Number Properties II

The ORDER OF OPERATIONS is important when doing problems on the SAT and ACT: Parentheses, Exponents, Multiplication/Division, and Addition/Subtraction.

The test writer wants to know if you can do problems in the right order. You will see both arithmetic and algebra questions that test your skills at doing the math steps in the correct sequence. Sometimes they look like algebra but you simply plug in the given numbers and treat it as an arithmetic question using: “Please Excuse My Dear Aunt Sally” or “PEMDAS”. Watch the signs! In some countries (e.g., Canada), students learn “BEMDAS,” which is the same thing except they say “brackets” instead of “parentheses.”

 What is the value of (-x)3 + (x + y) when x = -2 and y = -3?

More words of “Wiz-dom” on Order of Operations

The FACTORS of an integer are the integers that divide evenly into it without having a remainder. Every integer (other than 1) has at least two different factors: 1 and itself.

The test writer wants to know if you can determine all the factors of a given integer.

More words of “Wiz-dom” on Factors

The MULTIPLES of an integer are the numbers that it divides into evenly. It’s the opposite of factors.

The test writer wants to know if you realize that every integer has an infinite number of multiples.

More words of “Wiz-dom” on Multiples

A PRIME number is an integer that has exactly two different factors: 1 and itself.

The test writer wants to know if you realize that 2 is the smallest and only even prime number. 1 is NOT a prime number. (It doesn’t have two DIFFERENT factors.)

More words of “Wiz-dom” on a Prime Number

Integers are PROPORTIONALto one another if they are multiples or factors of one another.

The test writer wants to know if you understand directly (multiples) and indirectly proportional (reciprocal multiple, e.g., if one quantity is multiplied by 3, the other is multiplied by 1/3).

More words of “Wiz-dom” on Proportional

The REMAINDER is what’s left over if a division problem does not come out evenly.

The test writer wants to know if you realize the decimals on your calculator when you divide are not the remainder. In the test writer’s mind, the remainder is an integer that is represented by the numerator of a fraction with the denominator being the number you divided by.

More words of “Wiz-dom” on the Remainder

Sample Questions

6.  How many prime factors does the number 24 have?

(A) 6
(B) 4
(C) 3
(D) 2
(E) 0

Answer to Question #6

7.  In a division problem x/7, the remainder is r. How many possible odd values for r exist?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 6

Answer to Question #7

18.  If the sum of two consecutive odd numbers is 28, what is their product?

Answer to Question #18

5.  If m/9 is an integer, all of the following are possible values of m EXCEPT?

(A) 18
(B) 81
(C) 171
(D) 271
(E) 297

Answer to Question #5

20.  The sum of x consecutive integers is odd. The first integer in the sequence is even. Which of the following CANNOT be x?

(A) 2
(B) 3
(C) 4
(D) 6
(E) 7

Answer to Question #20

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