Practice Test 8 - 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 jar contains only water and sugar. The mixture is $20\%$ sugar by volume. If the jar contains $300$ milliliters of mixture, how many milliliters of sugar does it contain?
2. Points $C(2,1)$ and $D(-1,5)$ lie in the coordinate plane. What is the distance between $C$ and $D$?
3. Which of the following expressions is equivalent to $\sqrt[3]{a^2}\,\sqrt[3]{a}$ for real $a$?
4. If $a$ and $b$ are positive integers and $\text{lcm}(a,b)=60$ and $\gcd(a,b)=6$, what is the value of $ab$?
5. A bag contains only red and blue marbles. The probability of selecting a red marble at random is $\frac{2}{5}$. 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 ratio of red marbles to blue marbles Column B: $\frac{2}{3}$
6. A recipe uses $\frac{3}{4}$ cup of sugar. If the amount of sugar is increased by $25\%$, what is the new amount of sugar, in cups?
7. Points $Y(0,0)$ and $Z(6,8)$ lie in the coordinate plane. Which of the following equals the distance from $Y$ to $Z$?
8. In triangle $ABC$, $AB=AC$ and $\angle A = 40^\circ$. 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: $\angle B$ Column B: $70^\circ$
9. In a group of 60 students, let set $M$ be the students who study Math and set $P$ be the students who study Physics. If $|M|=35$, $|P|=28$, and $|M\cap P|=15$, how many students study neither Math nor Physics?
10. Which of the following points lies on the line given by $4x-2y=8$?
11. Which of the following is equivalent to $\dfrac{2}{3}(9-3w)$?
12. A laptop originally cost $800. The price was first decreased by 25% from the original price, and then the reduced price was increased by 25%. What is the final price of the laptop?
13. Which inequality is NOT equivalent to $x < -2$?
14. If $x$ and $y$ are real numbers such that $|x-2|=|y-2|$ and $x<2<y$, which of the following statements is true?
15. What is the value of $k^2-2k+1$ when $k=-3$?
16. A taxi charges a flat fee of $5 plus $2 per mile. If the total fare for a ride was $29, how many miles was the ride?
17. A commuter recorded travel time and distance for five trips. Table (Trips) Columns: Trip; Distance (miles); Time (minutes) Rows: - 1: 12; 24 - 2: 15; 30 - 3: 10; 20 - 4: 18; 45 - 5: 20; 40 Which trip had the lowest average speed, in miles per hour?
18. Points $M(0,-3)$ and $N(6,-3)$ lie in the coordinate plane. What is the distance between $M$ and $N$?
19. Which of the following statements about the quadratic function $g(x)=-2x^2+8x+3$ is true?
20. In a group of 80 students, 55 study French, 35 study Spanish, and 20 study both French and Spanish. How many students study neither French nor Spanish?

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