NBT Logical Reasoning & Problem Solving 4

Question 1

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

Accepted Answer

60 mph

Answer

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

Question 2

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

Accepted Answer

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

Answer

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

Question 3

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

Accepted Answer

7

Answer

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

Question 4

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

Accepted Answer

162

Answer

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

Question 5

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?

Accepted Answer

175 miles

Answer

3.5 inches × 50 miles/inch = 175 miles.

(NBT) National Benchmark Test Practice Test