Practice Test 5 - GRE Quantitative Reasoning

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

Start practice test

1. Which point is below the line $y=2x-1$ and above the x-axis?
2. Lines $l$ and $m$ are parallel. A transversal intersects $l$ and $m$. One of the interior angles on the same side of the transversal measures $104^\circ$. What is the measure of the other interior angle on the same side of the transversal?
3. A fair coin is flipped 3 times. The sample space consists of all length-3 sequences of H (heads) and T (tails), all equally likely. What is the probability of getting at least one head?
4. Line $\ell$ passes through the points $(2,5)$ and $(6,-3)$. What is the slope of line $\ell$?
5. If $b$ is a real number and $b^{\frac{1}{3}}=-2$, what is the value of $b$?
6. In a town of 150 households, let set $C$ be households that own a cat and set $O$ be households that own a dog. If 40 households own neither a cat nor a dog, and $|C\cap O|=25$, and $|C|=70$, what is the number of households that own a dog?
7. Lines $y=2x-5$ and $y=-x+1$ intersect. In which quadrant is the intersection?
8. Which of the following is equivalent to $\dfrac{x^2-4x}{x}$ for $x\neq 0$?
9. A dataset has values $\{5, 5, 5, 5, 25\}$. Another dataset has values $\{9, 9, 9, 9, 9\}$. Which of the following statements is true?
10. In a class of 80 students, let set $F$ be those who speak French and set $S$ be those who speak Spanish. If $|F|=42$, $|S|=38$, and $|F\cup S|=65$, what is the number of students who speak both French and Spanish?
11. A machine produces $180$ bolts in $12$ minutes at a constant rate. At the same rate, how many bolts does it produce in $50$ minutes?
12. A company is assigning 4 distinct tasks to 4 distinct employees. Employee $X$ cannot be assigned to Task 1 or Task 2. All other assignments are allowed. How many valid assignments are possible?
13. Real numbers $x$ and $y$ satisfy $|x|=|y|$ and $x<y$. Which of the following statements is true?
14. A committee of 4 people is to be selected from a group of 9 people. If two particular people, Alice and Bob, refuse to serve on the committee together, how many different committees can be formed?
15. The mean of 4 numbers is 10. If one of the numbers is 2, what is the mean of the remaining 3 numbers?
16. If $x\ne0,-1$, simplify $\frac{x^{-2}+x^{-1}}{x^{-1}+1}$.
17. At a dinner party, 4 men and 4 women are to be seated around a circular table. How many different seating arrangements are possible if no two women are to sit next to each other?
18. A bottle contains 500 milliliters of water. After some water is poured out, the amount of water decreases by 30% from the original amount. How many milliliters of water remain?
19. Which expression is equivalent to $(x+3)^2-(x-1)^2$?
20. In the $xy$-plane, the line $y=-3x+6$ intersects the $x$-axis at point $P$. What is the $x$-coordinate of $P$?

Practice tests