Question 1

Find the LCM for the given numbers by an appropriate method.
-48, 162, and 9

Accepted Answer

A) 324 
B) 648 
C) 1296 
D) 432 
A) 324 
B) 648 
C) 1296 
D) 432

Question 2

Use least common multiple or greatest common divisor to solve the problem.
-Planets A, B, and C orbit a certain star once every 2, 5, and 12 months, respectively. If the three planets are now in the same straight line, what is the smallest number of months that must pass Before they line up again?

Accepted Answer

A) 19 months 
B) 120 months 
C) 60 months 
D) 24 months 
A) 19 months 
B) 120 months 
C) 60 months 
D) 24 months

Question 3

Find the prime factorization.
-1606

Accepted Answer

A)  $11 ^ { 2 } \cdot 73$ 
B)  $2 ^ { 2 } \cdot 73$ 
C)  $2 \cdot 11 \cdot 73$ 
D)  $22 \cdot 73$ 
A)  $11 ^ { 2 } \cdot 73$ 
B)  $2 ^ { 2 } \cdot 73$ 
C)  $2 \cdot 11 \cdot 73$ 
D)  $22 \cdot 73$

Question 4

Without using a calculator, determine whether the first number is divisible by the second number.
-Is 62,656,837 divisible by 77?

Accepted Answer

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

Question 5

Find the GCD or LCM as indicated.
-Given 56 and 96, find the LCM.

Accepted Answer

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

Question 6

$$\text { If } \operatorname { GCD } ( \mathrm { a } , \mathrm { b } ) = 2 \text {, then a or b can be odd }$$

Accepted Answer

A) True 
 B)False

Question 7

Provide the appropriate response.
-How many twin prime pairs can be found from the numbers less than 100?

Accepted Answer

A) 9 
B) 8 
C) 10 
D) 7 
A) 9 
B) 8 
C) 10 
D) 7

Question 8

Solve the problem.
-The local bakery marked down some day-old pies from $4.00 but kept the price over $3.00. All of the pies were sold, and the total amount of money from the sale of the pies was $43.55. How many Pies were sold?

Accepted Answer

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

Question 9

Find the GCD or LCM as indicated.
-Given 60 and 30, find the GCD.

Accepted Answer

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

Question 10

Determine all possible digits to place in the square that make the statement true. If none exist, state this.
-$$4 , \square 21 \text { is divisible by } 4$$

Accepted Answer

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

Question 11

Find the GCD for the given numbers by an appropriate method.
-960 and 1800

Accepted Answer

A) 960 
B) 60 
C) 360 
D) 120 
A) 960 
B) 60 
C) 360 
D) 120

Question 12

Solve the problem.
-Jim has 56 trees that he wants to plant in a rectangular array. List the possible arrays.

Accepted Answer

A)  $1 \times 56,7 \times 8$ 
B)  $7 \times 8,8 \times 7$ 
C)  $2 \times 28,4 \times 14$ 
D)  $1 \times 56,2 \times 28,4 \times 14,7 \times 8$ 
A)  $1 \times 56,7 \times 8$ 
B)  $7 \times 8,8 \times 7$ 
C)  $2 \times 28,4 \times 14$ 
D)  $1 \times 56,2 \times 28,4 \times 14,7 \times 8$

Question 13

Use least common multiple or greatest common divisor to solve the problem.
-Bob's frog can travel 7 inches per jump, Kim's frog can travel 9 inches, and Jack's frog can travel 13 inches. If the three frogs start off at point 0 inches, how many inches will it be to the next point that All three frogs touch?

Accepted Answer

A) 819 inches 
B) 29 inches 
C) 117 inches 
D) 63 inches 
A) 819 inches 
B) 29 inches 
C) 117 inches 
D) 63 inches

Question 14

Use least common multiple or greatest common divisor to solve the problem.
-George has 336 donuts and 462 bagels. He wants to divide his bagels and donuts into stacks so that there are the same number of pastries in each stack. What is the greatest number of pastries that he Can place in each stack?

Accepted Answer

A) 42 
B) 45 
C) 44 
D) 43 
A) 42 
B) 45 
C) 44 
D) 43

Question 15

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

Accepted Answer

A) True 
 B)False

Question 16

Without using a calculator, determine whether the first number is divisible by the second number.
-Is 233,682 divisible by 3?

Accepted Answer

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

Find the LCM for the given numbers by an appropriate method. -48, 162, and 9

Use least common multiple or greatest common divisor to solve the problem. -Planets A, B, and C orbit a certain star once every 2, 5, and 12 months, respectively. If the three planets are now in the same straight line, what is the smallest number of months that must pass Before they line up again?

Find the prime factorization. -1606

Without using a calculator, determine whether the first number is divisible by the second number. -Is 62,656,837 divisible by 77?

Find the GCD or LCM as indicated. -Given 56 and 96, find the LCM.

$\text { If } \operatorname { GCD } ( \mathrm { a } , \mathrm { b } ) = 2 \text {, then a or b can be odd }$

Provide the appropriate response. -How many twin prime pairs can be found from the numbers less than 100?

Solve the problem. -The local bakery marked down some day-old pies from $4.00 but kept the price over $3.00. All of the pies were sold, and the total amount of money from the sale of the pies was $43.55. How many Pies were sold?

Find the GCD or LCM as indicated. -Given 60 and 30, find the GCD.

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - $4 , \square 21 \text { is divisible by } 4$

Find the GCD for the given numbers by an appropriate method. -960 and 1800

Solve the problem. -Jim has 56 trees that he wants to plant in a rectangular array. List the possible arrays.

Use least common multiple or greatest common divisor to solve the problem. -George has 336 donuts and 462 bagels. He wants to divide his bagels and donuts into stacks so that there are the same number of pastries in each stack. What is the greatest number of pastries that he Can place in each stack?

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

Without using a calculator, determine whether the first number is divisible by the second number. -Is 233,682 divisible by 3?

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