Deck 1: Some Basic Concepts of Arithmetic and Algebra

Question 1

Evaluate the algebraic expression for $x = 6$ and $y = 2$ . $( x + 3 y ) ( 3 x - y )$

A) 190
B) 188
C) 193
D) 192
E) 189

Answer 1

192

Question 2

Evaluate the algebraic expression for $$y = 4$$ . $$\frac { y + 16 } { 5 } + \frac { 56 - y } { 4 }$$

A) 13
B) 16
C) 15
D) 17
E) 20

Answer 2

17

Question 3

Evaluate the algebraic expression for n = 12. $$\frac { 36 } { n } + \frac { n } { 2 }$$

A) 59
B) -3
C) 21
D) 9
E) 102

Answer 3

9

Question 4

Evaluate the algebraic expression for n = 21 and w = 7. $\frac { n \cdot w } { 7 }$

A) 112
B) 21
C) 98
D) 630

Question 5

Simplify the numerical expression below. 4(17 9)

Question 6

Examples of numerical expressions are $2 x - y , 14 \div 2 + 1 \text {, and } 3 ( 6 )$ .

Question 7

Zero is an element of the null set.

Question 8

Simplify the numerical expression. 4(18 + 7) 3(9 2)

Question 9

Evaluate the algebraic expression for the given values of the variables for m = 11 and q = $-$ 4. $$m + 10 q + 7 m q$$

A) $-$ 326
B) $-$ 309
C) $-$ 348
D) $-$ 337
E) $-$ 3,355

Question 10

Simplify the numerical expression. 3(19 + 6) $-$ 2(8 $-$ 2)

A) 66
B) 63
C) 67
D) 62
E) 65

Question 11

The expression " 6-2 " indicates the difference of 2 and 6.

Question 12

Simplify the numerical expression below. 14 + 4 9

Question 13

The set of whole numbers can be listed using the roster method as $\{ 0,1,2,3 , \ldots \}$ .

Question 14

Evaluate the algebraic expression for the given values of the variables for y = 1, f = 13 and h = 20. $$7 y f - 6 y h + 10 f h$$

A) -2,390
B) -23,878
C) -2,377
D) -2,389
E) -2,388

Question 15

Evaluate the algebraic expression below for the given values of the variables for x = 20 and w = 19. $6 x + 8 w$

A) -52
B) -32
C) -281
D) 2
E) -12

Question 16

Simplify the numerical expression below.

Question 17

Find the value of $\frac { b h } { 2 }$ for the following set of values for the variables b and h . $b = 6$ and $h = 4$

A) 24
B) 12
C) 19
D) 11
E) 15

Question 18

Evaluate the algebraic expression for z = 2. $57 - 6 [ 8 ( z - 3 ) ]$

A) 1,052
B) 48
C) 105
D) 162
E) 176

Question 19

Evaluate the algebraic expression for n = 9, e = 18 and l = 54. $\frac { n \cdot ( e + l ) } { 9 }$

A) 441
B) 162
C) -36
D) 567

Question 20

Simplify the numerical expression below.

Question 21

Simplify the numerical expression below.

Question 22

The factors of a number are also divisors of the number.

Question 23

Evaluate the algebraic expression for y = 8.

Question 24

Evaluate the algebraic expression for and .

Question 25

Select the correct statement below.

A) 17 is not a multiple of 6
B) 72 is not a multiple of 8
C) 72 is not a multiple of 9
D) 17 is a multiple of 6

Question 26

Simplify the numerical expression below.

Question 27

Evaluate the algebraic expression for x = 22, e = 14 and c = 10.

Question 28

Select the correct statement below.

A) 56 is not divisible by 8
B) 56 is divisible by 7
C) 6 is a factor of 19
D) 56 is a factor of 8
E) 5 is a factor of 23

Question 29

Simplify the numerical expression below.

Question 30

Evaluate the algebraic expression for .

Question 31

Evaluate the algebraic expression for y = 19 and b = 14.

Question 32

Evaluate the algebraic expression for y = 18.

Question 33

Find the value of for the following set of values for the variables b and h . and

Question 34

All odd numbers are also prime numbers.

Question 35

Simplify the numerical expression below.

Question 36

The greatest common factor of two whole numbers is the number that can be divided by both whole numbers.

Question 37

Evaluate the algebraic expression below for x = 20 and q = 22.

Question 38

Every composite number can be expressed as a product of prime numbers.

Question 39

Simplify the numerical expression below.

Question 40

Simplify the numerical expression below.

Question 41

Find the greatest common factor of the numbers below. 51, 87 and 69

A) 4
B) 3
C) 2
D) 5
E) none of these

Question 42

Use the divisibility rules to help determine the prime factorization of the following number. 22

A) $3 \cdot 11$
B) $2 \cdot 10$
C) $4 \cdot 11$
D) $2 \cdot 11$
E) none of these

Question 43

What is the least common multiple of t and v if the greatest common factor of t and v is 8?

A) t
B) v
C) t + v
D) $\frac { tv } { 8 }$
E) none of these

Question 44

Use the divisibility rules to help determine the prime factorization of the number below. 51

A) $3 \cdot 16$
B) $3 \cdot 5 \cdot 17$
C) $9.17$
D) $3 \cdot 17$
E) none of these

Question 45

Use the divisibility rules to help determine the prime factorization of the following number. 22

A) $2 \cdot 10$
B) $4 \cdot 11$
C) $2 \cdot 11$
D) $3 \cdot 11$
E) none of these

Question 46

Use the divisibility rules to help determine the prime factorization of the number below. 261

A) $3.3 .29$
B) $3 \cdot 3 \cdot 3 \cdot 29$
C) $3.5 .29$
D) $3 \cdot 3 \cdot 30$
E) none of these

Question 47

Factor the composite number 100 into a product of prime numbers, for example $30 = 2 \cdot 3 \cdot 5$ .

A) $2 \cdot 2 \cdot 5 \cdot 5$
B) $2 \cdot 2 \cdot 5 \cdot 5 \cdot 5$
C) $2 \cdot 2 \cdot 2 \cdot 5 \cdot 5$
D) $2 \cdot 1 \cdot 5 \cdot 5$
E) none of these

Question 48

What is the greatest common factor of x and n if x and n are nonzero whole numbers and n is a multiple of x ?

A) xn
B) n
C) x + n
D) x
E) none of these

Question 49

Find the greatest common factor of the following numbers. 51 and 39

A) 5
B) 3
C) 2
D) 4
E) none of these

Question 50

Factor the composite number 90 into a product of prime numbers, for example $30 = 2 \cdot 3 \cdot 5$ .

A) $2 \cdot 3 \cdot 3 \cdot 5$
B) $2 \cdot 2 \cdot 3 \cdot 3 \cdot 5$
C) $2 \cdot 3 \cdot 3 \cdot 5 \cdot 5$
D) $2 \cdot 2 \cdot 3 \cdot 5$
E) none of these

Question 51

What is the greatest common factor of x and s if x and s are nonzero whole numbers and s is a multiple of x ?

A) x
B) s
C) x + s
D) xs
E) none of these

Question 52

Find the greatest common factor of the numbers below. 145, 115 and 235

A) 4
B) 7
C) 5
D) 6
E) none of these

Question 53

Find the least common multiple of the numbers below. 33 and 15

A) 55
B) 165
C) 3
D) 11
E) none of these

Question 54

Find the least common multiple of the numbers below. 114 and 138

A) 6
B) 19
C) 2,622
D) 437
E) none of these

Question 55

Use the divisibility rules to help determine the prime factorization of the number below. 87

A) $3 \cdot 28$
B) $3 \cdot 29$
C) $9.29$
D) $3.5 .29$
E) none of these

Question 56

Use the divisibility rules to help determine the prime factorization of the number below. 55

A) $7 \cdot 11$
B) $5 \cdot 11$
C) $3 \cdot 11$
D) $3 \cdot 5 \cdot 11$
E) none of these

Question 57

Find the least common multiple of the numbers below. 114, 66 and 30

A) 570
B) 95
C) 6,270
D) 1,045
E) none of these

Question 58

Find the least common multiple of the numbers below. 85, 65 and 15

A) 663
B) 3,315
C) 51
D) 255
E) none of these

Question 59

Find the greatest common factor of the following numbers. 52 and 92

A) 3
B) 5
C) 6
D) 4
E) none of these

Question 60

Find the correct statement.

A) 30 is divisible by 5
B) 8 is a factor of 29
C) 3 is a factor of 19
D) 30 is not divisible by 6

Question 61

Fill in the blanks with a pair of numbers that has the indicated product and the indicated sum. For example, $\frac { 8 } { 5 } \cdot \frac { 5 } { 2 } = 40$ and $\underline { 8 } + \underline { 5 } = 13$ . $- { } _ { - } = 18$ and $- ^ { + } - = 11$

A) 1, 9
B) 2, 9
C) 2, 7
D) 1, 7
E) 7, 9

Question 62

Find the least common multiple of the numbers below. 207, 45 and 153

Question 63

Find the greatest common factor of the numbers below. 174, 222 and 66

Question 64

What is the greatest common factor of m and s if m and s are nonzero whole numbers and s is a multiple of m ?

Question 65

Find the greatest common factor of the numbers below. 65, 205 and 185

Question 66

Find the least common multiple of the numbers below. 21 and 57

Question 67

Find the least common multiple of the numbers below. 76, 20 and 28

Question 68

What is the least common multiple of u and y if the greatest common factor of u and y is 9?

Question 69

Find the greatest common factor of the numbers below. 51 and 33

Question 70

Find the least common multiple of the numbers below. 38, 22 and 6

Question 71

Find the greatest common factor of the numbers below. 205, 35 and 95

Question 72

Use the divisibility rules to help determine the prime factorization of the number below. 85

A) $7 \cdot 17$
B) $5 \cdot 17$
C) $3 \cdot 5 \cdot 17$
D) $3 \cdot 17$
E) none of these

Question 73

Find the least common multiple of the numbers below. 174, 186 and 114

Question 74

Find the greatest common factor of the numbers below. 6 and 62

Question 75

Find the least common multiple of the numbers below. 136, 152 and 184

Question 76

Use the divisibility rules to help determine the prime factorization of the number below. 63

A) $3 \cdot 3 \cdot 7$
B) $3 \cdot 3 \cdot 3 \cdot 7$
C) $3.5 .7$
D) $3 \cdot 3 \cdot 8$
E) none of these

Question 77

Find the least common multiple of the numbers below. 203, 91 and 35

Question 78

Find the greatest common factor of the numbers below. 45 and 207

Question 79

Factor the composite number 330 into a product of prime numbers, for example .

Question 80

Find the least common multiple of the numbers below. 58 and 14