Practice Test 3 - SSAT Middle Level Quantitative

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

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1. A fitness trainer recorded the number of push-ups completed by 8 clients: 25, 32, 28, 35, 30, 26, 33, and 29. The trainer wants to compare this group's average to the gym's overall average of 31 push-ups. By how much does this group's average differ from the gym average?
2. If $\frac{k + 6}{2} = 9$, what is the value of $k$?
3. A road trip is $160$ km; using $1$ mi $=1.6$ km, what is it in mi?
4. An isosceles triangle has two sides of length 13 inches each and a perimeter of 35 inches. What is the length of the third side?
5. A water tank is being filled at a rate of 8 gallons per minute. If the tank already contains 45 gallons and has a total capacity of 165 gallons, how many minutes will it take to fill the tank completely?
6. A spherical water balloon is used in a science demo about volume. The balloon has a radius of 7 cm when fully inflated. The teacher wants the volume to discuss how much water it can hold. Use $V=\frac{4}{3}\pi r^3$ for a sphere. Give the result in cubic centimeters. Based on the dimensions, what is the volume of the sphere?
7. Josh earns $d$ dollars per day working at a bookstore. On weekdays, he works full days, but on Saturday he only works half a day. If he doesn't work on Sunday, which expression represents his total earnings for one week?
8. What is the result of the following expression when evaluated correctly? $\left(9-2\right)\times1.5-4$
9. The ratio of Sarah's age to her mother's age is $3:8$. If the sum of their ages is $44$ years, what is Sarah's age?
10. If $6^a = 36$ and $6^b = 216$, what is $6^{a+b}$?
11. Prime numbers have exactly two factors, 1 and itself; composite numbers have more than two. Using 2, 3, 4, 5, 6, and 7 as examples, decide: Is 29 prime or composite?
12. A rectangular aquarium has dimensions of 12 inches by 8 inches by 10 inches. How many cubic inches of water are needed to fill the aquarium to exactly 75% of its capacity?
13. The scale on a blueprint shows that 0.25 inches represents 2 feet of actual length. If a room measures 3.5 inches on the blueprint, what is the actual length of the room in feet?
14. Prime numbers have exactly two factors; composite numbers have more than two. Examples: 2, 3, 5, 7 are prime; 4 and 6 are composite. What is the smallest prime number greater than 24?
15. At the mall, Keisha buys a $40 jacket and a $18 shirt. The jacket is $30\%$ off, and the tax is $9\%$ on the discounted subtotal. A hat costs $14 but she does not buy it, and the food court opens at 11. Which details are critical to finding the amount she pays?
16. Exchange rate is $1\ \text{USD}=0.9\ \text{EUR}$. Using $e=0.9u$, find euros for $u=\$70$.
17. Which of the following numbers has the most prime factors (counting repetitions)?
18. The least common multiple of two positive integers is 180, and their greatest common factor is 12. If one of the integers is 36, what is the other integer?
19. Seven comic books cost $49$; solve $7x = 49$.
20. If $x$ and $y$ are integers such that $x < -5$ and $y > 3$, which of the following must be true about $x + y$?

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