) Callum is not in chess club
Question 26
B1 A) Zara is not picked for the team - chained contrapositives show Isla is picked, so Zara cannot be