Quantitative Reasoning and Math Flashcards

How many ways can 4 students be arranged in a line?

Answer: 24

The number of permutations of 4 students = 4! = 4 × 3 × 2 × 1 = 24.

What is the value of (2³)² ÷ 2²?

Answer: 16

(2³)² = 2⁶ = 64; then 64 ÷ 2² = 64 ÷ 4 = 16.

The ratio of boys to girls in a class is 3:5. If there are 24 boys, how many girls are there?

Answer: 40

If 3 parts = 24 boys, then 1 part = 8; girls = 5 × 8 = 40.

What is the solution to the system: x + y = 10 and x − y = 4?

Answer: x=7, y=3

Adding the equations: 2x = 14, so x = 7; substituting: y = 10 − 7 = 3.

A sphere has a radius of 3 cm. What is its surface area?

Answer: 36π cm²

Surface area of a sphere = 4πr² = 4π(3²) = 36π cm².

What is the value of the expression |−8| − |−3| + |2|?

Answer: 7

Absolute values: |−8| = 8, |−3| = 3, |2| = 2; result = 8 − 3 + 2 = 7.

A data set has a mean of 50 and a standard deviation of 5. What percentage of data falls within one standard deviation of the mean, assuming a normal distribution?

Answer: 68%

By the empirical rule (68-95-99.7 rule), approximately 68% of data falls within one standard deviation of the mean.