Practice Test 4 - HSPT Math

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

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1. If $\frac{x}{3} + \frac{x}{4} = \frac{x}{2} - 5$, what is the value of $x$?
2. A circular pizza with a 14-inch diameter is cut into 8 equal slices. What is the perimeter of one slice?
3. A photo is enlarged so that the ratio of the new area to the original area is $25:4$. If the original photo was $6$ inches wide, what is the width of the enlarged photo, and what is the ratio of the new perimeter to the original perimeter?
4. A bag has 3 red, 2 yellow, and 5 purple beads. One bead is drawn, replaced, and a second bead drawn. What is the probability both beads are purple?
5. A box contains 5 red, 4 blue, and 3 green marbles. If two marbles are drawn from the box at random without replacement, what is the probability that they are both of the same color?
6. Tickets to a concert cost $8 each plus a one-time $4 service fee. If Shawn has at most $60 to spend, which inequality gives the possible number of tickets, $n$, he can buy, and what is the greatest whole number of tickets he can afford?
7. If $p$ is the least common multiple of $24$ and $30$, and $q$ is their greatest common factor, what is $\dfrac{p}{q}$?
8. A rectangular box measures 10 cm by 6 cm by 4 cm. What is the volume of the box in cubic centimeters?
9. A recipe for $2 \frac{1}{2}$ dozen muffins requires $1 \frac{7}{8}$ cups of flour. How many cups of flour are needed to make exactly one dozen muffins?
10. Triangle FGH is a right triangle with the right angle at G. The length of leg FG is 9 and the length of leg GH is 12. An altitude GK is drawn from vertex G to the hypotenuse FH. What is the length of this altitude GK?
11. If $2|x - 3| + 5 = 17$, what is the sum of all possible values of $x$?
12. A survey of 200 students found that 120 students like pizza, 80 students like burgers, and 50 students like both pizza and burgers. If a student is randomly selected, what is the probability that the student likes pizza given that they like burgers?
13. Refer to the figure below. What is the total area of the L-shaped patio, in square meters?
14. In a right triangle, the legs measure $9\text{ cm}$ and $12\text{ cm}$. What is the length of the hypotenuse?
15. Which of the following is the prime factorization of $198$?
16. A square pyramid has a base whose sides are 9 yards long and a height of 12 yards. What is the volume of the pyramid?
17. A rectangular field is 80 feet long and 60 feet wide. Sarah walks diagonally across the field from one corner to the opposite corner. How far does Sarah walk?
18. Which of the following sets of three lengths can not be the side lengths of a right triangle?
19. The set of numbers is $\{x, x+4, x-1, x+7, x+2\}$. If $x > 1$, what is the median of this set?
20. A bag contains 5 red marbles, 3 green marbles, and 2 yellow marbles. If three marbles are drawn without replacement, what is the probability that exactly two are red and one is green?

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