### All GED Math Resources

## Example Questions

### Example Question #11 : Numbers

How many subsets with three elements does the set have?

**Possible Answers:**

**Correct answer:**

The number of ways to select three elements from a set of eight is the number of combinations of three elements chosen from eight:

### Example Question #12 : Numbers

.

and are integers; they may or may not be distinct.

Which of the following could be equal to ?

**Possible Answers:**

**Correct answer:**

20 can be factored as:

I)

II)

III)

The positive difference of the factors can be any of:

Of the four choices, only 8 is possible.

### Example Question #11 : Types Of Numbers And Number Theory

Which of the following numbers is a rational number but not an integer?

**Possible Answers:**

**Correct answer:**

is a well-known irrational number and is not the correct choice.

. The square root of an integer is rational only if it is itself an integer; calculation yields a result of 1.414... This is not the correct choice.

, since . This is an integer and is not the correct choice.

, so, by definition, . This is rational and is therefore the correct choice.

### Example Question #11 : Numbers

To how many of the following sets does the number belong?

I) The set of whole numbers

II) The set of integers

III) The set of rational numbers

**Possible Answers:**

Two

One

None

Three

**Correct answer:**

One

, which is not an integer. It is not a whole number either, as the whole numbers consist of all (nonnegative) integers.

. As the quotient of integers, it is rational.

Therefore, belongs to the set of rational numbers but not to the other two sets. The correct response is one.

### Example Question #12 : Numbers

Which of the following base ten numbers has a base sixteen representation of exactly three digits?

**Possible Answers:**

**Correct answer:**

A number in base sixteen has powers of sixteen as its place values; starting at the right, they are .

The lowest base sixteen number with three digits would be

in base ten.

The lowest base sixteen number with four digits would be

in base ten.

Therefore, a number that is expressed as a three-digit number in base sixteen must fall in the range

.

Of the four numbers listed, 1,000 falls in that range.

### Example Question #11 : Numbers And Operations

Which of the following sets does belong to?

(a) Whole numbers

(b) Integers

**Possible Answers:**

Both (a) and (b)

(a) only

(b) only

Neither (a) nor (b)

**Correct answer:**

(b) only

The set of whole numbers comprises 0 and the so-called natural, or counting, numbers; that is, it is the set . is not one of these numbers.

The set of integers comprises these numbers as well as their (negative) opposites; that is, it is the set . is one of these numbers.

### Example Question #11 : Types Of Numbers And Number Theory

Which number is prime?

**Possible Answers:**

**Correct answer:**

A prime number is a positive integer which has exactly two factors - 1 and the number itself. 36, 38, and 39 can each be shown to have at least one other factor:

, so 2 and 18 are factors of 36, making 36 not prime.

, so 2 and 19 are factors of 38, making 38 not prime.

, so 3 and 13 are factors of 39, making 39 not prime.

37, however, cannot be evenly divided by any number except for 1 and itself, as can be seen below:

We do not need to go higher, since any higher possible factors have square greater than 37. 37 has been proved a prime number.

### Example Question #11 : Numbers

How many integers are in this set?

**Possible Answers:**

**Correct answer:**

An integer is an element of the set of numbers

that is, the so-called natural, or "counting", numbers, their (negative) opposites, and 0. , 2, , and 1 are elements of this set; and are not. The correct response is 4.

### Example Question #12 : 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 function with the specified range.

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

**Possible Answers:**

**Correct answer:**

Remember that a complex number is any number that includes or .

is irrational but real.

Similarly, which is irrational but real.

### Example Question #16 : 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:**

A prime number is a number that is evenly divisible by , the number itself, and no other number.

is the only number that is not evenly divisible by a number other than and the number itself.