GED Math : GED Math

Study concepts, example questions & explanations for GED Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #21 : Numbers And Operations

The set of real numbers is divided into several subsets including positive numbers and negative numbers, prime numbers and composite number, rational numbers and irrational numbers, etc. For the following questions, select the answer that is a member of the stated subset.

Which number is composite?

Possible Answers:

Correct answer:

Explanation:

A composite number is any number that isn't prime.

 The remaining numbers are prime.

Example Question #21 : Numbers

The set of real numbers is divided into several subsets including positive numbers and negative numbers, prime numbers and composite number, rational numbers and irrational numbers, etc. For the following questions, select the answer that is a member of the stated subset.

Which number is prime?

Possible Answers:

Correct answer:

Explanation:

Finding just one factor eliminates a number from the set of prime numbers. For a large number , begin with the smallest prime and exhaust all possible prime factors , etc. 

 

 with  remaining

 with  remaining

 with  remaining

 with  remaining

 with  remaining

 with  remaining

 

For bonus points, explain why it is only necessary to test prime factors up to and including .

 and  so .

 with  remaining.

For any number   with  remaining .

Thus, for a number  to be a factor of , it must pair with another factor .

However, we have already exhausted all of the prime numbers  so no prime factor exists.

 

Example Question #21 : Ged Math

The set of real numbers is divided into several subsets including positive numbers and negative numbers, prime numbers and composite number, rational numbers and irrational numbers, etc. For the following questions, select the answer that is a member of the stated subset.

Which expression is both rational and real?

Possible Answers:

Correct answer:

Explanation:

 which is the only rational number listed. 

 is real but not rational, that is, it cannot be expressed in the form  where  is the set of all integers and .

 and  are complex numbers and therefore not real. A complex number is any number that contains the expression  or .

Example Question #21 : Ged Math

The set of real numbers is divided into several subsets including positive numbers and negative numbers, prime numbers and composite number, rational numbers and irrational numbers, etc. For the following questions, select the answer that is a member of the stated subset.

Which number is prime?

Possible Answers:

Correct answer:

Explanation:

A prime number is a number with with no integer divisors, or factors, other than  and the number itself. The prime factors of  are  and . (For technical reasons,  is not considered prime and the number itself is not considered a factor.) The prime factors of  are  and . The prime factor of  is . , however, cannot be divided evenly by any integer other than  and  thus is prime.

Example Question #21 : Types Of Numbers And Number Theory

The set of real numbers is divided into several subsets including positive numbers and negative numbers, prime numbers and composite number, rational numbers and irrational numbers, etc. For the following questions, select the answer that is a member of the stated subset.

Which number is irrational?

Possible Answers:

Correct answer:

Explanation:

A rational number is any number that can be expressed in the form  where  and  are integers. 

The bar notation over the  indicates that it is an infinitely repeating sequence of s.  is rational,  is rational,  is rational, but any infinitely repeating decimal must be irrational.

Example Question #21 : Ged Math

The set of real numbers is divided into several subsets including positive numbers and negative numbers, prime numbers and composite number, rational numbers and irrational numbers, etc. For the following questions, select the answer that is a member of the stated subset.

Which number is positive?

Possible Answers:

Correct answer:

Explanation:

A positive number is any number that is greater than zero.  is a negative decimal,  is a negative quotient,  is non-negative but it is not strictly to the right of zero on the number line. 

 

, or pi, is a mathematical symbol for the ratio of a circle's circumference  divided by twice its radius  or

  

and, though irrational, is the only number listed that is strictly greater than zero. Irrational numbers are defined more rigorously later in the problem set.

Example Question #22 : Types Of Numbers And Number Theory

The set of real numbers is divided into several subsets including positive numbers and negative numbers, prime numbers and composite number, rational numbers and irrational numbers, etc. For the following questions, select the answer that is a member of the stated subset.

Which number is irrational?

Possible Answers:

Correct answer:

Explanation:

This is a bit of a trick question.  is an irrational number and the incorrect answers listed are all approximations of . However, every number listed can be expressed as a quotient of integers  except . The square root of two is irrational as is the square root of any prime number. 

Example Question #23 : Ged Math

The set of real numbers is divided into several subsets including positive numbers and negative numbers, prime numbers and composite number, rational numbers and irrational numbers, etc. For the following questions, select the answer that is a member of the stated subset.

Which number is both rational and real?

Possible Answers:

Correct answer:

Explanation:

A rational number is a number that can be expressed in the form  where both  and  are integers. 

 which is not only rational but an integer.

. Any square root of a prime number, the number 2 here, is irrational.

Finally, any square root of a negative number is complex and not real.

Example Question #22 : Ged Math

The set of real numbers is divided into several subsets including positive numbers and negative numbers, prime numbers and composite number, rational numbers and irrational numbers, etc. For the following questions, select the answer that is a member of the stated subset.

Which expression is a positive, real number?

Possible Answers:

Correct answer:

Explanation:

Remember that  and that any number that includes either  or  is complex and therefore not real. 

 which is real but negative.

The other numbers evaluate as

 ,

 , and 

.

Only  is a positive, real number. 

Example Question #24 : Ged Math

The set of real numbers is divided into several subsets including positive numbers and negative numbers, prime numbers and composite number, rational numbers and irrational numbers, etc. For the following questions, select the function with the specified range.

Which expression is complex? Specifically, which number cannot be written as a real number?

Possible Answers:

Correct answer:

Explanation:

All of the numbers given are complicated, but only one is complex in the mathematical sense. A complex number is a number expressed in the form  where  and  are real numbers (the formal, mathematical expression for this is   ) and 

 

 so  and  is complex.

Learning Tools by Varsity Tutors