Practice Test 8 - GMAT Quantitative

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

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1. What is the largest integer $n$ such that $2^n$ divides $50!$?
2. Pipe X can fill a tank in 6 hours, and Pipe Y can fill the same tank in 9 hours. A drain can empty the full tank in 12 hours. If the two inlet pipes and the drain are all opened simultaneously when the tank is empty, approximately how many hours will it take to fill the tank completely?
3. A retailer raised the price of a jacket by 20 percent and later put the jacket on sale at a discount of 25 percent off the new price. By what percent did the final sale price differ from the jacket's original price?
4. Consider the equation $2^{2t}-5\cdot2^{t}+6=0$. What is the sum of all real solutions for $t$?
5. If $3 \leq 2x - 1 < 9$ and $x$ is an integer, how many possible values of $x$ satisfy the inequality?
6. For positive $x$, $\left(\dfrac{1}{x^{3}}\right)^{\,1/2}=x^{k}$. What is $k$?
7. A pharmaceutical company tests a drug's effectiveness by measuring improvement scores. The control group (n=50) has a mean improvement of 20 points with a standard deviation of 8 points. The treatment group (n=50) has a mean improvement of 28 points with a standard deviation of 12 points. A researcher claims that the treatment is more effective but also more variable in its effects. Which aspect of this claim requires the most careful evaluation?
8. If $\frac{1}{x-2} + \frac{1}{x+2} = \frac{2x}{x^2-4}$, then which statement about $x$ is correct?
9. Four cards are drawn at random without replacement from a standard deck. What is the probability that exactly two of the four cards are aces?
10. The inequality $(x-4)(x+1)(2-x)>0$ is equivalent to which of the following ranges for $x$?
11. Refer to the tree diagram. What is the expected value of the investment's one-year return, in percent?
12. A quality control manager measures the weights of products from two assembly lines. Line X produces items with weights that have a standard deviation of 2.4 grams, while Line Y produces items with weights that have a standard deviation of 1.8 grams. If the manager combines equal numbers of items from both lines into a single dataset, which statement best describes the standard deviation of the combined dataset?
13. Refer to the box-and-whisker plots below. If both data sets have the same mean, which additional statement must also be true?
14. A rectangular garden has an area of 48 square meters. The length of the garden is 2 meters greater than its width. What is the perimeter of the garden, in meters?
15. If $k$ is a positive integer and the remainder when $k$ is divided by 6 is 4, which of the following is the remainder when $k^2$ is divided by 6?
16. A food stand sells hot dogs for $3 each and sodas for $2 each. Yesterday the stand sold a total of 50 items and collected $128 in revenue. How many hot dogs were sold?
17. For non-zero $a$, the expression $\dfrac{a^{3}\,a^{-5}}{a^{-4}}$ can be written in the form $a^{k}$. What is the value of $k$?
18. If $\sqrt[3]{2^x \cdot 4^y \cdot 8^z} = 16$, what is the value of $x + 2y + 3z$?
19. For what value of $k$ does the system $kx + 3y = 6$ and $4x + 6y = 12$ have infinitely many solutions?
20. Simplify $\dfrac{x^{2}-1}{x-1}-\dfrac{x^{2}-1}{x+1}$ for all $x\neq\pm1.$

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