UMAT Problem Solving Strategies 1 — Questions and Answers
Question 1: A UMAT problem states: 'Five friends sit in a row. Anna is not next to Ben. Ben sits next to Carol. Carol sits at one end.' If Carol is at the left end, which of the following must be true?
- Anna sits immediately to the right of Carol
- Ben sits second from the left (Correct answer)
- Anna sits at the right end
- Ben and Anna are adjacent
Correct answer: Ben sits second from the left
Carol is at position 1 (left end); Ben is next to Carol, so Ben must be at position 2 (second from left).
Question 2: In a UMAT scheduling problem, five tasks must be completed in order. Task C must follow Task A. Task B must precede Task D. Task E can be done at any time. Which sequence is valid?
- B, C, A, D, E
- A, C, B, D, E (Correct answer)
- C, A, B, D, E
- B, D, A, C, E
Correct answer: A, C, B, D, E
A before C (A, C ✓), B before D (B, D ✓) — the sequence A, C, B, D, E satisfies both constraints.
Question 3: A logic grid puzzle states: 'Three doctors specialize in cardiology, neurology, and dermatology. Dr. Smith does not do surgery. Cardiologists perform surgery. Dr. Jones specializes in dermatology.' What is Dr. Smith's specialty?
- Cardiology
- Neurology (Correct answer)
- Dermatology
- Cannot be determined
Correct answer: Neurology
Dr. Jones has dermatology; Dr. Smith cannot be a cardiologist (surgery required); therefore Dr. Smith is the neurologist.
Question 4: A UMAT working-backwards problem: A patient needs medication 3 times a day for 10 days. Tablets come in bottles of 25. How many bottles are needed?
- 1
- 2 (Correct answer)
- 3
- 4
Correct answer: 2
Total tablets needed = 3 × 10 = 30 tablets; one bottle of 25 is insufficient, so 2 bottles (50 tablets) are required.
Question 5: In a UMAT problem, you are told that every student who passes the practical also passes the written exam, but not vice versa. Which conclusion is valid?
- Passing written guarantees passing practical
- Failing the practical does not necessarily mean failing the written (Correct answer)
- Passing written and practical are equivalent outcomes
- Failing written means failing practical
Correct answer: Failing the practical does not necessarily mean failing the written
Since passing practical → passing written (not the reverse), a student can fail the practical while having passed the written exam.
Question 6: When approaching a UMAT problem-solving question with many variables, the best first strategy is to:
- Guess and check all possible combinations
- Identify and apply the most restrictive constraint first to reduce possibilities (Correct answer)
- Start with the easiest constraint and work forward randomly
- List all possible arrangements before applying any rules
Correct answer: Identify and apply the most restrictive constraint first to reduce possibilities
Applying the most restrictive constraint first rapidly eliminates the most options, making subsequent steps much more efficient.
UMAT Problem Solving Strategies 1
A UMAT problem states: 'Five friends sit in a row.
Anna is not next to Ben.
Ben sits next to Carol.
Carol sits at one end.' If Carol is at the left end, which of the following must be true?