Each digit of a base six number has a place value that is a power of six. The lowest four powers of 6, beginning with 1, are , so

The whole numbers comprise 0 and the positive integers. is a negative integer, so it belongs to the set of integers, but not the set of whole numbers. Also, all integers are rational by definition, since every integer can be expressed as the quotient of two integers (the integer divided by 1, for example). Therefore, is an integer and a rational number, but not a whole number, and the correct response is two.

A set with elements has subsets. Since , a set with 64 subsets has 6 elements.

The number of subsets of a set with elements is , so this eight-element set has subsets.

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.

We need to find ways to factor 32 such that the three factors are different, and then find the sum of those factors in each case.

32 can be factored as the product of three integers in five differrent ways:

I)

II)

III)

IV)

V)

Of the five ways, only the second and third involve three distinct factors.

In Case II, the sum of the factors is

.

In Case III, the sum of the factors is

.

The only possible correct response is 19.

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

is irrational but real.

Similarly, which is irrational but real.

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.

The whole numbers comprise 0 and the positive integers. is a negative integer, so it belongs to the set of integers, but not the set of whole numbers. Also, all integers are rational by definition, since every integer can be expressed as the quotient of two integers (the integer divided by 1, for example). Therefore, is an integer and a rational number, but not a whole number, and the correct response is two.

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.