Quantitative Reasoning Flashcards

What is the value of sin(45°) × cos(45°)?

Answer: 1/2

sin(45°) = cos(45°) = √2/2; their product = (√2/2)² = 1/2.

A sequence is defined by aₙ = 2aₙ₋₁ − 3, with a₁ = 5. What is a₄?

Answer: 19

a₂ = 2(5)−3 = 7; a₃ = 2(7)−3 = 11; a₄ = 2(11)−3 = 19.

Simplify: (x² − 9) / (x − 3) for x ≠ 3.

Answer: x + 3

x² − 9 = (x−3)(x+3); dividing by (x−3) gives x + 3.

If 5% of a number is 17, what is 20% of the same number?

Answer: 68

5% of n = 17 → n = 340; 20% of 340 = 68.

Two angles of a triangle measure 47° and 83°. What is the measure of the exterior angle adjacent to the third interior angle?

Answer: 130°

Third interior angle = 180 − 47 − 83 = 50°; its adjacent exterior angle = 180 − 50 = 130°.

What is the slope of a line perpendicular to y = (3/4)x − 2?

Answer: −4/3

The slope of the given line is 3/4; the perpendicular slope is its negative reciprocal: −4/3.

A data set has values: 8, 12, 15, 15, 18, 22. What is the median?

Answer: 15

With 6 sorted values, median = average of 3rd and 4th values = (15 + 15)/2 = 15.