Number Properties I

An INTEGER is a whole number. It is evenly divisible by 1.

The test writer wants to know if you remember there are both positive AND negative integers.

More words of “Wiz-dom” on integers

A DIGIT is an integer from 0 through 9. Integers that are larger than 9 and smaller than -9 have more than one digit. Numbers that involve decimals (e.g., 2.91) also have more than one digit.

The test wants to know if you recognize the PLACE VALUE of a digit.

More words of “Wiz-dom” on Digits

CONSECUTIVE NUMBERS are a sequence of numbers where the distance between them is constant. In other words, the difference between any two consecutive numbers in the sequence is the same.

The test writer wants to know if you see the pattern in a sequence of numbers.

More words of “Wiz-dom” on consecutive numbers

ZERO TIMES any number is zero. 1 TIMES any number is that number.

The test writer wants to know if you recognize situations where multiplication by zero and/or 1 is not very obvious.

What is the product of all non-negative even integers that are less than 10?

More words of “Wiz-dom” on ZERO TIMES any number

EVEN integers are evenly divisible by 2. The unit’s (or one’s) digit of an EVEN integer is 0, 2, 4, 6, or 8. ODD integers are not evenly divisible by 2. The unit’s digit of an ODD integer is 1, 3, 5, 7, or 9.

The test writer wants to know if you realize that 0 is an even number and if you can distinguish between odd and even integers. She is especially fond of questions that concern the nature of answers (odd or even) when you multiply/divide and add/subtract odd and even numbers.

More words of “Wiz-dom” on EVEN integers

POSITIVE numbers are greater than zero. NEGATIVE numbers are smaller than zero. Zero is neither positive nor negative.

The test writer wants to know if you remember that multiplying two positive numbers results in a positive answer, multiplying two negative numbers results in a positive answer, and multiplying a positive times a negative (or a negative times a positive) results in a negative answer.

More words of “Wiz-dom” on POSITIVE integers

RATIONAL NUMBERS can be expressed as an integer or a quotient of integers. (That means if you divide two whole numbers, the answer is “rational.”)
IRRATIONAL NUMBERS are all the rest. (That means they are neither integers nor quotients of the division of integers.) Irrational numbers have non-repeating patterns of numbers after the decimal place. For example, 3.333 and  are rational numbers, and are irrational numbers.

The test writer wants to know if you can distinguish between rational and irrational numbers.

More words of “Wiz-dom” on RATIONAL NUMBERS

REAL NUMBERS are the positive and negative numbers you usually encounter. 22, pi and  are real numbers.
IMAGINARY NUMBERS are numbers that contain the square root of negative numbers. For example, is an imaginary number.

The test writer uses the phrase “real number.” Don’t worry about what it means when you see the phrase because it usually doesn’t mean anything special. In my experience, it just serves as a distracter. Any answer that comes to mind is going to be a “real number” unless it involves the square root of a negative value. You probably aren’t going to think of any of those!

More words of “Wiz-dom” on REAL NUMBERS

A RANGE of numbers refers to all possible values from the least to the greatest between two numbers.

The test writer wants to know if you remember that there are decimal and fraction values between integers unless a word like “included” or “inclusive” is used.

More words of “Wiz-dom” on RANGE

You need to recognize PLACE VALUE.

The test writer wants to know if you recognize and can name the value of a digit based on where it is located in a number. For example, in the number 1,234,567.890, the 3 is in the ten-thousands place and the 0 is in the thousandths place. Remember “units” means the “ones” place or column. Digits to the right of the decimal start with tenths, not “oneths.” All place values to the right of the decimal place end in “th” or “ths.”

The REAL NUMBER LINE represents all real positive and negative numbers on a standard axis that is drawn to scale.

The test writer wants to know if you realize:

  • An opaque (filled-in) dot at the end of the line means that value is included.
  • An open dot at the end of the line means that value is not included.

Which of the following represents the numbers greater than 5? Which one represents five plus numbers greater than 5?

More words of “Wiz-dom” on the REAL NUMBER LINE

The ABSOLUTE VALUE of a number has to do with the SIZE of the number without respect to the SIGN.

The test writer wants to know if you recognize the absolute value of –3 is the same as +3. It is noted as a number enclosed within two vertical bars, for example, and  have the same absolute value, 4.

Words of “Wiz-dom”—Deal with the values inside the bars just like you deal with values inside parentheses. That is, solve what’s inside the bars first, eliminate negative signs and then do what is outside the bars. When we get to algebra, you’ll see this issue is a little trickier. For now, we’ll worry about what it means for arithmetic.

since the sign is dropped from –1.

Sample Questions

1.  If n is an integer, which of the following expressions must result in an integer?

(A) 
(B) 
(C) 
(D) 
(E) 

Answer to question #1

2.  In a list of consecutive numbers that starts 1, 4, 7, 10…, what will the 15th number be?

A. 10-3(15)
B. 1+4+7+10
C. 10+3(11)
D. 1+3(15)
E. 10+3(15)

Answer to question #2

3.  If x is a positive even integer and y is a negative odd integer, which of the following must be true about their product?

A. It is an odd number that is smaller than y.
B. It is an even number that is smaller than y
C. It is an odd number that is larger than y.
D. It is an even number that is larger than y
E. It is an odd number between x and y.

Answer to question #3

4.  If all the digits of a three digit integer are either a 6 or a 0, the integer must be

A. evenly divisible by 6
B. evenly divisible by 10
C. an odd number
D. evenly divisible by 3
E. evenly divisible by 2

Answer to question #4

5.  If  and , xy =

Answer to question #5

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