Quantitative Reasoning and Math Flashcards

What is the value of 4! + 3! − 2!?

Answer: 28

4! = 24, 3! = 6, 2! = 2; so 24 + 6 − 2 = 28.

Two angles of a triangle are 45° and 75°. What is the measure of the third angle?

Answer: 60°

The angles of a triangle sum to 180°; the third angle = 180° − 45° − 75° = 60°.

What is the probability of rolling an odd number on a standard six-sided die?

Answer: 1/2

Odd numbers on a die are 1, 3, 5 — that's 3 out of 6 possible outcomes, so P = 1/2.

Simplify: (x³ · x⁴) / x²

Answer: x⁵

Numerator: x³⁺⁴ = x⁷; then x⁷ ÷ x² = x⁷⁻² = x⁵.

A car depreciates by 15% per year. If it is currently worth $20,000, what will it be worth after 2 years?

Answer: $14,450

After 2 years: $20,000 × (0.85)² = $20,000 × 0.7225 = $14,450.

What is the median of the data set: {3, 7, 7, 2, 9, 1, 5}?

Answer: 5

Sorted: {1, 2, 3, 5, 7, 7, 9}; the middle (4th) value is 5.

If the slope of line AB is 3/4, what is the slope of a line perpendicular to AB?

Answer: −4/3

The slope of a perpendicular line is the negative reciprocal of the original slope: −4/3.