Practice Test 10 - GRE Quantitative Reasoning

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

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1. Let $k$ be an integer. 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 remainder when $7k+5$ is divided by $7$ Column B: $5$
2. If $k$ is a real number and $k^4=16$, what is the value of $\sqrt{k^4}$?
3. A school had 800 students. Enrollment increased by 5% one year and then increased by 10% the next year, each time relative to the previous year's enrollment. What was the enrollment after the two increases?
4. Triangle $ABC$ is equilateral. Point $D$ lies on segment $BC$. What is the measure of $\angle ADB$ if $AD$ is perpendicular to $BC$?
5. The line $y=x-4$ is shifted upward by $6$ units to form a new line. What is the $y$-intercept of the new line?
6. A circle's radius is increased by 50%, from $r$ to $1.5r$. By what factor does the area of the circle increase?
7. In the coordinate plane, point $G$ is at $(1,-2)$ and point $H$ is at $(7,1)$. What is the distance between $G$ and $H$?
8. Which of the following is true for all real numbers $x$ such that the expressions are defined? $\sqrt{x^2} = \ ?$​
9. Two functions are defined by $f(x)=x-5$ and $g(x)=\dfrac{1}{x}$. What is the value of $g(f(2))$?
10. A store had 200 jackets in stock. After a sale, the number of jackets in stock decreased by 15% from the original stock. What is the new number of jackets in stock?
11. A line has equation $2x+5y=10$. What is the slope of the line?
12. For real numbers $x$ and $y$, $x-y=5$. 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: $x^2-y^2$ Column B: $5$
13. An investor tracked the closing price of a stock for five consecutive days. Table (Closing Price) Columns: Day; Closing price (USD) Rows: - 1: 48 - 2: 51 - 3: 50 - 4: 54 - 5: 57 Which of the following is closest to the percent increase in closing price from Day 1 to Day 5?
14. A jar contains 5 red balls and 7 blue balls. Two balls are drawn one after the other with replacement. What is the probability that both balls drawn are red?
15. A tank is $\frac{3}{5}$ full. After $20\%$ of the water currently in the tank is drained out, what fraction of the tank is full?
16. Integer $t$ is such that $t^2$ is divisible by $12$. Which of the following must be true?
17. A product's price increased from $40 to $50. The percent increase is based on the original price of $40. By what percent did the price increase?
18. A dataset of 8 values has mean 14. The largest value, 30, is removed, leaving 7 values. What is the mean of the remaining 7 values?
19. A value is increased by 25%, then decreased by 25%. The result is 90. What was the original value?
20. Line L has x-intercept -3 and y-intercept 5. What is the slope of a line perpendicular to L?

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