Problem Solving Strategies Flashcards

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?

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).

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?

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.

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?

Answer: Neurology

Dr. Jones has dermatology; Dr. Smith cannot be a cardiologist (surgery required); therefore Dr. Smith is the neurologist.

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?

Answer: 2

Total tablets needed = 3 × 10 = 30 tablets; one bottle of 25 is insufficient, so 2 bottles (50 tablets) are required.

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?

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.

When approaching a UMAT problem-solving question with many variables, the best first strategy is to:

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.