Practice Test 9 - GRE Quantitative Reasoning

20 questions. Answer them in any order, then submit to see your score and every explanation.

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1. In right triangle $ABC$ with right angle at $C$, the legs have lengths $AC=6$ and $BC=8$. What is the length of hypotenuse $AB$?
2. In the $xy$-plane, line $\ell$ passes through the points $(2,5)$ and $(6,-3)$. What is the slope of line $\ell$?
3. In the coordinate plane, point $S$ is at $(-4,1)$ and point $T$ is at $(2,1)$. Which of the following is the distance between $S$ and $T$?
4. A salary is decreased by $10\%$ and then increased by $10\%$. The final salary is what percent of the original salary?
5. A function $f$ is defined by $f(x)=3x-7$. What is the value of $f(5)$?
6. A delivery company tracked the number of packages delivered and total fuel used in one week. Table (Week Summary) Columns: Day; Packages delivered (packages); Fuel used (gallons) Rows: - Mon: 480; 32 - Tue: 520; 35 - Wed: 500; 30 - Thu: 560; 40 - Fri: 540; 36 According to the table, which day had the greatest fuel efficiency, measured in packages per gallon?
7. Which of the following describes the graph of the equation $y=2x+5$ in the coordinate plane?
8. If $2x - 3 = 5x + 12$, what is the value of $x$?
9. In the coordinate plane, point $J$ is at $(-3,2)$ and point $K$ is at $(1,-4)$. Which of the following is the distance between $J$ and $K$?
10. Let $g(x)=x^3-4x^2-x+4$. Which of the following represents $g(x)$ factored completely over the integers?
11. In the coordinate plane, point $T$ is at $(4,0)$ and point $U$ is at $(-2,-3)$. What is the distance between $T$ and $U$?
12. An investor buys a stock for $100 per share. The price increases by 30% and then decreases by 20%, each time relative to the most recent price. What is the final price per share?
13. A shipping company tracked the number of late deliveries and total deliveries by region in one month. Table (Deliveries) Columns: Region; Total deliveries (deliveries); Late deliveries (deliveries) Rows: - North: 1,200; 36 - South: 900; 27 - East: 1,500; 60 - West: 800; 16 Which region had the highest late-delivery rate?
14. An investment of $\$2{,}000$ increases in value by 12% in one year. What is the value of the investment after one year?
15. Two lines are given by $y=\frac{3}{4}x+1$ and $y=\frac{3}{4}x-5$. Which of the following best describes the relationship between the two lines?
16. A line has $y$-intercept $-3$ and passes through the point $(2,1)$. What is the slope of the line?
17. A bookstore sold 120 copies of a novel in January. In February, it sold 150 copies. The percent increase is based on the January sales of 120 copies. Which of the following represents the percent increase from January to February?
18. For which value(s) of $x$ is the inequality $\dfrac{x-5}{3} > 2$ true?
19. A convex polygon has $11$ sides. What is the sum of the interior angles of the polygon, in degrees?
20. Which of the following statements is true for all real numbers $x$?

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