Question 1

$$\text { If } \operatorname { GCD } ( a , b ) = 1 \text {, then } \operatorname { LCM } ( a , b ) = a b$$

Accepted Answer

A) True 
 B)False

Question 2

Find the GCD for the given numbers by an appropriate method.
-97,498 and 103,443

Accepted Answer

A) 1681 
B) 1 
C) 841 
D) 1189 
A) 1681 
B) 1 
C) 841 
D) 1189

Question 3

Determine all possible digits to place in the square that make the statement true. If none exist, state this.
-$$4,3 \square6 \text { is divisible by } 4 \text {. }$$

Accepted Answer

The answer of Determine all possible digits to place in...

Question 4

Use least common multiple or greatest common divisor to solve the problem.
-A brick layer is hired to build three walls of equal length. He has bricks which are 9 inches, 27 inches, and 15 inches long. He plans to build one wall out of each type of brick. What is the shortest Length of wall possible?

Accepted Answer

A) 405 inches 
B) 3645 inches 
C) 51 inches 
D) 135 inches 
A) 405 inches 
B) 3645 inches 
C) 51 inches 
D) 135 inches

Question 5

Classify as true or false, assuming that a, b, c, and d are whole numbers an $\mathrm { d } \neq 0$
-$$\text { If } \mathrm { d } \mid ( \mathrm { a } + \mathrm { b } ) \text {, then } \mathrm { d } \mid \mathrm { a } \text { and } \mathrm { d } \mid \mathrm { b } \text {. }$$

Accepted Answer

A) True 
 B)False

Question 6

Find the LCM for the given numbers by an appropriate method.
-168 and 126

Accepted Answer

A) 504 
B) 1008 
C) 42 
D) 1512 
A) 504 
B) 1008 
C) 42 
D) 1512

Question 7

Find the prime factorization.
-$15 ^ { 3 } \cdot 33 \cdot 343 ^ { 2 }$

Accepted Answer

A)  $3 ^ { 4 } \cdot 5 \cdot 7 ^ { 3 } \cdot 11$ 
B)  $3 ^ { 4 } \cdot 5 ^ { 3 } \cdot 7 ^ { 2 } \cdot 11$ 
C)  $3 ^ { 4 } \cdot 5 ^ { 3 } \cdot 7 ^ { 6 } \cdot 11$ 
D)  $3 ^ { 2 } \cdot 5 ^ { 3 } \cdot 7 ^ { 6 } \cdot 11$ 
A)  $3 ^ { 4 } \cdot 5 \cdot 7 ^ { 3 } \cdot 11$ 
B)  $3 ^ { 4 } \cdot 5 ^ { 3 } \cdot 7 ^ { 2 } \cdot 11$ 
C)  $3 ^ { 4 } \cdot 5 ^ { 3 } \cdot 7 ^ { 6 } \cdot 11$ 
D)  $3 ^ { 2 } \cdot 5 ^ { 3 } \cdot 7 ^ { 6 } \cdot 11$

Question 8

Solve the problem.
-In a football game a touchdown is worth 6 points, an extra point is worth 1 point, and a field goal is worth 3 points. Suppose that in a game the only scoring done by teams are touchdowns, extra Points and field goals. If a team scored 56 points with 7 touchdowns and 2 extra points, how many Field goals were scored?

Accepted Answer

A) 4 
B) 3 
C) 5 
D) 7 
A) 4 
B) 3 
C) 5 
D) 7

Question 9

Find the LCM for the given numbers by an appropriate method.
-56 and 96

Accepted Answer

A) 672 
B) 168 
C) 1344 
D) 224 
A) 672 
B) 168 
C) 1344 
D) 224

Question 10

Without using a calculator, determine whether the first number is divisible by the second number.
-Is 839,254 divisible by 9?

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 11

Determine all possible digits to place in the square that make the statement true. If none exist, state this.
-$$5,33 \square \text { is divisible by } 11 \text {. }$$

Accepted Answer

The answer of Determine all possible digits to place in...

Question 12

$$\text { For all natural numbers a and } b , \operatorname { GCD } ( a , b ) \mid a b \text {. }$$

Accepted Answer

A) True 
 B)False

Question 13

Solve the problem.
-If a plot of land contains a rectangular array of 160 strawberry plants, how many rows are in the array if there are 40 plants in each row?

Accepted Answer

A)  40 
B)  4 
C)  30 
D)  9 
A)  40 
B)  4 
C)  30 
D)  9

Question 14

If a number is divisible by 2, then it must also be divisible by 6.

Accepted Answer

A) True 
 B)False

Question 15

Find the GCD for the given numbers by an appropriate method.
-1562, 450, and 6750

Accepted Answer

A) 5 
B) 4 
C) 2 
D) 12 
A) 5 
B) 4 
C) 2 
D) 12

Question 16

Provide the appropriate response.
-Find the largest two-digit superprime.

Accepted Answer

A) 79 
B) 97 
C) 59 
D) 95 
A) 79 
B) 97 
C) 59 
D) 95

Question 17

Solve the problem.
-In a football game a touchdown is worth 6 points, an extra point is worth 1 point, and a field goal is worth 3 points. Suppose that in a game the only scoring done by teams are touchdowns, extra Points and field goals. If a team scored 66 points with 6 touchdowns and 6 extra points, how many Field goals were scored?

Accepted Answer

A) 6 
B) 8 
C) 9 
D) 7 
A) 6 
B) 8 
C) 9 
D) 7

Question 18

Determine all possible digits to place in the square that make the statement true. If none exist, state this.
-$$74,3 \square 2 \text { is divisible by } 6 \text {. }$$

Accepted Answer

The answer of Determine all possible digits to place in...

Question 19

Classify as true or false, assuming that a, b, c, and d are whole numbers an $\mathrm { d } \neq 0$
-$$\text { If } \mathrm { a } \mid \mathrm { b } \text { and } \mathrm { b } \mid \mathrm { a } \text {, then } \mathrm { a } = \mathrm { b } \text {. }$$

Accepted Answer

A) True 
 B)False

Question 20

Use least common multiple or greatest common divisor to solve the problem.
-Two runners run around a circular track. The first runner completes a lap in 6 minutes. The second runner completes the track in 13 minutes. If they both start at the same place and the same time and Go in the same direction, after how many minutes will they meet again at the starting place?

Accepted Answer

A) 19 
B) 156 
C) 78 
D) 79 
A) 19 
B) 156 
C) 78 
D) 79

$\text { If } \operatorname { GCD } ( a , b ) = 1 \text {, then } \operatorname { LCM } ( a , b ) = a b$

Find the GCD for the given numbers by an appropriate method. -97,498 and 103,443

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - $4,3 \square6 \text { is divisible by } 4 \text {. }$

Classify as true or false, assuming that a, b, c, and d are whole numbers an $\mathrm { d } \neq 0$ - $\text { If } \mathrm { d } \mid ( \mathrm { a } + \mathrm { b } ) \text {, then } \mathrm { d } \mid \mathrm { a } \text { and } \mathrm { d } \mid \mathrm { b } \text {. }$

Find the LCM for the given numbers by an appropriate method. -168 and 126

Find the prime factorization. - $15 ^ { 3 } \cdot 33 \cdot 343 ^ { 2 }$

Find the LCM for the given numbers by an appropriate method. -56 and 96

Without using a calculator, determine whether the first number is divisible by the second number. -Is 839,254 divisible by 9?

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - $5,33 \square \text { is divisible by } 11 \text {. }$

$\text { For all natural numbers a and } b , \operatorname { GCD } ( a , b ) \mid a b \text {. }$

Solve the problem. -If a plot of land contains a rectangular array of 160 strawberry plants, how many rows are in the array if there are 40 plants in each row?

If a number is divisible by 2, then it must also be divisible by 6.

Find the GCD for the given numbers by an appropriate method. -1562, 450, and 6750

Provide the appropriate response. -Find the largest two-digit superprime.

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - $74,3 \square 2 \text { is divisible by } 6 \text {. }$

Classify as true or false, assuming that a, b, c, and d are whole numbers an $\mathrm { d } \neq 0$ - $\text { If } \mathrm { a } \mid \mathrm { b } \text { and } \mathrm { b } \mid \mathrm { a } \text {, then } \mathrm { a } = \mathrm { b } \text {. }$

An Introduction to Problem Solving

Introduction to Logic and Sets

Numeration Systems and Whole Number Operations

Integers

Rational Numbers and Proportional Reasoning

Rational Numbers As Decimals and Percents

Real Numbers and Algebraic Thinking

Probability

Data Analysisstatistics: an Introduction

Introductory Geometry

Congruence and Similarity With Constructions

Congruence and Similarity With Transformations

Area, Pythagorean Theorem, and Volume

Filters

Exam 4: Number Theory

If GCD⁡(a,b)=1, then LCM⁡(a,b)=ab\text { If } \operatorname { GCD } ( a , b ) = 1 \text {, then } \operatorname { LCM } ( a , b ) = a b If GCD(a,b)=1, then LCM(a,b)=ab

Find the GCD for the given numbers by an appropriate method. -97,498 and 103,443

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - 4,3□6 is divisible by 4. 4,3 \square6 \text { is divisible by } 4 \text {. }4,3□6 is divisible by 4.

Find the LCM for the given numbers by an appropriate method. -168 and 126

Find the prime factorization. - 153⋅33⋅343215 ^ { 3 } \cdot 33 \cdot 343 ^ { 2 }153⋅33⋅3432

Find the LCM for the given numbers by an appropriate method. -56 and 96

Without using a calculator, determine whether the first number is divisible by the second number. -Is 839,254 divisible by 9?

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - 5,33□ is divisible by 11. 5,33 \square \text { is divisible by } 11 \text {. }5,33□ is divisible by 11.

For all natural numbers a and b,GCD⁡(a,b)∣ab. \text { For all natural numbers a and } b , \operatorname { GCD } ( a , b ) \mid a b \text {. } For all natural numbers a and b,GCD(a,b)∣ab.

Solve the problem. -If a plot of land contains a rectangular array of 160 strawberry plants, how many rows are in the array if there are 40 plants in each row?

If a number is divisible by 2, then it must also be divisible by 6.

Find the GCD for the given numbers by an appropriate method. -1562, 450, and 6750

Provide the appropriate response. -Find the largest two-digit superprime.

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - 74,3□2 is divisible by 6. 74,3 \square 2 \text { is divisible by } 6 \text {. }74,3□2 is divisible by 6.

An Introduction to Problem Solving

Introduction to Logic and Sets

Numeration Systems and Whole Number Operations

Integers

Rational Numbers and Proportional Reasoning

Rational Numbers As Decimals and Percents

Real Numbers and Algebraic Thinking

Probability

Data Analysisstatistics: an Introduction

Introductory Geometry

Congruence and Similarity With Constructions

Congruence and Similarity With Transformations

Area, Pythagorean Theorem, and Volume

Filters

$\text { If } \operatorname { GCD } ( a , b ) = 1 \text {, then } \operatorname { LCM } ( a , b ) = a b$

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - $4,3 \square6 \text { is divisible by } 4 \text {. }$

Find the prime factorization. - $15 ^ { 3 } \cdot 33 \cdot 343 ^ { 2 }$

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - $5,33 \square \text { is divisible by } 11 \text {. }$

$\text { For all natural numbers a and } b , \operatorname { GCD } ( a , b ) \mid a b \text {. }$

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - $74,3 \square 2 \text { is divisible by } 6 \text {. }$