Practice Test 12 - GRE Quantitative Reasoning

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

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1. Which of the following is true for all real numbers $t$ such that $t\neq 0$?
2. A cube has side length $5$ inches. What is the total surface area of the cube, in square inches?
3. In the coordinate plane, point $C$ is at $(3,1)$ and point $D$ is at $(-1,4)$. Which of the following equals the distance from $C$ to $D$?
4. For integer $k$, $k\ge 1$. 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: $k!$ Column B: $2^k$
5. An investor's account balance was originally $\$1{,}000$. It decreases by $20\%$ in one month. In the next month, it increases by $25\%$, based on the balance at the start of that month. What is the final balance?
6. A real number $p$ satisfies $-4\le p\le 2$. 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: $|p|$ Column B: $p+3$
7. A printing company charges $50 to set up a job plus $0.20 per page printed. If the total cost was $86, how many pages were printed?
8. A rectangle has perimeter $40$. Its length is $L$ and its width is $W$, where $L>W>0$. 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: $L$ Column B: $12$
9. Let $f(x)=x-2$ and $g(x)=3x+1$. What is the value of $f(g(4))$?
10. Integer $n$ satisfies $-3\le n\le 3$ and $n\equiv 1\pmod{2}$. Which of the following could be the value of $n$?
11. A group of 80 students are surveyed. 45 students are enrolled in Chemistry, 35 are enrolled in Physics, and 20 are enrolled in Biology. Every student is enrolled in at least one of the three subjects. If 15 students are enrolled in both Chemistry and Physics, 10 in both Physics and Biology, and 8 in both Chemistry and Biology, how many students are enrolled in all three subjects?
12. Let $p$ and $q$ be real numbers such that $p<q$ and $|p|=|q|$. Which of the following statements is true?
13. Points $G(-1,-1)$ and $H(5,3)$ lie in the coordinate plane. What is the distance between $G$ and $H$?
14. A circle has radius $9$. A sector of the circle has area $\frac{27\pi}{2}$. What is the measure of the central angle of the sector, in degrees?
15. Let $a$ and $b$ be integers such that $a$ is even and $b$ is odd. 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: $a+b$ Column B: $a-b$
16. A teacher must assign 5 different students to 5 different seats in a row. Two of the students, X and Y, must not sit next to each other. How many different seating arrangements are possible?
17. A store increases the price of an item by $20\%$ and then decreases the new price by $20\%$. The final price is what percent of the original price?
18. Points $R(-2, 1)$ and $S(4, 4)$ lie in the coordinate plane. What is the distance between $R$ and $S$?
19. Which of the following is equivalent to $x^2-9-(x-3)(x+3)$?
20. Which of the following is greatest?

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