Quantitative Reasoning and Math Flashcards

A train travels 240 miles in 3 hours, then 180 miles in 2 hours. What is the average speed for the entire trip?

Answer: 84 mph

Total distance = 420 miles, total time = 5 hours, so average speed = 420/5 = 84 mph.

If log₂(x) = 5, what is the value of x?

Answer: 32

log₂(x) = 5 means 2⁵ = x, so x = 32.

A cylinder has a radius of 4 cm and height of 10 cm. What is its volume in cm³?

Answer: 160π

Volume = πr²h = π(4²)(10) = 160π cm³.

What is the sum of the interior angles of a hexagon?

Answer: 720°

The sum of interior angles of an n-gon = (n−2)×180°; for a hexagon: (6−2)×180° = 720°.

If 3x − 7 = 2x + 5, what is the value of x?

Answer: 12

Subtracting 2x from both sides gives x − 7 = 5, so x = 12.

A rectangular room is 15 ft long and 12 ft wide. What is the length of the diagonal?

Answer: 19.2 ft

Using the Pythagorean theorem: diagonal = √(15² + 12²) = √(225 + 144) = √369 ≈ 19.2 ft.

A store sells a jacket at a 30% discount, then applies an additional 10% discount to the sale price. What is the total percent discount from the original price?

Answer: 37%

After 30% off, you pay 70%; after 10% more off, you pay 63%, meaning a total discount of 37%.