Multiple Choice

1. A sequence starts with $5, 12, 19, 26, \dots$. Following the strategy of 'Identifying and Extending Patterns', what is the 15th term in this arithmetic sequence?

   $96$

   $100$

   $103$

   $105$

2. A stack of blocks follows a sequence: 3, 7, 11, 15, ... If the pattern continues, how many blocks will be in the 10th stack?

   $37$

   $40$

   $35$

   $39$

3. A theatre has seating arranged such that the first row has 1 seat, the second row has 3 seats, the third row has 6 seats, and the fourth row has 10 seats. This is an example of a non-standard sequence (Triangular Numbers). How many seats are in the 7th row?

   $36$

   $28$

   $21$

   $24$

4. The number of dots needed to build a specific type of geometric shape follows the sequence $2, 6, 12, 20, 30, \dots$. What is the 7th term in this sequence?

   $48$

   $56$

   $50$

   $54$

5. An arithmetic sequence has a first term ($a$) of 10 and a common difference ($d$) of 6. Using the formula $T_n = a + (n-1)d$, which term number ($n$) has a value of 112?

   $18$

   $16$

   $17$

   $19$

6. A decreasing sequence is defined by $T_n = 50 - 3n$. What is the value of the 12th term?

   $11$

   $12$

   $14$

   $15$

7. The pattern for the number of square tiles needed to surround a pond is $4, 8, 12, 16, \dots$. If $N$ represents the $N$-th diagram, which formula correctly calculates the number of tiles, $T_n$?

   $T_n = 4N$

   $T_n = 2N + 2$

   $T_n = N + 4$

   $T_n = N^2 + 3N$

8. A specific sequence is given by the rule $T_n = n^2 - 1$. What is the sum of the first four terms?

   $20$

   $27$

   $26$

   $28$

9. The Fibonacci sequence starts $1, 1, 2, 3, 5, 8, \dots$ (where each term is the sum of the two preceding terms). What is the 10th term of this sequence?

   $55$

   $45$

   $68$

   $50$

10. The number of diagonals that can be drawn from one vertex of an $n$-sided polygon forms a pattern: $0, 1, 2, 3, \dots$ (starting with $n=3$). How many diagonals can be drawn from one vertex of a 12-sided polygon?

    $10$

    $11$

    $9$

11. A library fine increases daily. The fine is $\$0.50$ on day 1, $\$1.25$ on day 2, $\$2.00$ on day 3, and so on. What is the fine on day 8?

    $\\$6.25$

    $\\$6.00$

    $\\$5.50$

    $\\$5.75$

12. A taxi fare starts at a base rate of $\$4.50$ and increases by $\$1.80$ for every kilometre travelled ($K$). If $C$ is the total cost, what is the cost of a 12 km journey, using the formula $C = 4.50 + 1.80K$?

    $\$26.10$

    $\$27.00$

    $\$25.50$

13. A sequence is defined by alternating operations: starting at 10, the rule is 'add 5, then multiply by 2'. Term 1 is 10. Term 2 is $10+5=15$. Term 3 is $15 \times 2 = 30$. What is Term 6?

    $140$

    $75$

    $150$

    $135$

14. What is the missing number in the sequence: $1, 4, 9, \_\_\_, 25, 36$?

    $18$

    $15$

    $16$

    $17$

15. A gym membership costs $\$40$ up front, plus $\$15$ per week. If $W$ is the number of weeks, what is the total cost after 20 weeks?

    $\$300$

    $\$340$

    $\$360$

16. A number is squared, then 7 is added to the result. This new value is multiplied by 4, and the final result is $92$. Using the 'Working Backwards' strategy, what was the original number?

    $4$

    $7$

    $3$

    $6$

17. Liam spent half of his allowance on books. He then bought lunch for $\\$8$. He finally put the remaining $\$12$ into his savings. How much was his original allowance?

    $\$40$

    $\$42$

    $\$36$

    $\$38$

18. A beaker of water was filled. One-third of the water evaporated overnight. In the morning, 50 mL was added. If the final volume is 150 mL, what was the original volume?

    $180$ mL

    $150$ mL

    $200$ mL

19. Sarah received a number. She divided it by 4, subtracted 2.5, and then multiplied the result by 10. If the final answer was 75, what was the starting number?

    $45$

    $40$

    $50$

20. A baker sold 3 dozen cookies on Tuesday. On Wednesday, she doubled the remaining stock. If she had 70 cookies left at the end of Wednesday, how many cookies did she start with on Tuesday morning?

    $71$

    $142$

    $106$

21. I thought of a number. I multiplied it by itself, then divided by 2, and then subtracted 4. The result was 14. What number did I think of?

    $16$

    $4$

    $6$

    $8$

22. A bus journey took 4 hours and 15 minutes. This included a 30-minute stop for lunch and 5 minutes stuck in traffic. If the bus arrived at 14:00 (2:00 PM), what time did the journey originally start?

    09:30

    09:10

    09:45

23. A number is subject to three operations: 1. Divide by 6. 2. Add 11. 3. Multiply by 2. If the final result is 46, what was the original number?

    $72$

    $70$

    $75$

    $84$

24. Marcus collected stamps. He gave away 20 stamps, and then gave half of the remaining stamps to his sister. If he was left with 50 stamps, how many did he start with?

    $130$

    $110$

    $120$

25. In a competition, a player's final score of 120 resulted from multiplying their initial score by 5, then subtracting 30, and finally dividing by 3. What was the player's initial score?

    $78$

    $27$

    $15$

    $30$

26. Find the smallest positive number that satisfies the following conditions: When divided by 5, the remainder is 1. When divided by 6, the remainder is 2.

    $28$

    $26$

    $40$

27. A 3-digit number has the following properties: The hundreds digit is half the tens digit. The ones digit is 3 less than the tens digit. Find the smallest possible number greater than 100.

    $249$

    $129$

    $241$

28. I am thinking of a number between 30 and 50. When I divide it by 7, the remainder is 2. When I divide it by 3, the remainder is 1. What is the number?

    $40$

    $44$

    $37$

29. A 4-digit number is divisible by 9. The digits are $1, 3, 5$, and $X$ (in some order). Applying 'Logical Deduction and Constraints', find the value of the missing digit $X$ (where $X \neq 0$).

    $9$

    $6$

    $8$

    $0$

30. Three positive integers have a product of 18. If their sum is 10, what is the largest of the three numbers?

    $10$

    $9$

    $8$

    $6$

31. A group of 40 students was surveyed. 25 students play soccer, and 18 students play basketball. If 5 students play neither sport, how many students play both soccer and basketball?

    $5$

    $10$

    $8$

32. The weight of 3 identical apples and 1 banana is 450 grams. The weight of 1 apple and 1 banana is 200 grams. Using logical deduction, what is the weight of one banana?

    $75$ grams

    $100$ grams

    $50$ grams

33. I am an odd number greater than 20 but less than 35. I am a prime number. The sum of my digits is 5. What number am I?

    $31$

    $29$

    $23$

34. A farmer counts the number of sheep he owns. When he groups them in 4s, he has a remainder of 3. When he groups them in 5s, he has a remainder of 4. What is the smallest possible number of sheep the farmer could have?

    $19$

    $14$

    $21$

35. The perimeter of a rectangle is 30 cm. If the area of the rectangle must be greater than $50 \text{ cm}^2$ but less than $55 \text{ cm}^2$, and the sides must be integers, what is the length of the shorter side?

    $6$ cm

    $7$ cm

    $4$ cm

    $5$ cm

36. Two numbers, $A$ and $B$, satisfy the constraints $A > 10$ and $B < 5$. If $A+B=18$, and both $A$ and $B$ are whole numbers, what is the largest possible value for $A$?

    $14$

    $18$

    $15$

37. Three different digits are used to form a 3-digit number. If the number is even and the product of the digits is 12, what is the largest possible number that can be formed?

    $612$

    $621$

    $341$

38. If today is Saturday, what day of the week will it be 80 days from now? (Strategy: Pattern/Cyclical deduction)

    Monday

    Thursday

    Wednesday

    Tuesday

39. A student has nickels (5 cents) and dimes (10 cents). They have 10 coins in total, summing up to 75 cents. How many dimes does the student have?

    $6$

    $4$

    $5$

40. Alice, Ben, and Chloe are lined up. Ben is not last. Chloe is standing immediately behind Alice. Applying logical constraints, what must be the order from first to last?

    Chloe, Alice, Ben

    Alice, Chloe, Ben

    Ben, Chloe, Alice

    Ben, Alice, Chloe

41. A sequence starts with the terms $3, 10, 17, 24, \dots$. Following the arithmetic progression formula $T_n = a + (n-1)d$, which term number ($n$) in this sequence has the value $325$?

    47th

    50th

    48th

    45th

42. A delivery service charges a fixed base fee of $\$12.50$ plus $\$0.85$ for every kilometre travelled. If $C$ is the total cost and $K$ is the distance in kilometres, calculate the total cost for a delivery of $35$ kilometres.

    $\$40.75$

    $\$47.50$

    $\$42.25$

    $\$37.85$

43. A special numbering system yields the sequence $2, 5, 10, 17, 26, \dots$. This sequence follows a rule where the difference between consecutive terms increases by 2 each time. What is the 8th term in this sequence?

    70

    63

    55

    65

44. A large stack of spheres is built such that the top layer has 1 sphere, the next has 3, the third has 6, and the fourth has 10, following the pattern of Triangular Numbers. How many spheres are in the bottom layer if the stack has $12$ layers in total?

    91

    66

    78

    72

45. A biological experiment starts with a culture of $10 \, \text{cm}^2$ of mold. The mold doubles its coverage area every $5$ hours. What will the total coverage area be after $25$ hours?

    $250 \, \text{cm}^2$

    $160 \, \text{cm}^2$

    $320 \, \text{cm}^2$

    $300 \, \text{cm}^2$

46. A sequence is defined such that the first term is $3$ and the second term is $4$. Every term after that is the sum of the two preceding terms. What is the 7th term in the sequence?

    51

    42

    47

    36

47. A series of square tables are pushed together to form a long rectangular table. One square table seats 4 people. Two tables pushed together seat 6 people. Three tables pushed together seat 8 people. How many people can be seated if $15$ square tables are pushed end-to-end?

    32

    34

    38

    36

48. Alice chose a number. She added $18$, divided the result by $5$, and then multiplied that result by $4$. Finally, she subtracted $10$ to get a final answer of $46$. What was the number Alice originally chose?

    52

    48

    62

    58

49. A farmer sold $\frac{1}{3}$ of his sheep on Monday. On Tuesday, he bought $12$ new sheep. On Wednesday, he sold exactly half of the sheep he then owned. If he ended the week with $40$ sheep, how many sheep did he start with?

    108

    96

    112

    102

50. A computer was marked down by $20\%$ in January. In February, the discounted price was then increased by $10\%$. If the final price in February was $\\$1,056$, what was the original price in December?

    $\\$1,250$

    $\\$1,200$

    $\\$1,180$

    $\\$1,161.60$

51. To save up for a concert, Liam started with an initial deposit. After $4$ weeks, he had tripled his initial deposit through earnings. In the 5th week, he withdrew $\$45$. If he was left with $\$150$, how much was his initial deposit?

    $\$65$

    $\$75$

    $\$60$

    $\$55$

52. A scientist measures the population of bacteria every hour. The population triples and then $15$ bacteria are removed immediately afterward. If the population measured at 4:00 PM was $180$, and the last measurement was taken at 3:00 PM, what was the population measured at 3:00 PM?

    65

    55

    60

    75

53. Find the smallest positive integer $N$ such that when $N$ is divided by $5$, the remainder is $3$, and when $N$ is divided by $6$, the remainder is $4$.

    18

    48

    28

    58

54. A four-digit number $ABCD$ (where $A, B, C, D$ are single digits) has the following properties: $A$ is one-third of $C$. $B$ is twice $A$. $D$ is the sum of $B$ and $C$. If $A$ is not $0$, what is the digit $D$?

    7

    6

    8

    5

55. Three athletes run laps on a track. Athlete A completes a lap in $30$ seconds, B in $40$ seconds, and C in $50$ seconds. If they all start at the same line at the same time, how many seconds will pass before all three athletes cross the starting line together again?

    300

    400

    1200

    600

56. Four friends went fishing. The average number of fish caught by the friends was $7.5$. No one caught the same number of fish. The most any one person caught was $12$. What is the minimum number of fish any one friend could have caught?

    2

    3

    0

    1

57. A farmer stores $150$ eggs. He knows that when he divides the total number of eggs into groups of $7$, there is a remainder of $3$. If he divides the eggs into groups of $11$, there is a remainder of $7$. If he divides the eggs into groups of $5$, what is the remainder?

    3

    4

    0

    2

58. How many positive integers less than $100$ contain the digit $7$? (This includes numbers like $7, 17$, and $70$.)

    9

    18

    19

    20

59. A rectangle has an area of $144 \, \text{cm}^2$. The length and width are both integers. If the ratio of the length to the width is $4:1$, what is the perimeter of the rectangle?

    $48 \, \text{cm}$

    $60 \, \text{cm}$

    $54 \, \text{cm}$

    $72 \, \text{cm}$

60. A total of $35$ animals are in a barnyard. Some are chickens (2 legs) and some are goats (4 legs). If there is a total of $94$ legs in the barnyard, how many goats are there?

    10

    18

    15

    12