Tài liệu Master the Gre 2010 - Part 27 ppt

24. a + b = 30

2b = 60 2 2a

Column A Column B

a b

(A) The quantity in Column A is greater.

(B) The quantity in Column B is greater.

(C) The quantities are equal.

(D) The relationship cannot be determined from the information given.

The correct answer is (D). An unwary test taker might waste time trying to

find the values of a and b, because the centered data appears at first glance to

provide a system of two linear equations with two unknowns. But you can easily

manipulate the second equation so that it is identical to the first:

2b = 60 2 2a

2b = 2~30 2 a!

b = 30 2 a

a + b = 30

As you can see, you’re really dealing with only one equation. Since you cannot

solve one equation in two unknowns, you cannot make the comparison.

Whenever you encounter a Quantitative Comparison question that calls for solving

one or more linear equations, stop in your tracks before taking pencil to paper. Size up

the equation to see whether it’s one of the two unsolvable kinds you learned about

here. If so, unless you’re given more information, the correct answer will be choice (D).

FACTORABLE QUADRATIC EXPRESSIONS WITH ONE

VARIABLE

A quadratic expression includes a “squared” variable, such as x2

. An equation is

quadratic if you can express it in this general form:

ax2 1 bx 1 c 5 0

Where:

x is the variable

a, b, and c are constants (numbers)

a Þ 0

b can equal 0

c can equal 0

Here are four examples (notice that the b-term and c-term are not essential; in other

words, either b or c, or both, can equal zero (0)):

Chapter 10: Math Review: Number Theory and Algebra 243

................................................................. .............................................................................................. ALERT!

If the centered information in

a Quantitative Comparison

consists of one or more linear

equations, never assume you

can solve for the variable(s).

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