Number Properties I

The following are terms and concepts that are frequently part of the SAT and ACT tests.  Be sure to pay special attention to the information in the box following each explanation.  They reveal the basis of some of the tricks and traps that are used by the test writers and common mistakes made by test takers.

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

More words of “Wiz-dom” on Digits

PLACE VALUE refers to the position of a single digit in a number.

The west writer wants to know if you understanding the digits to the left of the decimal are called “ones” (or “units”), “tens,” “hundreds,” “thousands,” “ten thousands,” etc. and to the right of the decimal they are called “tenths,” “hundredths,” “thousandths,” etc.

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

The test writer wants to know if you see the pattern in a sequence of integers.  This concept is often part of arithmetic average (mean) questions.  For example, “If the sum of 7 consecutive even integers is …”

More words of “Wiz-dom” on Consecutive Integers

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

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/Odd 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/Negative 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 a Range of Numbers

The NUMBER LINE organizes all numbers in sequence based on their size.

The test writer wants to know if you remember that 1) there are fractions (or decimals) between integers and 2) negative numbers with larger absolute values are smaller numbers. For example, -8 is smaller than -3 and -1/3 is smaller than -1/12.

More words of “Wiz-dom” on the Number Line

EQUIVALENT FORMS of a number means that a number can be expressed in a variety of ways without changing its value. For example, .

The test writer wants to know if you can convert numbers that are expressed in different forms into the same form so that you can perform calculations with them. For example, add the following

More Words of “Wiz-dom” on Equivalent Forms

Sample Questions

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

(A) n/5
(B) n/4
(C) n/3
(D) n/2
(E) n/1

Answer to Question #3

2. Which of the following is the thousands digit in the number 12,345.6789?

(A) 1
(B) 2
(C) 5
(D) 8
(E) 9

Answer to Question #2

12. 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 #12

14. 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 #14

18.  What is one possible number that comes between 1/3 and 1/4?

Answer to Question #18

5.  If all the digits of a three digit integer are either a 6 or a 0, which of the following must me true?

(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 #7

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