Practice Test 1 - SSAT Upper Level Quantitative

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

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1. Quadrilateral $MNPQ$ is inscribed in a circle. If angle $M = 3y + 15°$, angle $N = 2y + 25°$, and angle $P = 4y - 10°$, what is the measure of angle $Q$?
2. If $x = 0.4\overline{5}$ and $y = \frac{41}{90}$, which statement about $x$ and $y$ is true?
3. A bookstore offers a membership plan where customers pay an annual fee of $25 and then receive a 15% discount on all purchases. If a member buys books worth $d$ dollars (before discount) during the year, which expression represents the total amount the member pays for the year including the membership fee?
4. A student claims that $\frac{3}{7} > 0.42$ because $\frac{3}{7} = 0.428571...$ and $0.428571 > 0.42$. What is wrong with this reasoning?
5. Triangle $ABC$ has an exterior angle at vertex $B$ that measures $142°$. If angle $A$ is $28°$ more than angle $C$, what is the measure of angle $A$?
6. If $n$ is the smallest positive integer such that $2n + 1$ is composite, what is the value of $2n + 1$?
7. A recipe calls for $20\%$ more flour than sugar. If the recipe uses $360$ grams of flour, and the baker wants to reduce the sugar by $15\%$, how many grams of sugar will be used?
8. If a and b are different primes and $a + b = 21$, what is $ab$?
9. A regular pentagon has a perimeter of 45 cm. If the apothem (distance from center to the middle of any side) is 6.2 cm, what is the area?
10. A fair coin is flipped repeatedly until either 3 consecutive heads or 3 consecutive tails appear. What is the probability that the sequence ends with 3 consecutive heads?
11. Company A's profits increased by $25\%$ while Company B's profits decreased by $20\%$. If both companies now have the same profit of $150,000, what was the difference between their original profits?
12. A school cafeteria sells lunch combinations where students choose one item from each category. There are $s$ sandwich options, $d$ drink options, and $c$ chips options. If the cafeteria removes 2 sandwich options but adds 3 new drink options, which expression represents the new total number of possible lunch combinations?
13. A positive integer $k$ has the property that both $k$ and $k + 2$ are prime. If $k > 3$, how many possible values of $k$ are there less than 50?
14. Two events A and B are such that P(A) = 0.6, P(B) = 0.4, and P(A ∪ B) = 0.8. If event C is independent of the event A ∩ B, and P(C) = 0.3, what is P((A ∩ B) ∪ C)?
15. What is the value of $2 + 3 \cdot 4^2 - 5 \cdot (6 - 4) \div 2$?
16. A movie theater has rows of seats where the first row has $f$ seats, and each subsequent row has 2 more seats than the previous row. Which expression represents the total number of seats in the first $n$ rows?
17. Which of the following lists these interest rates in ascending order: $12\%$, $0.09$, $\frac{1}{10}$, $8\%$, $0.11$?
18. If $p$ is prime, how many positive factors does $p^2$ have?
19. A assembly line produces 240 units per hour. After 2 hours of operation, a quality control check takes 30 minutes, during which production stops. The line then resumes at 90% efficiency. If the total production target is 1560 units, how many total hours (including the quality control time) are needed?
20. A sequence of rational numbers is defined by the pattern: $-\frac{3}{2}, -\frac{5}{4}, -\frac{7}{8}, -\frac{9}{16}, ...$ If this pattern continues, which of the following represents the correct ordering of the 6th, 7th, and 8th terms from least to greatest?

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