Question 1

Determine whether or not one or more pairs of twin primes exist between the pair of numbers given. If so, identify the twin primes.
-99 and 107

Accepted Answer

A) 101, 103, 105 
B) 101, 103 
C) 103, 105 
D) No 
A) 101, 103, 105 
B) 101, 103 
C) 103, 105 
D) No B

Question 2

Find the least common multiple of the numbers in the group.
-8, 28

Accepted Answer

A) 56 
B) 28 
C) 224 
D) 14 
A) 56 
B) 28 
C) 224 
D) 14 A

Question 3

Solve the problem relating to the Fibonacci sequence.
-If an 8-inch wide rectangle is to approach the golden ratio, what should its length be?

Accepted Answer

A) 10 in 
B) 5 in 
C) 13 in 
D) 12 in 
A) 10 in 
B) 5 in 
C) 13 in 
D) 12 in C

Question 4

Determine all values for the digit x that make the first number divisible by the second number. If none exist, so state.
-214,21x is divisible by 11.

Accepted Answer

The answer of Determine all values for the digit x...

Question 5

A natural number which is not deficient must be abundant.

Accepted Answer

A) True 
 B)False

Question 6

Determine whether the statement is true or false.
-Every natural number of the form 4k + 5 is prime.

Accepted Answer

A) True 
 B)False

Question 7

Answer the question.
-Three clocks chime every 10 minutes, 22 minutes, and 55 minutes, respectively. If the three clocks chime together, how much time must pass before they will chime together again?

Accepted Answer

A) 1210 minutes 
B) 220 minutes 
C) 110 minutes 
D) 87 minutes 
A) 1210 minutes 
B) 220 minutes 
C) 110 minutes 
D) 87 minutes

Question 8

Find the greatest common factor of the numbers in the group.
-60, 72

Accepted Answer

A) 6 
B) 12 
C) 2 
D) 1 
A) 6 
B) 12 
C) 2 
D) 1

Question 9

All prime numbers are also deficient numbers.

Accepted Answer

A) True 
 B)False

Question 10

Use divisibility tests to decide whether the first number is divisible by the second.
-348,951; 10

Accepted Answer

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

Question 11

Determine all values for the digit x that make the first number divisible by the second number. If none exist, so state.
-414,3x2 is divisible by 8 but not 16.

Accepted Answer

The answer of Determine all values for the digit x...

Question 12

Write the number as the sum of two primes. There may be more than one way to do this.
-18

Accepted Answer

A) 5 + 13, 7 + 11 
B) 3 + 15, 7 + 11 
C) 9 + 9 
D) 3 + 15, 5 + 13 , 7 + 11 
A) 5 + 13, 7 + 11 
B) 3 + 15, 7 + 11 
C) 9 + 9 
D) 3 + 15, 5 + 13 , 7 + 11

Question 13

Give the prime factorization of the number. Use exponents when possible.
-177

Accepted Answer

A)  $3 \cdot 57$ 
B)  $3 \cdot 59$ 
C)  $3 ^ { 2 } \cdot 59$ 
D)  $3 ^ { 2 }$ 
A)  $3 \cdot 57$ 
B)  $3 \cdot 59$ 
C)  $3 ^ { 2 } \cdot 59$ 
D)  $3 ^ { 2 }$

Question 14

Fermat proved that every odd prime number can be expressed as the difference of two
squares in one and only one way. Express each of the first 6 odd prime numbers as the
difference of two squares.

Accepted Answer

3 = 4 - 1
5 = 9 - 4

Question 15

Find the greatest common factor of the numbers in the group.
-104, 567

Accepted Answer

A) 6 
B) 1 
C) 91 
D) 52 
A) 6 
B) 1 
C) 91 
D) 52

Question 16

Use the formula indicated to determine the prime number generated for the given value of n.
-$p = n ^ { 2 } - 79 n + 1,601 ; n = 9$

Accepted Answer

A) 2393 
B) 113 
C) -809 
D) 971 
A) 2393 
B) 113 
C) -809 
D) 971

Question 17

Write the number as the sum of two primes. There may be more than one way to do this.
-12

Accepted Answer

A) 2 + 10 
B) 3 + 9 
C) 5 + 7 
D) 6 + 6 
A) 2 + 10 
B) 3 + 9 
C) 5 + 7 
D) 6 + 6

Question 18

Use divisibility tests to decide whether the first number is divisible by the second.
-827,711; 5

Accepted Answer

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

Question 19

Solve the problem.
-Primorial primes are those of the form $p \# \pm 1$.
Apply this formula to the value $p = 11$ to obtain two numbers and state whether both, neither, or exactly one of these numbers is prime.

Accepted Answer

11# - 1 = 2309 and 1

Question 20

For the following amicable pair, determine whether neither, one, or both of the members are happy, and whether the pair is a happy amicable pair.
-2620 and 2924

Accepted Answer

A) both; happy 
B) one; happy 
C) neither; not happy 
D) one; not happy 
A) both; happy 
B) one; happy 
C) neither; not happy 
D) one; not happy

Determine whether or not one or more pairs of twin primes exist between the pair of numbers given. If so, identify the twin primes. -99 and 107

Find the least common multiple of the numbers in the group. -8, 28

Solve the problem relating to the Fibonacci sequence. -If an 8-inch wide rectangle is to approach the golden ratio, what should its length be?

Determine all values for the digit x that make the first number divisible by the second number. If none exist, so state. -214,21x is divisible by 11.

A natural number which is not deficient must be abundant.

Determine whether the statement is true or false. -Every natural number of the form 4k + 5 is prime.

Answer the question. -Three clocks chime every 10 minutes, 22 minutes, and 55 minutes, respectively. If the three clocks chime together, how much time must pass before they will chime together again?

Find the greatest common factor of the numbers in the group. -60, 72

All prime numbers are also deficient numbers.

Use divisibility tests to decide whether the first number is divisible by the second. -348,951; 10

Determine all values for the digit x that make the first number divisible by the second number. If none exist, so state. -414,3x2 is divisible by 8 but not 16.

Write the number as the sum of two primes. There may be more than one way to do this. -18

Give the prime factorization of the number. Use exponents when possible. -177

Fermat proved that every odd prime number can be expressed as the difference of two squares in one and only one way. Express each of the first 6 odd prime numbers as the difference of two squares.

Find the greatest common factor of the numbers in the group. -104, 567

Use the formula indicated to determine the prime number generated for the given value of n. - $p = n ^ { 2 } - 79 n + 1,601 ; n = 9$

Write the number as the sum of two primes. There may be more than one way to do this. -12

Use divisibility tests to decide whether the first number is divisible by the second. -827,711; 5

Solve the problem. -Primorial primes are those of the form $p \# \pm 1$ . Apply this formula to the value $p = 11$ to obtain two numbers and state whether both, neither, or exactly one of these numbers is prime.

For the following amicable pair, determine whether neither, one, or both of the members are happy, and whether the pair is a happy amicable pair. -2620 and 2924

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Voting and Apportionment

Filters

Exam 5: Number Theory

Determine whether or not one or more pairs of twin primes exist between the pair of numbers given. If so, identify the twin primes. -99 and 107

Find the least common multiple of the numbers in the group. -8, 28

Solve the problem relating to the Fibonacci sequence. -If an 8-inch wide rectangle is to approach the golden ratio, what should its length be?

Determine all values for the digit x that make the first number divisible by the second number. If none exist, so state. -214,21x is divisible by 11.

A natural number which is not deficient must be abundant.

Determine whether the statement is true or false. -Every natural number of the form 4k + 5 is prime.

Answer the question. -Three clocks chime every 10 minutes, 22 minutes, and 55 minutes, respectively. If the three clocks chime together, how much time must pass before they will chime together again?

Find the greatest common factor of the numbers in the group. -60, 72

All prime numbers are also deficient numbers.

Use divisibility tests to decide whether the first number is divisible by the second. -348,951; 10

Determine all values for the digit x that make the first number divisible by the second number. If none exist, so state. -414,3x2 is divisible by 8 but not 16.

Write the number as the sum of two primes. There may be more than one way to do this. -18

Give the prime factorization of the number. Use exponents when possible. -177

Fermat proved that every odd prime number can be expressed as the difference of two squares in one and only one way. Express each of the first 6 odd prime numbers as the difference of two squares.

Find the greatest common factor of the numbers in the group. -104, 567

Use the formula indicated to determine the prime number generated for the given value of n. - p=n2−79n+1,601;n=9p = n ^ { 2 } - 79 n + 1,601 ; n = 9p=n2−79n+1,601;n=9

Write the number as the sum of two primes. There may be more than one way to do this. -12

Use divisibility tests to decide whether the first number is divisible by the second. -827,711; 5

Solve the problem. -Primorial primes are those of the form p#±1p \# \pm 1p#±1 . Apply this formula to the value p=11p = 11p=11 to obtain two numbers and state whether both, neither, or exactly one of these numbers is prime.

For the following amicable pair, determine whether neither, one, or both of the members are happy, and whether the pair is a happy amicable pair. -2620 and 2924

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Voting and Apportionment

Filters

Use the formula indicated to determine the prime number generated for the given value of n. - $p = n ^ { 2 } - 79 n + 1,601 ; n = 9$

Solve the problem. -Primorial primes are those of the form $p \# \pm 1$ . Apply this formula to the value $p = 11$ to obtain two numbers and state whether both, neither, or exactly one of these numbers is prime.