Practice Test 3 - GRE Quantitative Reasoning

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

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1. If $x$ is a real number and $x^2-5x+6=0$, which of the following is a possible value of $x$?
2. Integers $a$ and $b$ satisfy $a\mid b$ and $b\mid a$. Which of the following must be true?
3. Let $t$ be a real number such that $|t-4|\ge 3$. Which of the following values satisfies the inequality?
4. If $x>0$ and $\frac{\sqrt{x^3}}{x^2}=x^k$, what is $k$?
5. A class has 30 students. The ratio of juniors to seniors is $2:3$. 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 number of juniors in the class Column B: $12$
6. A circle has radius $r$, where $r>0$. 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: The circumference of the circle Column B: The perimeter of a square with side length $r$
7. A function $g$ is defined by $g(x)=x^2-2x$. What is the value of $g(-3)$?
8. Which of the following represents the complete factorization of $x^2-9x+14$ over the integers?
9. If $n$ is a positive integer and $n^2$ is divisible by 6, what is the greatest integer that must divide $n$?
10. A regular octagon has all sides equal and all interior angles equal. What is the measure, in degrees, of each interior angle of the octagon?
11. A circle has radius $7$ centimeters. What is the circumference of the circle, in centimeters?
12. The ratio of students who study French to students who study Spanish in a school is $7:9$. If $144$ students study Spanish, how many students study French?
13. A fair coin is flipped 3 times. The sample space consists of all sequences of length 3 made of H and T, with each of the 8 sequences equally likely. What is the probability of getting at least one head?
14. An investment account had a value of $10,000. It decreased by 10% in the first month (based on the starting value), and then increased by 10% in the second month (based on the value after the first month). What is the value of the account after the second month?
15. The height (in meters) of a ball $t$ seconds after it is thrown is given by $H(t)=-5t^2+20t+1$. At what time $t$ does the ball reach its maximum height?
16. Two lines intersect at point $O$. One of the angles formed is $38^\circ$. What is the measure of an angle adjacent to the $38^\circ$ angle?
17. A cyclist travels $18$ kilometers in $45$ minutes at a constant speed. What is the cyclist's speed, in kilometers per hour?
18. Integers $n$ and $k$ satisfy that $n$ is divisible by $4$ and $n+2k$ is odd. Which of the following must be true?
19. Which of the following is equal to $\left(\sqrt{50}\right)\left(\sqrt{2}\right)$?
20. A company's revenue was $500,000 last year. This year, revenue increased by 20% from last year's revenue and then decreased by 10% from the increased amount. What is the company's revenue this year?

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