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TMUA 2016 · Paper 2 · Question 4 of 20

TMUA 2016 Paper 2 Question 4

Logic and arguments — Logic puzzle · exactly one true statement. Try it first; the answer and a full worked solution are below.

TMUA 2016 · Paper 2Logic and argumentsLogic puzzle · exactly one true statement5 options
Five sealed urns, labelled P, Q, R, S, and T, each contain the same (non-zero) number of balls. The following statements are attached to the urns.

Urn P    This urn contains one or four balls.
Urn Q   This urn contains two or four balls.
Urn R   This urn contains more than two balls and fewer than five balls.
Urn S    This urn contains one or two balls.
Urn T    This urn contains fewer than three balls.

Exactly one of the urns has a true statement attached to it.

Which urn is it?

  1. AUrn P
  2. BUrn Q
  3. CUrn R
  4. DUrn S
  5. EUrn T
Show the answer and worked solution
answer · C
  1. AUrn P
  2. BUrn Q
  3. CUrn R
  4. DUrn S
  5. EUrn T
Every urn holds the same number n, so just test each value of n and count how many statements come out true. For n=1: P, S and T are true — three. For n=2: Q, S and T — three. For n=3: only R — exactly one. For n=4: P, Q and R — three. For n ≥ 5 none is true. So n=3 and the single true statement is on urn R.