Deck 1: An Introduction to Problem Solving

Question 1

How many different amounts of money can you pay if you use two coins including only nickels, dimes, and quarters?

A)6
B)4
C)7
D)5

Answer 1

A

Question 2

Find the following sum: 4 + 10 + 16 + . . . + 112

A)1102
B)1106
C)1110
D)1094

Answer 2

A

Question 3

Complete the magic (addition)square.
Use each number 10, 11, 12, 13, 14, 15, 16, 17, and 18 once.

Answer 3

A

Question 4

How many different ways can you make change for a 25-cent coin using nickels and pennies?

A)4
B)7
C)6
D)5

Question 5

How many different amounts of money can you pay if you use three coins including nickels, dimes, and quarters?

A)8
B)11
C)9
D)10

Question 6

Complete the magic (addition)square.
Use each number 24, 25, 26, 27, 28, 29, 30, 31, and 32 once.

Question 7

How many different amounts of money can you pay if you use five coins including quarters and dimes?

A)4
B)6
C)7
D)5

Question 8

How many different ways can you make change for 75 cents using quarters, dimes, and nickels?

A)18
B)15
C)16
D)17

Question 9

Complete the magic (addition)square.
Use each number 37, 38, 39, 40, 41, 42, 43, 44, and 45 once.

Question 10

Which is greater, E or P, and by how much?

Question 11

Complete the magic (addition)square.
Use each number 16, 17, 18, 19, 20, 21, 22, 23, and 24 once.

Question 12

Find the following sum: 6 + 20 + 34 + . . . + 986

A)35,204
B)35,216
C)35,222
D)35,228

Question 13

Find the following sum: 19 + 27 + 35 + . . . + 195

A)2423
B)2461
C)2266
D)2480

Question 14

Find the following sum: 5 + 405 + 805 + . . . + 4005

A)22,050
B)22,055
C)18,045
D)22,060

Question 15

How many different ways can you make change for a 50-cent coin using nickels and dimes?

A)4
B)5
C)7
D)6

Question 16

How many different amounts of money can you pay if you use four coins including quarters, nickels, and dimes?

A)14
B)13
C)12
D)15

Question 17

How many different ways can you make change for a 25-cent coin using dimes, nickels, and pennies?

A)11
B)12
C)10
D)13

Question 18

Find the following sum: 5 + 7 + 9 + . . . + 103

A)2710
B)2705
C)2700
D)2690

Question 19

How many different amounts of money can you pay if you use four coins including dimes and quarters?

A)4
B)3
C)5
D)6

Question 20

How many different ways can you make change for a 50-cent coin using quarters, dimes, and nickels?

A)11
B)10
C)9
D)8

Question 21

Provide an appropriate response.
Look for a pattern in the sequence of figures shown below, and use your reasoning to draw the next figure.

Question 22

Determine how many of the indicated shape there are in the figure.
Cubes (of any size)

Question 23

Complete the magic (addition)square.
Use each number 26, 27, 28, 29, 30, 31, 32, 33, and 34 once.

Question 24

A pencil box and a notebook together cost $6.28. The notebook costs $0.50 more than the pencil box. How much does the notebook cost?

A)$2.39
B)$3.39
C)$3.89
D)$2.89

Question 25

Find the requested term in the sequence.
The next term in 8, 32, 96, 288, 864, . . .

A)7776
B)23,328
C)2592
D)69,984

Question 26

Determine how many of the indicated shape there are in the figure.
Squares (of any size)

Question 27

Provide an appropriate response.
Look for a pattern in the sequence of figures shown below, and use your reasoning to draw the next figure.

Question 28

Provide an appropriate response.
Look for a pattern in the sequence of figures shown below, and use your reasoning to draw the next figure.

Question 29

Alamo, Brushy, Chet, and Dolly are in an armadillo race. Chet is the slowest. Dolly is faster than Alamo, but slower than Brushy. Name the finishing order of the armadillos.

A)Brushy, Alamo, Dolly, Chet
B)Alamo, Dolly, Brushy, Chet
C)Alamo, Brushy, Dolly, Chet
D)Brushy, Dolly, Alamo, Chet

Question 30

Determine how many of the indicated shape there are in the figure.

Question 31

Determine how many of the indicated shape there are in the figure.
Triangles (of any size)

Question 32

Provide an appropriate response.
Use a traditional clock face to determine the next three terms in the following sequence: 1, 11, 9, 7, 5, . . .

A)3, 1, 11
B)3, 3, 10
C)2, 2, 11
D)4, 2, 12

Question 33

Complete the magic (addition)square.
Use each number 47, 48, 49, 50, 51, 52, 53, 54, and 55 once.

Question 34

Find the first five terms in the sequence whose nth term is given.

A)2, 8, 18, 32, 50
B)3, 6, 11, 14, 22
C)3, 6, 11, 18, 27
D)4, 6, 8, 10, 12

Question 35

Provide an appropriate response.
Look for a pattern in the sequence of figures shown below, and use your reasoning to draw the next figure.

Question 36

Find the requested term in the sequence.

Question 37

The temperature rose 7 degrees from 10:00 A.M. to noon. By 3:00 P.M. the temperature had doubled. From 3:00 P.M. to 6:00 P.M. the temperature rose 6 degrees to 94 degrees. What was the
Temperature at 10:00 A.M. that morning?

A)51 degrees
B)43 degrees
C)37 degrees
D)81 degrees

Question 38

What is the sum of three consecutive integers in terms of the middle number x? What
would the sum be in terms of the middle number for five and seven consecutive integers?
What can you generalize about the sum of n consecutive integers where n is odd?

Question 39

Question 40

A drink and a sandwich together cost $4.75. The sandwich costs $1.25 more than the drink. How much does the sandwich cost?

A)$0.50
B)$4.25
C)$1.75
D)$3.00

Question 41

Indicate whether the sequence is arithmetic, geometric, or neither. Give the next two terms in the sequence.
13, 14, 21, 28, 35, . . .

A)Geometric; 42; 49
B)Arithmetic; 42; 49
C)Neither; 42; 49

Question 42

Indicate whether the sequence is arithmetic, geometric, or neither. Give the next two terms in the sequence.
6, 15, 18, 21, 24, . . .

A)Neither; 27; 30
B)Arithmetic; 24; 27
C)Geometric; 33; 30

Question 43

Indicate whether the sequence is arithmetic, geometric, or neither. Give the next two terms in the sequence.
10, 35, 60, 85, 110, . . .

A)Geometric; 135; 145
B)Arithmetic; 135; 160
C)Neither; 135; 160

Question 44

Provide an appropriate response.
Look for a pattern in the sequence of figures shown below. How many triangles are needed for the 4th figure? The nth figure?

Question 45

Indicate whether the sequence is arithmetic, geometric, or neither. Give the next two terms in the sequence.
1, 10, 11, 21, 32, . . .

A)Geometric; 53; 85
B)Neither; 53; 85
C)Arithmetic; 53; 85

Question 46

Find the requested term in the sequence.
The 10th term in 20, 20.2, 20.4, 20.8, 20.16, . . .

A)20.256
B)512
C)20.512
D)20.1024

Question 47

Find the requested term in the sequence.
The 100th term in 8, 13, 18, 23, 28, . . .

A)498
B)504
C)503
D)508

Question 48

Provide an appropriate response.
Look for a pattern in the sequence of figures shown below. How many squares are needed for the 4th figure? The nth figure?

Question 49

Indicate whether the sequence is arithmetic, geometric, or neither. Give the next two terms in the sequence.
15, 75, 375, 1875, 9375, . . .

A)Geometric; 46,875; 234,375
B)Neither; 93,750; 468,750
C)Arithmetic; 468,750; 703,125

Question 50

Indicate whether the sequence is arithmetic, geometric, or neither. Give the next two terms in the sequence.
2, 30, 300, 3000, 30,000, . . .

A)Arithmetic; 300,000; 3,000,000
B)Geometric; 300,000; 3,000,000
C)Neither; 300,000; 3,000,000

Question 51

Find the first five terms in the sequence whose nth term is given.

A)20, 40, 60, 80, 100
B)9, 14, 19, 24, 29
C)9, 13, 17, 21, 25
D)9, 18, 27, 36, 45

Question 52

Find the requested term in the sequence.

Question 53

Indicate whether the sequence is arithmetic, geometric, or neither. Give the next two terms in the sequence.
1, 8, 15, 22, 29, . . .

A)Geometric; 36; 44
B)Neither; 37; 44
C)Arithmetic; 36; 43

Question 54

Indicate whether the sequence is arithmetic, geometric, or neither. Give the next two terms in the sequence.
4, 12, 120, 1200, 12,000, . . .

A)Arithmetic; 120,000; 1,200,000
B)Neither; 120,000; 1,200,000
C)Geometric; 120,000; 1,200,000

Question 55

Find the requested term in the sequence.
The nth term in 15, 30, 45, 60, 75, . . .

A)15n + 2
B)15n
C)15n + 15
D)15n - 15

Question 56

Find the requested term in the sequence.
The 10th term in 13, 19, 20, 21, 22, . . .

A)27
B)29
C)28
D)26

Question 57

Provide an appropriate response.
Following is a sequence of black balls and white balls. How many black balls are needed for the 100th term?

Question 58

Find the requested term in the sequence.
The 100th term in 6, 8, 17, 26, 35, . . .

A)899
B)881
C)908
D)890

Question 59

Indicate whether the sequence is arithmetic, geometric, or neither. Give the next two terms in the sequence.
5, 15, 45, 135, 405, . . .

A)Neither; 411; 415
B)Geometric; 1215; 3645
C)Arithmetic; 408; 414

Question 60

Find the first five terms in the sequence whose nth term is given.

Question 61

Find the number of terms in the sequence or the sum of the sequence as requested.
Find the sum of the following arithmetic sequence. 1 + 2 + 3 + . . . + 500

A)125,000
B)251,001
C)62,500
D)125,250

Question 62

Which terms, n and m, in the arithmetic sequence 175, 250, 325, . . . and the geometric
sequence 1, 10, 100, . . ., respectively, have the same value? What is the value?

Question 63

Find the number of terms in the sequence or the sum of the sequence as requested.
The first difference of a sequence is 2, 4, 6, 8, 10, . . . Find the first six terms of the original sequence if the first term in the original sequence is 8.

A)10, 14, 20, 28, 38, 50
B)8, 10, 14, 20, 28, 38
C)8, 16, 32, 48, 64, 80
D)8, 10, 12, 14, 16, 18

Question 64

Provide an appropriate response.
The following sequence is made of black circles. How many circles are needed for the 10th figure? The 15th figure?

Question 65

The population of a town was 33,100 at the beginning of 1970. If the population decreased 300 people per year, how many people lived in the town at the beginning of 1985?

A)4500
B)28,900
C)28,300
D)28,600

Question 66

Find the number of terms in the sequence or the sum of the sequence as requested.
Find the number of terms in the following arithmetic sequence. 3, 9, 15, 21, . . ., 129

A)16
B)22
C)25
D)19

Question 67

Provide an appropriate response.
In the following sequence, the figures are made of cubes that are glued together. If the exposed surface is to be painted, then how many squares will be painted in the 10th figure?

Question 68

Find the number of terms in the sequence or the sum of the sequence as requested.
The first difference of a sequence is 3, 6, 9, 12, 15, . . . Find the first six terms of the original sequence if the sum of the first two terms is 17.

A)7, 10, 16, 25, 37, 52
B)17, 20, 26, 35, 47, 62
C)17, 20, 23, 26, 29, 32
D)7, 10, 13, 16, 19, 22

Question 69

Find the number of terms in the sequence or the sum of the sequence as requested.
Find the number of terms in the following arithmetic sequence. 8, 11, 14, 17, . . ., 89

A)28
B)30
C)81
D)84

Question 70

If a person puts 1¢ in a piggy bank on the first day, 2¢ on the second day, 3¢ on the third day, and so forth, how much money will be in the bank after 30 days?

A)$ 9.30
B)$ 2.33
C)$ 4.65
D)$ 0.30

Question 71

Find the number of terms in the sequence or the sum of the sequence as requested.
Find the sum of the following arithmetic sequence. 11 + 13 + . . . + 601

A)89,975
B)90,601
C)90,576
D)76,176

Question 72

Find the number of terms in the sequence or the sum of the sequence as requested.
The first difference of a sequence is 2, 4, 6, 8, 10, . . . Find the first six terms of the original sequence if the third term of the original sequence is 61.

A)61, 63, 65, 67, 69, 71
B)55, 57, 61, 67, 69, 71
C)59, 57, 61, 67, 69, 71
D)55, 57, 61, 67, 75, 85

Question 73

A man earned $ 3000 the first year he worked. If he received a raise of $400 at the end of each year, what was his salary during the 15 th year?

A)$ 9000
B)None of these
C)$ 8600
D)$ 5600

Question 74

At what term will the geometric sequence 1, 2, 4, 8, . . . become greater than the arithmetic
sequence 0, 20, 40, 60, . . .?

Question 75

Find the number of terms in the sequence or the sum of the sequence as requested.
Find the number of terms in the following arithmetic sequence. 1, 3, 5, 7, . . ., 51

A)28
B)26
C)25
D)51

Question 76

A collection of dimes is arranged in a triangular array with 11 coins in the base row, 10 in the next, 9 in the next, and so forth. Find the value of the collection.

A)$ 0.66
B)$ 13.20
C)$ 3.30
D)$ 6.60

Question 77

A rose garden has 16 bushes in one row, 13 bushes in the next row, then 10 , and so on. If there are 51 bushes in the garden, in how many rows are they planted?

A)3
B)5
C)7
D)6

Question 78

Find the number of terms in the sequence or the sum of the sequence as requested.
Find the sum of the following arithmetic sequence. 10 + 11 + 12 + . . . + 500

A)125,205
B)124,714
C)125,250
D)125,214

Question 79

An auditorium has 15 rows with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. How many seats are in the auditorium?

A)390
B)300
C)255
D)360

Question 80

Find the number of terms in the sequence or the sum of the sequence as requested.
Find the sum of the following arithmetic sequence. 4 + 8 + 12 + . . . + 100

A)1300
B)1250
C)156.25
D)10,000