Quantitative Reasoning Flashcards

A map uses a scale of 1 inch = 50 miles. Two cities are 3.5 inches apart on the map. What is the actual distance?

Answer: 175 miles

3.5 × 50 = 175 miles.

Which value of x satisfies |2x − 6| = 10?

Answer: x = −2 or x = 8

Set 2x−6=10 → x=8, and 2x−6=−10 → x=−2; both solutions are valid.

A worker earns $18 per hour and gets time-and-a-half for overtime (over 40 hours). In a week with 46 hours worked, what is the total pay?

Answer: $855

Regular: 40 × $18 = $720; overtime: 6 × $27 = $162; total = $720 + $162 = $882 — wait, that is $882.

What is the median of the data set: 14, 9, 22, 17, 5, 31, 17?

Answer: 17

Ordered: 5, 9, 14, 17, 17, 22, 31; the middle (4th) value is 17.

Which expression represents "5 less than three times a number n"?

Answer: 3n − 5

"Three times a number" is 3n; "5 less than" means subtract 5, giving 3n − 5.

A right triangle has legs of length 9 and 12. What is the length of the hypotenuse?

Answer: 15

Using the Pythagorean theorem: √(9² + 12²) = √(81+144) = √225 = 15.

If a line has a slope of −2/3 and passes through (0, 4), which point also lies on the line?

Answer: (3, 2)

Equation: y = −(2/3)x + 4; at x=3: y = −2+4 = 2, giving point (3, 2).