Practice Test 7 - 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 the coordinate plane, point $A$ is at $(2,5)$ and point $B$ is at $(8,1)$. What is the distance between $A$ and $B$?
2. In triangle $ABC$, $AB=10$ and $AC=10$. Point $D$ is on $BC$ such that $AD$ is perpendicular to $BC$. If $BC=12$, what is the length of $AD$?
3. If $x$ is a real number such that $x\ne 0$ and $x^{-1/2}=2$, what is the value of $x$?
4. For real number $t$, $0<t<1$. 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: $t$ Column B: $t^2$
5. A car rental company charges a flat fee of $F$ dollars plus $0.25$ dollars per mile driven. If a customer drove $m$ miles and was charged a total of $37.50$ dollars, which of the following equations represents this situation?
6. A map uses a scale of $1$ inch to represent $25$ miles. Two cities are $3.6$ inches apart on the map. What is the actual distance between the cities, in miles?
7. A jar contains 4 white balls and 6 black balls. Two balls are drawn without replacement. What is the probability that both balls drawn are white?
8. Which of the following is equivalent to $\dfrac{x}{2}-\dfrac{3x}{4}$?
9. Which of the following is closest to $0.18$ expressed as a fraction in simplest form?
10. A square and a rectangle have the same perimeter. The square has side length 7 cm. The rectangle has length 10 cm. What is the width of the rectangle, in centimeters?
11. Let $f(x)=x+4$ and $g(x)=\dfrac{x}{2}$. What is the value of $f(g(10))$?
12. Which of the following is equivalent to $4x-(2-3x)$?
13. A right circular cylinder has radius 3 centimeters and height 10 centimeters. What is the volume of the cylinder, in cubic centimeters? (Use $\pi$ in your answer.)
14. A data set consists of 5 numbers with mean $10$. Four of the numbers are $8, 9, 10,$ and $13$. 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: The median of the data set Column B: $10$
15. How many different 8-character strings can be formed using only the letters A, B, and C if the string contains at least one A and at least one B?
16. A right circular cylinder has radius $3$ inches and height $10$ inches. What is the volume of the cylinder, in cubic inches?
17. A tank contains 90 liters of fuel. After refueling, the amount of fuel increases by 20% from the original amount. Then, 15 liters are used. How many liters of fuel remain?
18. A car was listed at $18,000. The dealer offered a discount of 15% from the listed price. What is the sale price of the car?
19. Line $p$ has equation $y=-2x+9$. Line $q$ is obtained by shifting the graph of line $p$ up 4 units. Which of the following is an equation of line $q$?
20. Line $s$ passes through $(2,-1)$ and $(2,5)$. Which of the following best describes the graph of line $s$?

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