Deck 1: The Art of Problem Solving

Question 1

Determine the most probable next term in the sequence.
5, 7, 9, 11, 13

A)14
B)17
C)18
D)15

Answer 1

D

Question 2

Decide whether the argument is an example of inductive or deductive reasoning.
His last four at bats were strikeouts. Therefore, the next will be a strikeout.

A)Deductive
B)Inductive

Answer 2

B

Question 3

Determine the most probable next term in the sequence.
8, 13, 20, 29, 40, 53

A)66
B)64
C)68
D)70

Answer 3

C

Question 4

Determine the most probable next term in the sequence.

Question 5

Use inductive reasoning to predict the next equation.
76 - 74 + 72 - 70 = 77 - 75 + 73 - 71 86 - 84 + 82 - 80 = 87 - 85 + 83 - 81

A)96 + 94 - 92 - 90 = 97 + 95 - 93 + 91
B)96 - 94 - 92 + 90 = 97 - 95 + 93 - 91
C)96 + 94 - 92 + 90 = 97 + 95 - 93 + 91
D)96 - 94 + 92 - 90 = 97 - 95 + 93 - 91

Question 6

Decide whether the argument is an example of inductive or deductive reasoning.
Practice makes perfect. I have practiced. Therefore, I'll be perfect.

A)Inductive
B)Deductive

Question 7

Question 8

Determine the most probable next term in the sequence.
6, -24, 96, -384, 1536

A)-2688
B)6144
C)-6144
D)2688

Question 9

Determine the most probable next term in the sequence.
2, 5, 4, 10, 8, 20

A)40
B)12
C)30
D)16

Question 10

Question 11

Determine the most probable next term in the sequence.
34, 28, 22, 16, 10

A)4
B)0
C)2
D)6

Question 12

Decide whether the argument is an example of inductive or deductive reasoning.
All U.S. Presidents have come from the original 48 states. Therefore, no U.S. President can be from Alaska.

A)Deductive
B)Inductive

Question 13

Decide whether the argument is an example of inductive or deductive reasoning.
Every coach knows his sport well. John Madden is a football coach. Therefore John Madden knows football well.

A)Deductive
B)Inductive

Question 14

Determine the most probable next term in the sequence.
0005, 0050, 0500, 5000, 5005

A)5006
B)5050
C)5500
D)5000

Question 15

Use inductive reasoning to predict the next equation.
10 × 12 = 11 × 13 - 23 12 × 14 = 13 × 15 - 27

A)14 × 16 = 17 × 27 - 31
B)14 × 16 = 15 × 17 + 29
C)14 × 16 = 15 × 17 - 31
D)14 × 16 = 15 × 17 - 29

Question 16

Decide whether the argument is an example of inductive or deductive reasoning.
5 + 31 = 36, 17 + 5 = 22, 17 + 37 = 54. Therefore, the sum of two prime numbers is even.

A)Inductive
B)Deductive

Question 17

Determine the most probable next term in the sequence.
486, 162, 54, 18, 6

Question 18

Decide whether the argument is an example of inductive or deductive reasoning.
Fresh fruit costs more in winter. This is January. Therefore these fresh strawberries will cost more.

A)Deductive
B)Inductive

Question 19

Determine the most probable next term in the sequence.

Question 20

Determine the most probable next term in the sequence.
1, 4, 1, 4, 4, 1, 4, 4, 4, 1, 4, 4, 4, 4, 1, 4, 4, 4, 4, 4

Question 21

Use the method of Gauss to find the sum.
4 + 8 + 12 + . . . + 500

A)31,500
B)31,250
C)3906.25
D)250,000

Question 22

Use the method of Gauss to find the sum.
1 + 2 + 3 + . . . + 375

A)35,156.25
B)141,376
C)70,312.5
D)70,500

Question 23

Use the method of Gauss to find the sum.
1 + 2 + 3 + . . . + 650

A)105,625
B)211,575
C)422,500
D)211,250

Question 24

Use the method of Gauss to find the sum.
2 + 4 + 6 + . . . + 400

A)161,604
B)40,200
C)40,000
D)10,000

Question 25

Find a pattern and use it to solve the problem.
Find the next term: 1, 1, 2, 3, 5, 8, 13

A)16
B)21
C)15
D)18

Question 26

Use inductive reasoning to predict the next equation.
37,037 × 3 = 111,111 37,037 × 6 = 222,222
37,037 × 9 = 333,333
37,037 × 12 = 444,444

A)37,037 × 15 = 555,555
B)37,037 × 18 = 666,666
C)111,111 × 15 = 1,666,665
D)37,037 × 13 = 481,481

Question 27

Use the method of Gauss to find the sum.
1 + 2 + 3 + . . . + 1000

A)500,500
B)500,000
C)250,000
D)1,002,001

Question 28

Find a pattern and use it to solve the problem.
Find the next term: T, F, S, E, T, T, F

A)S
B)F
C)T
D)E

Question 29

Use inductive reasoning to predict the next equation.
(4 × 1)x (2 × 1)= 8 (4 × 10)x (2 × 2)= 160
(4 × 100)x (2 × 3)= 2400

A)(4 × 1000)x (2 × 4)= 36,000
B)(4 × 1000)x (2 × 4)= 3200
C)(4 × 1000)x (2 × 4)= 28,000
D)(4 × 1000)x (2 × 4)= 32,000

Question 30

Use inductive reasoning to predict the next equation.
9 × 10 = 11 × 12 - (9 + 10 + 11 + 12) 10 × 11 = 12 × 13 - (10 + 11 + 12 + 13)

A)12 × 13 = 14 × 15 - (11 + 10 + 9 + 8)
B)12 × 13 = 14 × 15 - (12 + 13 + 14 + 15)
C)11 × 12 = 13 × 14 - (9 + 10 + 11 + 12 + 13 + 14)
D)11 × 12 = 13 × 14 - (11 + 12 + 13 + 14)

Question 31

Use inductive reasoning to predict the next equation.

Question 32

Use inductive reasoning to predict the next equation.

Question 33

Find a pattern and use it to solve the problem.
Find the next term: 5, 10, 15, 25

A)30
B)35
C)50
D)55

Question 34

How many triangles are in the next figure?

Question 35

Find a pattern and use it to solve the problem.
Find the next term: S, S, M, T, W

A)S
B)T
C)F
D)M

Question 36

Use inductive reasoning to predict the next equation.
(1 × 9)- 7 = 2 (21 × 9)- 7 = 182
(321 × 9)- 7 = 2882

A)(4321 × 9)- 7 = 3881
B)(4321 × 9)- 7 = 28,882
C)(432 × 9)- 7 = 38,882
D)(4321 × 9)- 7 = 38,882

Question 37

Find a pattern and use it to solve the problem.
Find the next term: 21, 4, 17, 6, 11, 8

A)0
B)19
C)3
D)7

Question 38

How many line segments are used in the next figure?

Question 39

Use inductive reasoning to predict the next equation.
9 × 9 = 81 99 × 99 = 9801
999 × 999 = 998,001

A)9999 × 9999 = 999,001
B)999 × 9999 = 99,980,001
C)9999 × 9999 = 1,000,001
D)9999 × 9999 = 99,980,001

Question 40

Find a pattern and use it to solve the problem.
Find the next term: 2, 3, 5, 7, 11, 13

A)17
B)16
C)19
D)15

Question 41

Determine if the sequence is an arithmetic sequence, a geometric sequence, or neither. If it is either arithmetic or
geometric, give the next term in the sequence.
10, 13, 16, 19, 22, . . .

A)neither
B)arithmetic; 25
C)geometric; 25

Question 42

Use the method of successive differences to determine the next term in the sequence.
4, 18, 90, 264, 605, 1199, . . .

A)2143
B)2132
C)2174
D)2153

Question 43

Determine what the next equation would be, and verify that it is indeed a true statement.
11 × 11 = 121 101 × 101 = 10,201

A)1001 × 1001 = 101,101
B)1001 × 101 = 1,002,001
C)1001 × 1001 = 100,200
D)1001 × 1001 = 1,002,001

Question 44

Determine if the sequence is an arithmetic sequence, a geometric sequence, or neither. If it is either arithmetic or
geometric, give the next term in the sequence.
224, 112, 56, 28, 14, . . .

A)neither
B)geometric; 7
C)arithmetic; 7

Question 45

Determine if the sequence is an arithmetic sequence, a geometric sequence, or neither. If it is either arithmetic or
geometric, give the next term in the sequence.
6, 12, 18, 30, 48, . . .

A)neither
B)geometric; 78
C)arithmetic; 78

Question 46

Draw the next figure in the pattern.

Question 47

Determine what the next equation would be, and verify that it is indeed a true statement.
40 - 9 = 31 400 - 89 = 311
4000 - 789 = 3211

A)400,000 - 6,789 = 33,211
B)40,000 - 6,789 = 393,211
C)4000 - 6,789 = 33,211
D)40,000 - 6,789 = 33,211

Question 48

Determine if the sequence is an arithmetic sequence, a geometric sequence, or neither. If it is either arithmetic or
geometric, give the next term in the sequence.
7, 13, 13, 19, 19, . . .

A)arithmetic; 25
B)geometric; 25
C)neither

Question 49

Draw the next figure in the pattern.

Question 50

Determine if the sequence is an arithmetic sequence, a geometric sequence, or neither. If it is either arithmetic or
geometric, give the next term in the sequence.
2, 5, 10, 17, 26, . . .

A)arithmetic; 37
B)neither
C)geometric; 37

Question 51

Determine if the sequence is an arithmetic sequence, a geometric sequence, or neither. If it is either arithmetic or
geometric, give the next term in the sequence.
4, 12, 36, 108, 324, . . .

A)arithmetic; 972
B)geometric; 972
C)neither

Question 52

Determine what the next equation would be, and verify that it is indeed a true statement.
15 + 51 = 66 16 + 61 = 77

A)17 + 71 = 102
B)71 + 17 = 88
C)17 + 71 = 88
D)55 + 33 = 88

Question 53

Use the method of successive differences to determine the next term in the sequence.
8, 25, 79, 170, 298, . . .

A)499
B)426
C)500
D)463

Question 54

Use the method of successive differences to determine the next term in the sequence.
20, 31, 45, 62, 82, . . .

A)107
B)102
C)108
D)105

Question 55

Determine if the sequence is an arithmetic sequence, a geometric sequence, or neither. If it is either arithmetic or
geometric, give the next term in the sequence.
0, 5, 10, 20, 30, . . .

A)geometric; 40
B)arithmetic; 40
C)neither

Question 56

Use the method of successive differences to determine the next term in the sequence.
8, 17, 35, 64, 106, 163, . . .

A)239
B)246
C)237
D)235

Question 57

Determine what the next equation would be, and verify that it is indeed a true statement.
(6 × 1)× (2 × 1)= 12 (6 × 10)× (2 × 2)= 240
(6 × 100)× (2 × 3)= 3600

A)(6 × 1000)× (2 × 4)= 42,000
B)(6 × 1000)× (2 × 4)= 4800
C)(6 × 1000)× (2 × 4)= 54,000
D)(6 × 1000)× (2 × 4)= 48,000

Question 58

Determine what the next equation would be, and verify that it is indeed a true statement.
32 + 10 = 42 43 + 21 = 64
54 + 32 = 86

A)56 + 43 = 99
B)64 + 53 = 117
C)65 + 43 = 108
D)65 + 32 = 97

Question 59

Determine if the sequence is an arithmetic sequence, a geometric sequence, or neither. If it is either arithmetic or
geometric, give the next term in the sequence.
9, 29, 49, 69, 89, . . .

A)geometric; 109
B)neither
C)arithmetic; 109

Question 60

Determine what the next equation would be, and verify that it is indeed a true statement.
(1 × 9)- 8 = 1 (21 × 9)- 8 = 81
(321 × 9)- 8 = 2881

A)(4,321 × 9)- 8 = 38,881
B)(432 × 9)- 8 = 38,881
C)(4,321 × 9)- 8 = 28,881
D)(4,321 × 9)- 8 = 3880

Question 61

Use the indicated formula to find the sum.

Question 62

Solve the problem using inductive reasoning.
How many line segments are determined by joining dots on the last two circles?

Question 63

Use the indicated formula to find the sum.

Question 64

Use the indicated formula to find the sum.

Question 65

Use the appropriate formula to find the indicated figurate number.
the 14th hexagonal number

A)

Question 66

Determine what the next equation would be, and verify that it is indeed a true statement.
2 × 4 = 3 × 5 - 7 4 × 6 = 5 × 7 - 11

A)6 × 8 = 7 × 9 - 15
B)6 × 8 = 7 × 9 - 13
C)6 × 8 = 7 × 9 + 13
D)6 × 8 = 9 × 11 - 15

Question 67

Use the appropriate formula to find the indicated figurate number.
the 8th square number

A)

Question 68

Use the indicated formula to find the sum.

Question 69

Use the indicated formula to find the sum.

Question 70

Solve the problem using inductive reasoning.
Find the number of games played in a round robin tournament for the given numbers of
teams. In a round robin tournament every team plays every other team once.

Question 71

Use the appropriate formula to find the indicated figurate number.
the 8th heptagonal number

A)

Question 72

Use the indicated formula to find the sum.

Question 73

Solve the problem using inductive reasoning.
Write the next three "square" figurate numbers.

Question 74

Use the appropriate formula to find the indicated figurate number.
the 6th pentagonal number

A)

Question 75

Use the appropriate formula to find the indicated figurate number.
the 15th octagonal number

A)

Question 76

Determine what the next equation would be, and verify that it is indeed a true statement.
7 × 8 = 9 × 10 - (7 + 8 + 9 + 10) 8 × 9 = 10 × 11 - (8 + 9 + 10 + 11)

A)10 × 11 = 12 × 13 - (10 + 11 + 12 + 13)
B)9 × 10 = 11 × 12 - (9 + 10 + 11 + 12)
C)9 × 10 = 11 × 12 - (7 + 8 + 9 + 10 + 11 + 12)
D)10 × 11 = 12 × 13 - (9 + 8 + 7 + 6)

Question 77

Use the indicated formula to find the sum.

A)8020
B)80,200
C)79,800
D)80,000

Question 78

Determine what the next equation would be, and verify that it is indeed a true statement.

Question 79

Use the appropriate formula to find the indicated figurate number.
the 6th triangular number

A)

Question 80

Use the indicated formula to find the sum.