Practice Test 4 - 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 real numbers $p$ and $q$, $p+q=0$. 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. Column A: $p^3+q^3$ Column B: $0$
2. A tank is $\frac{2}{5}$ full. After $30\%$ of the water currently in the tank is drained, what fraction of the tank is full?
3. Which of the following is equal to $\sqrt[4]{81}$?
4. Which of the following is equivalent to the polynomial expression $x^2-9$?
5. A function $m$ is defined by $m(x)=|x-3|$. Which of the following is the value of $m(-1)$?
6. If $x^{\frac{3}{2}}=8$ and $x$ is a real number, what is the value of $x$?
7. A tank is filled by Pipe A in 6 hours and by Pipe B in 8 hours. If both pipes fill the tank at constant rates and are opened together, how many hours will it take to fill the tank?
8. A rectangular prism has length $10$ cm, width $4$ cm, and height $3$ cm. What is the volume of the prism, in cubic centimeters?
9. For real numbers $m$ and $n$, $m+n=10$ and $mn=21$. 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: $m$ Column B: $n$
10. Which of the following statements is true about the polynomial $q(x)=-2x^2+7x-3$?
11. If $\frac{5}{x} = \frac{2}{7}$, what is the value of $x$?
12. Which of the following equals $\left(3^4\right)\left(3^{-2}\right)$?
13. A company's monthly rent was originally $\$2{,}000$. The rent is increased by $10\%$ for one year and then decreased by $10\%$ the next year. What is the rent after the two changes?
14. In a jar of marbles, the ratio of red marbles to blue marbles is $3:5$. If there are $40$ blue marbles, how many red marbles are there?
15. In a group of $90$ people, $50$ are in set $G$ (people who have been to Germany) and $45$ are in set $I$ (people who have been to Italy). If $20$ people have been to both Germany and Italy, what is the number of people who have been to exactly one of the two countries?
16. If $a$ is a nonzero real number and $a^{5/2}=32$, what is the value of $a$?​
17. If $a$ is a real number and $\sqrt{a^2}=7$, which of the following must be true?
18. In a class of 90 students, let set $G$ be those who play a musical instrument and set $H$ be those who play a sport. If $|G|=40$, $|H|=55$, and $|G\cup H|=70$, what is the number of students who play both a musical instrument and a sport?
19. Which of the following statements is true about the quadratic $y=ax^2+bx+c$ if $a>0$ and $c<0$?
20. In a survey of 100 employees, let set $T$ be those who took a training course and set $C$ be those who earned a certification. If $|T|=64$, $|C|=46$, and 18 employees did both, what is the number of employees who did neither?

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