Practice Test 1 - GRE Quantitative Reasoning

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

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1. A company's monthly website visits were 50,000 in January. In February, visits increased by 20% from January, and in March, visits decreased by 25% from February. What were the website visits in March?
2. In the coordinate plane, point $C$ is at $(2,2)$ and point $D$ is at $(5,-2)$. Which of the following is the distance between $C$ and $D$?
3. A rectangle has length $9$ ft and width $4$ ft. If both the length and width are doubled, what is the area of the new rectangle, in square feet?
4. Which of the following is true for all real numbers $p$ such that $p\ne 0$?
5. A fair six-sided die is rolled twice. The sample space consists of all ordered pairs $(a,b)$ where $a$ is the first roll and $b$ is the second roll, with each of the 36 outcomes equally likely. What is the probability that the sum of the two rolls is 7?
6. Which of the following is equivalent to $5(1-2z)+4z$?
7. If $f(x) = x^2 - 4x + 1$, what is the value of $f(5)$?
8. A square has area $81$ square units. What is the perimeter of the square, in units?
9. A polynomial is defined by $p(x)=(x-1)(x+4)(x-2)$. Which of the following statements is true?
10. For all real numbers $t$, which of the following is equivalent to $(t-1)^2-(t+1)(t-1)$?
11. In a group of 160 students, let set $A$ be those enrolled in Art, set $B$ be those enrolled in Biology, and set $C$ be those enrolled in Chemistry. If $|A|=60$, $|B|=70$, $|C|=55$, $|A\cap B|=25$, $|A\cap C|=20$, $|B\cap C|=18$, and $|A\cap B\cap C|=8$, what is the number of students enrolled in Biology only (in $B$ but not in $A$ or $C$)?
12. In the $xy$-plane, line $r$ passes through $(1,6)$ and $(5,2)$. What is the $y$-intercept of line $r$?
13. If $f(x)=2x-1$ and $f(g(x))=3x+4$, what is $g(x)$?
14. A dataset consists of $\{1, 2, 2, 2, 9\}$. If 9 is replaced by 3, which of the following statements is true?
15. How many distinct 6-letter strings can be formed using the letters in the word $\text{BANANA}$ if each string uses all 6 letters?
16. In right triangle $RST$ with right angle at $S$, the hypotenuse $RT$ has length $13$, and one leg $RS$ has length $5$. What is the length of the other leg $ST$?
17. A solution is made by mixing acid and water in the ratio $1:9$ by volume. If the total volume of the solution is $500$ milliliters, what volume of acid is in the solution?
18. A bag contains 10 chips: 4 labeled A, 3 labeled B, and 3 labeled C. Two chips are drawn at random without replacement. What is the probability that the two chips have different labels?
19. A set of 7 quiz scores is $\{6, 7, 7, 8, 8, 9, 20\}$. If the score 20 is replaced with 10, which of the following statements is true about the mean and the median of the set?
20. A fair coin is flipped 4 times. The sample space consists of all sequences of length 4 made of H and T, with each of the 16 sequences equally likely. What is the probability of getting exactly 2 heads?

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