Tài liệu Master the Gre 2010 - Part 25 ppt

1. |21 2 2| 2 |5 2 6| 2 |23 1 4| 5

(A) 25

(B) 23

(C) 1

(D) 3

(E) 5

The correct answer is (C). First, determine each of the three absolute values:

|21 2 2| 5 |23| 5 3

|5 2 6| 5 |21| 5 1

|23 1 4| 5 |1| 5 1

Then combine the three results: 3 2 1 2 1 5 1.

Because multiplication (or division) involving two negative terms always results in a

positive number:

• Multiplication or division involving any even number of negative terms gives you

a positive number.

• Multiplication or division involving any odd number of negative terms gives you

a negative number.

2. A number M is the product of seven negative numbers, and the number N

is the product of six negative numbers and one positive number. Which of

the following holds true for all possible values of M and N ?

I. M 3 N , 0

II. M 2 N , 0

III. N 1 M , 0

(A) I only

(B) II only

(C) I and II only

(D) II and III only

(E) I, II, and III

The correct answer is (C). The product of seven negative numbers is always a

negative number. (M is a negative number.) The product of six negative numbers

is always a positive number, and the product of two positive numbers is always a

positive number. (N is a positive number.) Thus, the product of M and N must be

a negative number; I is always true. Subtracting a positive number N from a

negative number M always results in a negative number less than M; II is always

true. However, whether III is true depends on the values of M and N. If |N| . |M|,

then N 1 M . 0, but if |N| , |M|, then N 1 M , 0.

Integers and the Four Basic Operations

When you combine integers using a basic operation, whether the result is an odd

integer, an even integer, or a non-integer depends on the numbers you combined. Here

are all the possibilities:

Chapter 10: Math Review: Number Theory and Algebra 223

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