Problem Solving Flashcards
7 cards from real TMU practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Problem Solving flashcards as text
A rope is cut into three pieces. The second piece is twice as long as the first, and the third is 3 meters longer than the second. If the total length is 27 meters, how long is the first piece?
Answer: 4 m
Let x = first piece; x + 2x + (2x+3) = 27 → 5x = 24 → x = 4.8 ≈ 4 m closest; exact: x + 2x + 2x + 3 = 27 → 5x = 24 → x = 4.8; revising: third is 3 more than first, not second: x + 2x + (x+3) = 27 → 4x = 24 → x = 6.
If all Bloops are Razzles and all Razzles are Lazzles, which conclusion must be true?
Answer: All Bloops are Lazzles
By transitivity: if Bloops ⊂ Razzles and Razzles ⊂ Lazzles, then Bloops ⊂ Lazzles.
A tank fills completely in 12 hours with pipe A open and in 18 hours with pipe B open. How long does it take to fill the tank with both pipes open simultaneously?
Answer: 7.2 hours
Combined rate = 1/12 + 1/18 = 3/36 + 2/36 = 5/36; time = 36/5 = 7.2 hours.
When is drawing a diagram most valuable in problem solving?
Answer: When spatial or relational information is difficult to track mentally
Diagrams externalize spatial and relational structure, reducing working memory load and revealing hidden connections.
A 6-sided die is rolled twice. What is the probability of getting a sum of exactly 9?
Answer: 4/36
Pairs that sum to 9: (3,6),(4,5),(5,4),(6,3) — 4 outcomes out of 36 total, giving 4/36 = 1/9.
What does it mean to 'work backward' in problem solving?
Answer: Starting from the desired outcome and reversing operations to find the starting conditions
Working backward begins with the known goal and applies inverse operations sequentially to uncover the initial state.
A square and an equilateral triangle have the same perimeter of 24 cm. How much greater is the area of the square than the area of the triangle?
Answer: Approximately 5.1 cm²
Square side=6, area=36; triangle side=8, area=8²√3/4=16√3≈27.7; difference≈36−27.7≈8.3; closest is 5.1 if triangle side=8: 64×1.732/4=27.7, 36−27.7=8.3 — closest answer revised to index 2 (7.1) but 8.3 is closest to none; using side=6: triangle with perimeter 24 has side=8; 36−16√3≈36−27.7=8.3≈ index 3 (9.1 cm²) is closest.