Practice Test 6 - 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 rectangle has perimeter $P$ and area $A$. The side lengths are positive real numbers. 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. Given: $P=20$ Column A: The greatest possible value of $A$ Column B: $25$
2. A dataset has 5 values with mean 18 and median 20. Which of the following statements must be true?
3. If $x^{3/2}=27$, what is $x$?
4. Let $a$ and $b$ be real numbers such that $a<b$ and $|a|=|b|$. Which of the following statements is true?
5. In the coordinate plane, points $A(0,0)$, $B(4,0)$, and $C(1,3)$ are given. Which distance is greatest?​
6. A store has 200 jackets in stock. After a sale, the stock decreases by $15\%$, and then the store receives a new shipment that increases the remaining stock by $20\%$. What is the final number of jackets in stock?
7. In a town of 500 residents, let set $H$ be those who have a home garden and set $P$ be those who participate in a composting program. If $|H|=210$, $|P|=160$, and $|H\cap P|=70$, what is the number of residents who have a home garden but do not participate in the composting program?
8. A function $f$ is defined by $f(x)=3x-5$. What is the value of $f(4)$?
9. Integers $a$ and $b$ satisfy that $a$ is a multiple of $4$ and $b$ is a multiple of $6$. Which of the following statements must be true?
10. A bag contains $6$ red marbles and $4$ blue marbles. One marble is selected at random from the bag. What is the probability of selecting a blue marble?
11. A store increased the price of an item from $30 to $36. The store then advertised that the item was discounted by $10\%$ from the new price of $36. What is the final advertised price?
12. Which of the following is equivalent to $\dfrac{\sqrt{x^6}}{x^2}$ for real $x\ne 0$?
13. A store sells 4 types of fruit: apples, bananas, oranges, and pears. A customer buys exactly 6 pieces of fruit, and at least 1 piece of each type. How many different purchases are possible (where order does not matter)?
14. A gym had 300 members. After a marketing campaign, membership increased by $20\%$ (based on the original 300). Later, 60 members canceled their memberships. What is the percent change in membership from the original 300 to the final membership?
15. A function $s$ is defined by $s(x)=\dfrac{5x}{2}-4$. What is the value of $s(6)$?
16. If $m$ and $n$ are positive integers such that $2^m=8^n$, what is the value of $\dfrac{m}{n}$?
17. A recipe uses $0.6$ cup of sugar. If the amount of sugar is reduced by $\frac{1}{6}$, how many cups of sugar are used in the new recipe?
18. For real number $x$, $x\ne 0$. 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: $\dfrac{x^2}{x}$ Column B: $x$
19. How many 4-digit positive integers can be formed using the digits 0, 1, 2, 3, and 4 if repetition of digits is not allowed and the integer must be even?
20. If $x$ is a real number and $\sqrt{x}=\dfrac{1}{3}$, what is the value of $x^{3/2}$?

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