Practice Test 2 - GRE Quantitative Reasoning

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

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1. For the quadratic function $f(x)=x^2-10x+m$, the graph has its vertex on the $x$-axis. What is the value of $m$?
2. What is the value of $\sqrt{50} - \sqrt{8}$?
3. A bill is split among three coworkers, Alex, Bri, and Chen, in the ratio $2:3:5$. If Chen pays $45$ dollars, how much is the total bill, in dollars?
4. A function $f$ is defined by $f(x)=x^2-1$. Which of the following equals $f(x+1)$?
5. A research team tracked the number of participants who completed a survey. Table (Survey Completion) Columns: Group; Invited (people); Completed (people) Rows: - A: 120; 90 - B: 150; 105 - C: 80; 60 - D: 200; 140 Which group had the highest completion rate?
6. Which of the following is equivalent to $\dfrac{6}{x} + \dfrac{2}{x}$ for $x\neq 0$?
7. For real number $t$, $-2 \le t \le 3$. Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the following four answer choices. Column A: $t^2$ Column B: $t$
8. A store sells a jacket for $25\%$ off its original price. If the sale price of the jacket is $72, what was the original price of the jacket?
9. A runner recorded distance run each day for a week. Table (Distance Run) Columns: Day; Distance (kilometers) Rows: - Mon: 5 - Tue: 8 - Wed: 6 - Thu: 10 - Fri: 0 - Sat: 12 - Sun: 9 According to the table, what is the median daily distance run (in kilometers) for the week?
10. A line has equation $y= -\frac{3}{2}x+6$. If the line is shifted right by 2 units (with no vertical shift), which of the following is an equation of the new line?
11. In a right triangle, the two legs have lengths $a$ and $b$, where $a>0$ and $b>0$. Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the following four answer choices. Given: $a^2+b^2=25$ Column A: $a+b$ Column B: $7$
12. A bookstore had 150 copies of a novel. It sold 40% of the copies, based on the original number of copies. How many copies remain?
13. In the coordinate plane, point $A$ is at $(-2,6)$ and point $B$ is at $(1,2)$. What is the distance between $A$ and $B$?
14. The line with equation $3x+2y=12$ is graphed in the $xy$-plane. What is the $y$-intercept of the line?​
15. Which of the following is equal to $\sqrt[3]{a^4}$ for real $a$?
16. A data set consists of the numbers 4, 7, 7, 10, and $x$. If the mean of the data set is 8, what is the value of $x$?
17. If $r(x)=(x-2)(x-5)$, which of the following statements is true?
18. A cylindrical tank has radius $3$ m and height $10$ m. What is the volume of the tank, in cubic meters? (Express your answer in terms of $\pi$.)
19. A company recorded average weekly hours worked by department. Table (Average Weekly Hours) Columns: Department; Average hours per employee (hours/week); Number of employees (employees) Rows: - Sales: 38; 25 - Engineering: 45; 40 - Support: 34; 30 - HR: 36; 10 Which of the following is closest to the overall company-wide average weekly hours per employee?
20. In the coordinate plane, point $P$ is at $(-2,3)$ and point $Q$ is at $(4,-1)$. Which of the following is the distance from $P$ to $Q$?

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