Question 1

Determine all possible digits to place in the square that make the statement true. If none exist, state this.
-$$4,3 \square 2 \text { is divisible by } 9 .$$

Accepted Answer

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

Question 2

Without using a calculator, determine whether the first number is divisible by the second number.
-Is 210,270 divisible by 30?

Accepted Answer

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

Question 3

Without using a calculator, determine whether the first number is divisible by the second number.
-Is 23,868 divisible by 6?

Accepted Answer

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

Question 4

Solve the problem.
-If all of 47 available apple trees are to be planted on a plot of land, is there more than one possible array in which they can be arranged with the same number of trees in each row? If so, how many Different arrays are there?

Accepted Answer

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

Question 5

Determine all possible digits to place in the square that make the statement true. If none exist, state this.
-$$417,30 \square \text { is divisible by } 8 \text { but not } 16$$

Accepted Answer

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

Question 6

Solve the problem.
-A group of teachers order markers for their classrooms. The bill was $3.91. If the original price per marker was 17¢ and the price has risen, how much does each marker cost now?

Accepted Answer

A) 23¢ 
B) 24¢ 
C) 22¢ 
D) 21¢ 
A) 23¢ 
B) 24¢ 
C) 22¢ 
D) 21¢

Question 7

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

Accepted Answer

A) True 
 B)False

Question 8

Solve the problem.
-If all of 48 available apple trees are to be planted in a rectangular array, what are the possible numbers of rows in the array, all rows having the same number of trees?

Accepted Answer

A) 1, 2, 3, 4, and 6 
B) 8, 12, 16, 24, and 48 
C) 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48 
D) 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 24, and 48 
A) 1, 2, 3, 4, and 6 
B) 8, 12, 16, 24, and 48 
C) 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48 
D) 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 24, and 48

Question 9

Find the GCD for the given numbers by an appropriate method.
-60 and 90

Accepted Answer

A) 10 
B) 30 
C) 15 
D) 6 
A) 10 
B) 30 
C) 15 
D) 6

Question 10

$$\text { If } \operatorname { GCD } ( a , b ) = 1 \text {, then } a \text { and } b \text { can both be even. }$$

Accepted Answer

A) True 
 B)False

Question 11

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

Accepted Answer

A) True 
 B)False

Question 12

Solve the problem.
-If a group of 247 people is to be split into equal-sized subgroups of at least two people and no more than 30 people, what are the possible group sizes?

Accepted Answer

A) 19 
B) 9 and 13 
C) 13 and 19 
D) 7, 13, and 19 
A) 19 
B) 9 and 13 
C) 13 and 19 
D) 7, 13, and 19

Question 13

Without using a calculator, determine whether the first number is divisible by the second number.
-Is 18,871 divisible by 6?

Accepted Answer

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

Question 14

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

Accepted Answer

A) True 
 B)False

Question 15

$$\text { If } a \text { and } b \text { are even, then } \operatorname { GCD } ( a , b ) \text { must be } 2 .$$

Accepted Answer

A) True 
 B)False

Question 16

Provide the appropriate response.
-List all digits that cannot appear in a superprime number.

Accepted Answer

A) 4, 6, 8, 0 
B) 4, 6, 8 
C) 4, 6, 8, 5 
D) 4, 6, 8, 0, 5 
A) 4, 6, 8, 0 
B) 4, 6, 8 
C) 4, 6, 8, 5 
D) 4, 6, 8, 0, 5

Question 17

Without using a calculator, determine whether the first number is divisible by the second number.
-Is 203 divisible by 3?

Accepted Answer

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

Question 18

Provide the appropriate response.
-What is the greatest prime number you must consider to test whether 3599 is prime?

Accepted Answer

A) 59 
B) 63 
C) 64 
D) 31 
A) 59 
B) 63 
C) 64 
D) 31

Question 19

Without using a calculator, determine whether the first number is divisible by the second number.
-Is 952,042 divisible by 4?

Accepted Answer

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

Question 20

Classify as true or false, assuming that a, b, c, and d are whole numbers an $\mathrm { d } \neq 0$
-$$\text { If } \mathrm { d } \mid \mathrm { a } ^ { 3 } \text {, then } \mathrm { d } \mid \mathrm { a } \text {. }$$

Accepted Answer

A) True 
 B)False

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - $4,3 \square 2 \text { is divisible by } 9 .$

Without using a calculator, determine whether the first number is divisible by the second number. -Is 210,270 divisible by 30?

Without using a calculator, determine whether the first number is divisible by the second number. -Is 23,868 divisible by 6?

Solve the problem. -If all of 47 available apple trees are to be planted on a plot of land, is there more than one possible array in which they can be arranged with the same number of trees in each row? If so, how many Different arrays are there?

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - $417,30 \square \text { is divisible by } 8 \text { but not } 16$

Solve the problem. -A group of teachers order markers for their classrooms. The bill was $3.91. If the original price per marker was 17¢ and the price has risen, how much does each marker cost now?

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

Solve the problem. -If all of 48 available apple trees are to be planted in a rectangular array, what are the possible numbers of rows in the array, all rows having the same number of trees?

Find the GCD for the given numbers by an appropriate method. -60 and 90

$\text { If } \operatorname { GCD } ( a , b ) = 1 \text {, then } a \text { and } b \text { can both be even. }$

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

Solve the problem. -If a group of 247 people is to be split into equal-sized subgroups of at least two people and no more than 30 people, what are the possible group sizes?

Without using a calculator, determine whether the first number is divisible by the second number. -Is 18,871 divisible by 6?

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

$\text { If } a \text { and } b \text { are even, then } \operatorname { GCD } ( a , b ) \text { must be } 2 .$

Provide the appropriate response. -List all digits that cannot appear in a superprime number.

Without using a calculator, determine whether the first number is divisible by the second number. -Is 203 divisible by 3?

Provide the appropriate response. -What is the greatest prime number you must consider to test whether 3599 is prime?

Without using a calculator, determine whether the first number is divisible by the second number. -Is 952,042 divisible by 4?

Classify as true or false, assuming that a, b, c, and d are whole numbers an $\mathrm { d } \neq 0$ - $\text { If } \mathrm { d } \mid \mathrm { a } ^ { 3 } \text {, then } \mathrm { d } \mid \mathrm { a } \text {. }$

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

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - 4,3□2 is divisible by 9.4,3 \square 2 \text { is divisible by } 9 .4,3□2 is divisible by 9.

Without using a calculator, determine whether the first number is divisible by the second number. -Is 210,270 divisible by 30?

Without using a calculator, determine whether the first number is divisible by the second number. -Is 23,868 divisible by 6?

Solve the problem. -If all of 47 available apple trees are to be planted on a plot of land, is there more than one possible array in which they can be arranged with the same number of trees in each row? If so, how many Different arrays are there?

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - 417,30□ is divisible by 8 but not 16417,30 \square \text { is divisible by } 8 \text { but not } 16417,30□ is divisible by 8 but not 16

Solve the problem. -A group of teachers order markers for their classrooms. The bill was $3.91. If the original price per marker was 17¢ and the price has risen, how much does each marker cost now?

Solve the problem. -If all of 48 available apple trees are to be planted in a rectangular array, what are the possible numbers of rows in the array, all rows having the same number of trees?

Find the GCD for the given numbers by an appropriate method. -60 and 90

If GCD⁡(a,b)=1, then a and b can both be even. \text { If } \operatorname { GCD } ( a , b ) = 1 \text {, then } a \text { and } b \text { can both be even. } If GCD(a,b)=1, then a and b can both be even.

Solve the problem. -If a group of 247 people is to be split into equal-sized subgroups of at least two people and no more than 30 people, what are the possible group sizes?

Without using a calculator, determine whether the first number is divisible by the second number. -Is 18,871 divisible by 6?

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

If a and b are even, then GCD⁡(a,b) must be 2.\text { If } a \text { and } b \text { are even, then } \operatorname { GCD } ( a , b ) \text { must be } 2 . If a and b are even, then GCD(a,b) must be 2.

Provide the appropriate response. -List all digits that cannot appear in a superprime number.

Without using a calculator, determine whether the first number is divisible by the second number. -Is 203 divisible by 3?

Provide the appropriate response. -What is the greatest prime number you must consider to test whether 3599 is prime?

Without using a calculator, determine whether the first number is divisible by the second number. -Is 952,042 divisible by 4?

Classify as true or false, assuming that a, b, c, and d are whole numbers an d≠0\mathrm { d } \neq 0d=0 - If d∣a3, then d∣a. \text { If } \mathrm { d } \mid \mathrm { a } ^ { 3 } \text {, then } \mathrm { d } \mid \mathrm { a } \text {. } If d∣a3, then d∣a.

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

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - $4,3 \square 2 \text { is divisible by } 9 .$

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - $417,30 \square \text { is divisible by } 8 \text { but not } 16$

$\text { If } \operatorname { GCD } ( a , b ) = 1 \text {, then } a \text { and } b \text { can both be even. }$

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

$\text { If } a \text { and } b \text { are even, then } \operatorname { GCD } ( a , b ) \text { must be } 2 .$

Classify as true or false, assuming that a, b, c, and d are whole numbers an $\mathrm { d } \neq 0$ - $\text { If } \mathrm { d } \mid \mathrm { a } ^ { 3 } \text {, then } \mathrm { d } \mid \mathrm { a } \text {. }$