Victory for the ACT Student Text 15e

210 • M ATH

PROPERTIES OF NUMBERS

If n ‹• –Š‡ ϐ‹”•– —„‡” ‹ ƒ •‡”‹‡• ‘ˆ –Š”‡‡ consecutive even numbers, which of the following expressions represents the sum of the three numbers? F. n + 2 G. n + 4 H. n If n is an odd number, which of the following expressions represents the third odd number following n ? A. n If x 0 1 , which of the following expressions is the largest? F. x G. x 2 H. x 6 J. n 3 6 K. ( ) n 6 3 + 3 B. n + 4 C. n + 6 D. 3 n + 3 E. 4 n + 4

17. Two cables with lengths 360 inches and 420 inches are to be cut into pieces of all the same length without any waste. If the pieces are to be the greatest possible length, how many pieces can be cut? A. 6 B. 7 C. 13 D. 20 E. 60

14.

Throwback to Math Class Recall the following †‡ϐ‹‹–‹‘• ‘ˆ –Š‡ different types of numbers: Natural: all positive whole numbers plus zero Integers: all negative and positive whole numbers, plus zero Rational: all numbers that can be written as a ratio (fraction) Re l numbers: all rational and irrational numbers Complex numbers: all real and imaginary numbers Consecutive numbers: numbers in counting order

2 3 4 − + − − = ? F. –5 G. –4 H. –1 J. 1 K. 9

15.

18.

For all nonzero values of a and b , the value of which of the following expressions is always positive? A. | | a b − + B. | | a b

19.

16.

C. | | | | a b − + D. | | | | a b E. | | | | a b − + −

2 J. x 3 K. x

+ 1

Throwback to Math Class Memorize the following principles of positive and negative numbers: ( ) ( ) ( ) + + = + ( ) ( ) ( ) − − = + ( ) ( ) + − or ( ) ( ) ( ) − + = −

( ) ( ) ( ) ' + + = + ( ) ( ) ( ) ' − − = + ( ) ( ) ' + −

or ( ) ( ) ( ) ' − + = −

Plug & Chug Be careful when using the plug-and-chug strategy for items such as #16. In some of the previous problems, you could plug in any value for x , but item #16 states that x must be between 0 and 1. Thus, choose a simple fraction between 0 and 1 to test. If you pick a value outside of this range, you will arrive at an incorrect answer.