Logical Reasoning & Problem Solving Flashcards

A train travels 120 miles in 2 hours, then 90 miles in 1.5 hours. What is its average speed for the entire trip?

Answer: 60 mph

Total distance = 210 miles; total time = 3.5 hours; average speed = 210/3.5 = 60 mph.

Which of the following is an example of circular reasoning (begging the question)?

Answer: The Bible is true because it says so in the Bible.

Using the Bible to prove the Bible is true assumes the very thing that needs to be proven.

In a group of 30 students, 18 play soccer and 14 play basketball. If 5 play neither, how many play both?

Answer: 7

Using inclusion-exclusion: 30 − 5 = 25 play at least one sport; 18 + 14 − x = 25, so x = 7.

What is the missing number? 2, 6, 18, 54, __

Answer: 162

Each term is multiplied by 3: 54 × 3 = 162.

A map uses a scale of 1 inch = 50 miles. If two cities are 3.5 inches apart on the map, what is their actual distance?

Answer: 175 miles

3.5 inches × 50 miles/inch = 175 miles.

Dana says, 'If I study, I will pass.' Dana did not pass. What can you conclude?

Answer: Dana did not study

By modus tollens (contrapositive): if 'study → pass' is true and 'not pass', then 'not study'.

Which shape has exactly 5 faces, 6 vertices, and 9 edges?

Answer: Triangular prism

A triangular prism has 5 faces, 6 vertices, and 9 edges, satisfying Euler's formula (5+6−9=2).