UCAT · Decision Making

Logic, syllogisms and ordering

38 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 38 questions

  1. A fair six-sided die is rolled twice. What is the probability that the total is 8?
  2. Of 60 students, 34 play football and 26 play tennis. 21 do both. How many do neither?
  3. On an island each person either always tells the truth or always lies. Isla says: "At least two of the three of us are liars." Kiran says: "Isla and I are the same type." Hugo says: "Kiran is a truth…
  4. 4 people (Amira, Chloe, Isla, Zara) are ranked from oldest to youngest. Zara is older than Isla. Amira is immediately older than Zara. Zara is immediately older than Chloe. Chloe is immediately older…
  5. All nurses on ward 4 are trained in resuscitation. Some trained in resuscitation also work on the night shift. Which conclusion must be true?
  6. 5 people (Amira, Femi, Grace, Jamal, Leah) are ranked from oldest to youngest. Amira is older than Femi. Jamal is immediately older than Femi. Grace is older than Leah. Femi is older than Leah. Amira…
  7. A bag holds 4 red, 6 blue and 5 green counters. Two are taken at random without replacement. What is the probability that neither is red?
  8. 5 people (Elena, Isla, Leah, Owen, Tom) are ranked from tallest to shortest. Owen is taller than Leah. Tom is taller than Elena. Isla is taller than Owen. Leah is taller than Elena. Tom is immediately…
  9. A town council says: 'Crime fell after we installed CCTV, so CCTV reduces crime.' Which finding best supports the council's claim?
  10. 5 people (Amira, Ben, Dev, Elena, Zara) are ranked from oldest to youngest. Amira is older than Zara. Dev is older than Amira. Amira is immediately older than Ben. Zara is immediately older than Elena…
  11. All carbon-neutral companies publish annual reports. Zenith Ltd does not publish an annual report. What follows?
  12. On an island each person either always tells the truth or always lies. Kiran says: "Chloe is a liar." Dev says: "Kiran and Chloe are both truth-tellers." Chloe says: "Dev is a truth-teller." Which of…
  13. A bag holds 6 red, 4 blue and 3 green counters. Two are taken at random without replacement. What is the probability that one is red and one is blue (in either order)?
  14. Of 80 students, 28 take the bus, 44 take the train and 10 do neither. How many do both?
  15. 4 people (Amira, Leah, Owen, Zara) are ranked from oldest to youngest. Leah is immediately older than Owen. Zara is the oldest. Amira is the youngest. Who is the fourth oldest?
  16. A council claims: 'Recycling rates rose from 30 to 36 per cent.' By what percentage did the rate rise, in relative terms?
  17. A bag has 5 red and 3 blue counters. Two are drawn without replacement. What is the probability that both are red?
  18. 4 people (Ben, Femi, Grace, Isla) are ranked from tallest to shortest. Isla is taller than Ben. Isla is immediately taller than Ben. Isla is taller than Femi. Isla is the tallest. Ben is immediately t…
  19. If the server is online, then the alarm is armed. If the alarm is armed, then the screen is lit. Given that the server is online, which statement must be true?
  20. On an island each person either always tells the truth or always lies. Dev says: "Exactly one of the three of us is a liar." Sana says: "Dev and Grace are both truth-tellers." Grace says: "Dev and San…
  21. 4 people (Ben, Elena, Kiran, Marcus) are ranked from tallest to shortest. Elena is taller than Ben. Elena is the tallest. Ben is taller than Marcus. Marcus is taller than Kiran. Elena is taller than M…
  22. No reptile is warm-blooded. All snakes are reptiles. Which statement must be true?
  23. In a class of 30 pupils, 18 study French, 14 study Spanish and 5 study neither. How many study both?
  24. Of 120 students, 88 play football, 68 play tennis and 27 do neither. How many do both?
  25. On an island each person either always tells the truth or always lies. Femi says: "Exactly one of the three of us is a liar." Hugo says: "Femi is a liar." Priya says: "Hugo and I are the same type." W…
  26. All the members of a choir can read music. Some who can read music play the piano. Priya plays the piano. Which conclusion is valid?
  27. Anna is taller than Ben. Ben is taller than Chloe. Dev is shorter than Chloe. Who is second tallest?
  28. 4 people (Ben, Grace, Priya, Tom) are ranked from fastest to slowest. Tom is faster than Priya. Tom is immediately faster than Grace. Priya is the slowest. Tom is faster than Ben. Who is the fastest?
  29. On an island each person either always tells the truth or always lies. Kiran says: "Nia is a liar." Owen says: "Kiran and I are the same type." Nia says: "Owen is a truth-teller." Which of the followi…
  30. 5 people (Chloe, Hugo, Marcus, Owen, Priya) are ranked from fastest to slowest. Hugo is immediately faster than Priya. Priya is faster than Marcus. Owen is the fastest. Chloe is faster than Priya. Who…
  31. Of 60 students, 43 take the bus, 30 take the train and 2 do neither. How many do both?
  32. If the alarm is armed, then the report is filed. If the report is filed, then the door is locked. It is known that the door is locked. Which statement is correct?
  33. Of 120 students, 89 have a bicycle, 39 have a scooter and 21 do neither. How many have a bicycle but do not have a scooter?
  34. If the alarm is armed, then the gate is open. If the gate is open, then the heating runs. It is known that it is not the case that the heating runs. Which statement must be true?
  35. 4 people (Amira, Grace, Leah, Nia) are ranked from fastest to slowest. Leah is faster than Nia. Leah is the fastest. Grace is faster than Amira. Leah is faster than Grace. Nia is immediately faster th…
  36. If the alarm sounds, the doors lock. The doors are locked. What can be concluded?
  37. A claim: 'Our new road reduced journey times, so the average speed must have risen.' Which statement, if true, would most weaken this claim?
  38. 5 people (Grace, Hugo, Marcus, Sana, Zara) are ranked from tallest to shortest. Hugo is the tallest. Zara is taller than Sana. Sana is taller than Grace. Marcus is immediately taller than Grace. Zara…

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