THE NUMERIC ENTRY FORMAT NEW The Quantitative Reasoning section of the computer-based GRE might include one numeric entry question, which you answer by entering a number via the keyboard
Trang 1Handle Lengthy, Confusing Questions One Part at a Time
Data interpretation questions can be wordy and confusing Don’t panic Keep in mind
that lengthy questions almost always call for a sequence of two discrete tasks For the
first task, read just the first part of the question When you’re done, go back to the
question and read the next part
Know the Overall Size of the Number That the Question Requires
The test designers will lure careless test takers with wrong answer choices that result
from common computational errors So always ask yourself how great (or small) a value
you’re looking for in the correct answer For instance:
• Is it a double-digit number, or an even greater number?
• Is it a percentage that is obviously greater than 50 percent?
By keeping the big picture in mind, you’re more likely to detect whether you made an
error in your calculation
To Save Time, Round Off Numbers—But Don’t Distort Values
Some data interpretation questions will ask for approximate values, so it’s okay to round
off numbers to save time; rounding off to the nearest appropriate unit or half-unit
usually suffices to give you the correct answer But don’t get too rough in your
approximations Also, be sure to round off numerators and denominators of fractions in
the same direction (either both up or both down), unless you’re confident that a rougher
approximation will suffice Otherwise, you’ll distort the size of the number
Don’t Split Hairs When Reading Line Charts and Bar Graphs
These are the two types of figures that are drawn to scale If a certain point on a chart
appears to be about 40 percent of the way from one hash mark to the next, don’t hesitate
to round up to the halfway point (The number 5 is usually easier to work with than 4
or 6.)
THE NUMERIC ENTRY FORMAT (NEW)
The Quantitative Reasoning section of the computer-based GRE might include one
numeric entry question, which you answer by entering a number via the keyboard
instead of selecting among multiple choices If you encounter a numeric entry question
on your exam, it may or may not count toward your GRE score But you should assume
that it counts, and you should try your best to answer it correctly
A numeric entry question is inherently more difficult than the same question
accom-panied by multiple choices because you cannot use the process of elimination or
consult the answer choices for clues as to how to solve the problem What’s more, the
numeric entry format practically eliminates the possibility of lucky guesswork
Nev-ertheless, just as with multiple-choice questions, the difficulty level of numeric entry
questions runs the gamut from easy to challenging
A numeric entry question might call for you to enter a positive or negative integer or
decimal number (for example, 125 or 214.2) Or it might call for you to enter a
Trang 2fraction by typing a numerator in one box and typing a denominator below it in another box In this section, you’ll look at some examples of these variations
Decimal Number Numeric Entries
A numeric entry question might ask for a numerical answer that includes a decimal point In working these problems, do NOT round off your answer unless the question
explicitly instructs you to do so The following question, for example, calls for a precise
decimal number answer In working the problem, you should not round off your answer.
(The instructions below the fill-in box are the same for any numeric entry question.)
17 What is the sum of=0.49,3
4, and 80% ?
The correct answer is 2.25 To calculate the sum, first convert all three
values to decimal numbers:
=0.49 = 0.7,3
4= 0.75, and 80% = 0.8 Now combine by addition:
0.7 + 0.75 + 0.8 = 2.25
To receive credit for a correct answer, you must enter 2.25 in the answer box
Positive vs Negative Numeric Entries
A numeric entry question might be designed so that its answer might conceivably be either a positive or negative number In working this type of problem, should you decide that the correct answer is a negative number, use the keyboard’s hyphen (dash) key to enter a “minus” sign before the integer (To erase a “minus” sign, press the hyphen key again.) Here’s an example:
18 If ,x = (x + 1) 2 (x + 2) 2 (x 2 1) + (x 2 2), what is the value of ,100.
+ ,99.?
The correct answer is 24 To answer the question, substitute 100 and
99, in turn, for x in the defined operation:
,100 = 101 2 102 2 99 + 98 = 22 ,99 = 100 2 101 2 98 + 97 = 22 Then combine by addition: ,100 + ,99 = 22 + (22) = 24
PART IV: Quantitative Reasoning 174
NOTE
The GRE testing service plans
to gradually increase the
number of numeric entry
questions on the GRE, but
probably not in 2009 Check
the official GRE Web site for
updates to this policy.
www.petersons.com
Trang 3To receive credit for a correct answer, you must enter 24 in the answer
box
Numeric Entries That Are Fractions
A numeric entry problem might call for an answer that is a fraction—either positive or
negative To answer this type of question, you enter one integer in a numerator (upper)
box and another integer in a denominator (lower) box Fractions do not need to be
reduced to their lowest terms Here’s an example:
19 A 63-member legislature passed a bill into law by a 5 to 4 margin No
legislator abstained from voting What fractional part of the votes on the
bill were cast in favor of passing the bill?
Give your answer as a fraction
The correct answer is 35
63 You know that for every 5 votes cast in favor
of the bill, 4 were cast against it Thus, 5 out of every 9 votes, or 35 of all
63 votes, were cast in favor of the bill To receive credit for this question,
you must enter 35 in the upper (numerator) box and 63 in the lower
(denominator) box
Numeric Entries Involving Units of Measurement
If the answer to a numeric entry question involves a unit of measurement (such as
percent, degrees, dollars, or square feet), the question will clearly indicate the unit of
measurement in which you should express your answer—as in the following example
20 Four of the five interior angles of a pentagon measure 110°, 60°, 120°, and
100° What is the measure of the fifth interior angle?
degrees
The correct answer is 150 Notice that the question makes clear that
you are to express your numerical answer in terms of degrees Since the
figure has five sides, the sum of the angle measures is 540 Letting x equal
the fifth interior angle:
540 = x + 110 + 60 + 120 + 100
540 = x + 390
150 = x
To receive credit for the question, you must enter 150 in the answer box
ALERT!
If a numeric entry question asks you to enter a fraction,
you do not need to reduce
the fraction to lowest terms, but the numerator and denominator must each be an integer.
Trang 4SUMMING IT UP
• The 45-minute Quantitative Reasoning section tests your proficiency in per-forming arithmetical operations and solving algebraic equations and inequalities
It also tests your ability to convert verbal information into mathematical terms;
to visualize geometric shapes and numerical relationships; to interpret data presented in charts, graphs, tables, and other graphical displays; and to devise intuitive and unconventional solutions to conventional mathematical problems
• Problem Solving is one of two basic formats for questions in the Quantitative Reasoning section of the GRE (the other is Quantitative Comparison)
• All Problem Solving questions are five-item multiple-choice questions (although you might encounter one numeric entry question as well) About one half of the questions are story problems Numerical answer choices are listed in either ascending or descending order
• Some Problem Solving questions involve the interpretation of graphical data such
as tables, charts, and graphs The focus is on skills, not number crunching
• Follow and review the five basic steps for handling GRE Problem Solving ques-tions outlined in this chapter and apply them to this book’s Practice Tests Then review them again just before exam day
PART IV: Quantitative Reasoning 176
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Trang 5OVERVIEW
• Key facts about GRE Quantitative Comparisons
• The 6-step plan
• Quantitative Comparison strategies
• Summing it up
In this chapter, you’ll focus exclusively on the Quantitative Comparison
format, one of the two basic formats on the GRE Quantitative Reasoning
section First, you’ll learn a step-by-step approach to handling any
Quanti-tative Comparison Then you’ll apply that approach to some GRE-style
examples Later in the chapter, you’ll learn useful strategies for comparing
quantities and for avoiding mistakes that test takers often commit when
comparing quantities
You first looked at GRE Quantitative Comparisons in Chapter 2 and in this
book’s Diagnostic Test Let’s quickly review the key facts about the
Quanti-tative Comparison format
KEY FACTS ABOUT GRE QUANTITATIVE COMPARISONS
Where: The 45-minute Quantitative Reasoning section
How Many: Approximately 14 test items (out of 28 total), mixed in with
Problem Solving questions
What’s Tested:
• Your understanding of the principles, concepts, and rules of arithmetic,
algebra, and geometry
• Your ability to devise intuitive and unconventional methods of comparing
quantitative expressions
• Your ability to visualize numerical relationships and geometric shapes
• Your ability to convert verbal information into mathematical terms
Areas Covered: Any of the Quantitative Reasoning areas listed in the
Quan-titative Reasoning section of Chapter 2 is fair game for QuanQuan-titative
Com-parisons, which cover the same mix of arithmetic, algebra, and geometry as
Problem Solving questions
.
Trang 6Directions: Quantitative Comparison directions are similar to the following The
“Notes” are the same as for Problem Solving questions:
Directions: The following questions consist of two quantities, one in Column A
and one in Column B You are to compare the two quantities and choose whether
(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.
Common Information: Information concerning one or both of the quantities to
be compared is centered above the two columns A symbol that appears in both columns represents the same thing in Column A as it does in Column B
Notes:
• All numbers used are real numbers
• All figures lie on a plane unless otherwise indicated
• All angle measures are positive
• All lines shown as straight are straight Lines that appear jagged can also be assumed to be straight (lines can look somewhat jagged on the computer screen)
• Figures are intended to provide useful information for answering the ques-tions However, except where a figure is accompanied by a “Note” stating that the figure is drawn to scale, solve the problem using your knowledge of
mathematics, not by visual measurement or estimation.
Other Key Facts:
• There are only four answer choices, and they’re the same for all Quantitative Comparison questions
• All information centered above the columns applies to both columns Some Quan-titative Comparisons will include centered information; others won’t
• The same variable (such as x) in both columns signifies the same value in both
expressions
• As in Problem Solving questions, figures are not necessarily drawn to scale, so don’t rely solely on the visual appearance of a figure to make a comparison
• Quantitative Comparisons are not inherently easier or tougher than Problem Solving questions, and their level of difficulty and complexity varies widely, as determined by the correctness of your responses to previous questions on the computer-adaptive version of the GRE
• You’ll make fewer calculations and solve fewer equations for Quantitative Com-parison questions than for Problem Solving questions What’s being tested here is mainly your ability to recognize and understand principles, not your ability to work step-by-step toward a solution
• Calculators are prohibited, but scratch paper is provided
PART IV: Quantitative Reasoning 178
NOTE
In this book, the four choices
for answering Quantitative
Comparisons are labeled (A),
(B), (C), and (D) On the
computer-based GRE, they
won’t be lettered, but they’re
always listed in the same order
as they are here.
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Trang 7THE 6-STEP PLAN
The first task in this lesson is to learn the 6 basic steps for handling any GRE
Quantitative Comparison Just ahead, you’ll apply these steps to three GRE-style
Quantitative Comparisons
Step 1: Size Up the Question
What general area does the question deal with? What mathematical principles and
formulas are likely to come into play? Does it appear to require a simple arithmetical
calculation, or does it seem more “theoretical”—at least at first glance?
Step 2: Check for Shortcuts and Clues
Check both quantities for possible shortcuts and for clues as to how to proceed Here are
three different features to look for:
If both quantities contain common numbers or other terms, you might be able to
simplify by canceling them Be careful, though; sometimes you can’t cancel terms
(See the strategies later in this chapter.)
If one quantity is a verbal description but the other one consists solely of numbers
and variables, you’re dealing with a Problem Solving question in disguise Your
task is to work from the verbal expression to a solution, then compare that
solution to the other quantity
If the centered information includes one or more equations, you should probably
solve the equation(s) first
Step 3: Deal with Each Quantity
If the problem includes any centered information (above the two quantities), ask
yourself how the quantity relates to it Then do any calculations needed
Step 4: Consider All Possibilities for Unknowns (Variables)
Consider what would happen to each quantity if a fraction, negative number, or the
number zero (0) or 1 were plugged in to the expression
Step 5: Compare the Two Quantities
Compare the quantities in Columns A and B Select one of the four answer choices, based
on your analysis
Step 6: Check Your Answer
If you have time, double-check your answer It’s a good idea to make any calculations
with pencil and paper so you can double-check your computations before confirming the
answer Also, ask yourself again:
• Did I consider all possibilities for unknowns?
• Did I account for all the centered information (above the two quantities)?
Trang 8Applying the 6-Step Plan
Let’s apply these 6 steps to three GRE-style Quantitative Comparisons At the risk of giving away the answers up front, the correct answer—(A), (B), (C), or (D)—is different for each question
4
13 52
5 6
5
3 10
10 12
This is a relatively easy question Approximately 85 percent of test takers respond correctly to questions like this one Here’s how to compare the two quantities using the 6-step approach:
Step 1: Both quantities involve numbers only (there are no variables), so this
com-parison appears to involve nothing more than combining fractions by adding them Since the denominators differ, then what’s probably being covered is the concept of
“common denominators.” There’s nothing theoretical or tricky here
Step 2: You can cancel 5
6 from Quantity A and
10
12 from Quantity B, because these
two fractions have the same value You don’t affect the comparison at all by doing so Canceling across quantities before going to step 3 will make that step far easier
Step 3: For each of the two quantities, find a common denominator, then add the two
fractions:
Quantity A: 1
4
13 52
1 4
1 4
1 2
Quantity B: 1
5+
3
10=
2
10+
3
10=
5
10or
1 2
Step 4: There are no variables, so go on to step 5.
Step 5: Since 1
2
1 2
= , the two quantities are equal
Step 6: Check your calculations (you should have used pencil and paper) Did you
convert all numerators properly? If you are satisfied that your calculations are
correct, confirm your response and move on The correct answer is (C).
PART IV: Quantitative Reasoning 180
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Trang 92. O lies at the center of the circle.
This is a moderately difficult question Approximately 55 percent of test takers
respond correctly to questions like this one Here’s how to compare the two quantities
using the 6-step approach:
Step 1: One quick look at this problem tells you that you need to know the formula for
finding a circle’s circumference and that you should look for a relationship between
the triangle and the circle If you recognize the key as the circle’s radius, then you
shouldn’t have any trouble making the comparison
Step 2: A quick glance at the two quantities should tell you that you should proceed
by finding the circumference of the circle in terms x (Quantity B), then comparing it to
Quantity A
Step 3: Because the angle at the circle’s center is 60°, the triangle must be
equi-lateral All three sides are congruent (equal in length), and they are all congruent to
the circle’s radius (r) Thus, x = r A circle’s circumference (distance around the circle)
is defined as 2pr, and p ' 3.1 Since x = r, the circumference of this circle equals
approximately (2)(3.1)(x), or a little more than 6x.
Step 4: You’ve already determined the value of x to the extent it’s possible, given the
information Its value equals r (the circle’s radius) The comparison does not provide
any information to determine a precise value of x.
Step 5: Since the circumference of this circle must be greater than 6x, Quantity B is
greater than Quantity A There’s no need to determine the circumference any more
precisely As long as you’re confident that it’s greater than x, that’s all the number
crunching you need to do
Step 6: Check your calculation again (you should have used pencil and paper) Make
sure you used the correct formula (It’s surprisingly easy to confuse the formula for a
circle’s area with the one for its circumference—especially under exam pressure!) If
you are satisfied your analysis is correct, confirm your response and move on The
correct answer is (B).
Trang 103. xy Þ 0
This is a relatively difficult question Approximately 40 percent of test takers respond correctly to questions like this one Here’s how to compare the two quantities using the 6-step approach:
Step 1: This question involves quadratic expressions and squaring a binomial Since
there are two variables here (x and y) but no equations, you won’t be calculating
precise numerical values for either variable Note the centered information, which
establishes that neither x nor y can be zero (0).
Step 2: On their faces, the two quantities don’t appear to share common terms that
you can simply cancel across quantities But they’re similar enough that you can bet
on revealing the comparison by manipulating one or both expressions
Step 3: Quantity A is simplified, so leave it as is—at least for now Square Quantity B:
2
Notice that the result is the same expression as the one in Column A, with the
addition of the middle term 2xy Now you can cancel common terms across columns, so you’re left to compare zero (0) in Column A with 2xy in Column B.
Step 4: The variables x and y can each be either positive or negative Be sure to
account for different possibilities For example, if x and y are both positive or both
negative, then Quantity B is greater than zero (0), and thus greater than Quantity A However, if one variable is negative and the other is positive, then Quantity B is less than zero (0), and thus less than Quantity A
Step 5: You’ve done enough work already to determine that the correct answer must
be choice (D) You’ve proven that which quantity is greater depends on the value of at least one variable There’s no need to try plugging in different numbers The rela-tionship cannot be determined from the information given
Step 6: Check your squaring in step 3, and make sure your signs (plus and minus) are
correct If you’re satisfied that your analysis is correct, confirm your response and
move on The correct answer is (D).
PART IV: Quantitative Reasoning 182
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