Master gmat 2010 part 20 pdf

PLUG IN NUMBERS FOR “DEFINED OPERATION” QUESTIONSAt least one of your 25–26 Problem Solving questions will probably be an example of what’s called a “defined operation.” These questions

PLUG IN NUMBERS FOR “DEFINED OPERATION” QUESTIONS

At least one of your 25–26 Problem Solving questions will probably be an example of what’s

called a “defined operation.” These questions look weird and therefore might strike you as

difficult But they’re really not In fact, the math turns out to be ridiculously easy What’s

being tested is your ability to understand what the problem requires and then to perform the

simple arithmetical calculations—carefully!

12 Let a b c

d be defined for all numbers a, b, c, and d by a c

b

d 5 ac 2 bd.

If x 5 542

1 , what is the value of x 2

10

1 ?

(A) 1

(B) 2

(C) 18

(D) 38

(E) 178

The correct answer is (B) In defining the diamond-shaped figure as “ac 2 bd,” the test

makers are saying that whenever you see four numbers in a diamond like this, you should

plug them into the mathematical expression shown in the order given The question itself

then requires you to perform this simple task twice

First, let’s figure out the value of x If x is the diamond labeled as x, then a 5 5, b 5 4, c 5 2,

and d 5 1 Now, we plug those numbers into the equation given, and do the simple math:

x 5 ~5 3 2! 2 ~4 3 1!

x 510 2 4

x 5 6

Now, we tackle the second step Having figured out the value of x, we can plug it into our

second diamond, where a 5 6, b 5 10, c 5 2, and d 5 1 Again, plug in the numbers and do

the math:

(6 3 2) 2 (10 3 1) 5 12 2 10 5 2

As you can see, the math is very easy; the trick is understanding what the test makers are

doing, which is “defining” a new math operation and then carefully plugging in the numbers

and working out the solution With a little practice, you’ll never get a “defined operation”

question wrong

KEYS TO SUCCESSFUL GMAT PROBLEM SOLVING

Here are some basic tips you should follow for any type of Problem Solving question Apply

these “keys” to the Practice Tests in Part VI, and then review them again just before

exam day

Narrow Down Answer Choices Up Front by Sizing Up the Question

If the question asks for a number value, you can probably narrow down the answer choices by estimating the value and type of number you’re looking for Use your common sense and real-world experience to formulate a “ballpark” estimate for word problems

QUESTION 1

You can narrow down answer choices by looking at the problem from a “commonsense” viewpoint The five answer choices in this question provide some useful clues Notice that they range in value from 4.8 to 13.0 That’s a wide spectrum, isn’t it? But what general value should you be looking for in a correct answer to this question? Without crunching any numbers, it’s clear that most of the juice will still remain in the bottle, even after lunch So you’re looking for a value much closer to 13 than to 4 So you can safely eliminate (A) and (B)

Common Sense Can Sometimes Reveal the Right Answer

In many questions, you can eliminate all but the correct answer without resorting to precise calculations

QUESTION 1

Look at the question from a broader perspective If you subtract 10% from a number, then

20% from the result, that adds up to a bit less than a 30% decrease from the original number.

Thirty percent of 16 ounces is 4.8 ounces So the solution must be a number that is a bit greater than 11.2 (16 2 4.8) Choice (D), 11.5, is the only choice that fits the bill!

QUESTION 3

In Question 3, notice that we made c a much greater number than either p or q Only a fraction with c in the numerator and a large number in the denominator (or vice versa) is

likely to yield a quotient you’re looking for With this in mind, choice (B) jumps off the paper

at you as the likely choice!

Scan the Answer Choices for Clues to Solving the Problem

Scan the answer choices to see what all or most of them have in common—such as radical signs, exponents, factorable expressions, or fractions Then try to formulate a solution that looks like the answer choices

QUESTION 3

Notice that each answer choice includes all three letters (p, q, and c) So the solution you’re

aiming for must also include all three letters Also, notice that every answer but choice (E) is

a fraction So anticipate building a fraction to solve the problem.

Don’t Be Fooled by Too-Obvious Answer Choices

The test makers will intentionally tempt or “bait” you with wrong-answer choices that result

from making common errors in calculation and in setting up and solving equations Don’t

assume that your response is correct just because your solution appears among the five

answer choices! Rely instead on your sense for whether you understood what the question

called for and performed the calculations and other steps carefully and accurately

QUESTION 1

In this question, each of the four incorrect choices is sucker bait:

(A) 4.8 You performed the wrong calculation:

30% of 16 ounces 5 4.8 ounces

(B) 5.5 This is the number of ounces Susan drank (The question asks

for the amount remaining.)

(C) 11.2 You performed the wrong calculation:

30% of 16 ounces 5 4.8 ounces

16 2 4.8 5 11.2

(D) 11.5 This is the correct answer

(E) 13.0 You confused percentages with raw numbers, erroneously

converting 30% (10% 1 20%) into 3.0:

16 2 3.0 5 13.0

QUESTION 2

This question contains two sucker answer choices:

(A) 2 This would be the correct answer to the question:

“What is the difference between 19 and 21?”

But this question is asking something entirely different

(E) 20 20 is simply 19 1 21 divided by 2

If this solution strikes you as too simple, you’ve got good instincts

Don’t Do More Work Than Needed to Get to the Answer

If the question asks for an approximation, that’s a huge clue that precise calculations

aren’t necessary

QUESTION 1

Notice that each answer choice is carried to exactly one decimal place, and that the question

asks for an approximate value These two features are clues that you can probably round off

your calculations to the nearest tenth as you go

Look for Shortcuts to Conventional Ways of Solving Problems

The adage “There’s more than one way to skin a cat” applies to many GMAT Problem Solving questions

QUESTION 2

You can solve this problem quickly by simply comparing the two sums Before the sixth

number is removed, the sum of the numbers is 114 (6 3 19) After removing the sixth number, the sum of the remaining numbers is 105 (5 3 21) The difference between the two sums is 9, which must be the value of the number

Know When to Plug In Numbers for Variables

If the answer choices contain variables (like x and y), the question might be a good candidate

for the “plug-in” strategy Pick simple numbers (so the math is easy) and substitute them for the variables You’ll definitely need your pencil for this strategy

QUESTION 3

This question was a perfect candidate for the plug-in strategy Instead of trying to figure out how to set up and solve an algebraic equation, in step 3 we used easy numbers for the three variables, then plugged those numbers into each answer choice to see which choice worked

Know When to Work Backward from Numerical Answer Choices

If a Problem Solving question asks for a number value and if you draw a blank about how to set up and solve the problem, don’t panic You might be able work backward by testing each answer choice This might take a bit of time, but if you test the answer choices in random order, the statistical odds are that you’ll only need to test three choices to find the correct one

QUESTION 2

You already learned that comparing the two sums is the quickest shortcut to the answer But

if this strategy didn’t occur to you, working backward from the answer choices would be the next quickest method After the sixth number is removed, the sum of the five remaining numbers is 21 3 5 5 105 So to test an answer choice, add this sum to the number provided

in the choice, dividing the new sum by 6 If the result is 19, you’ve found the correct choice Here’s how to do the math for choice (C), which is the correct answer:

105 1 9

114

6 5 19 Problem Solving questions always list numerical answer choices in ascending order of value

So if you use the strategy of working backward, start with the median value: choice (C) If (C) turns out too great, you know the correct answer must be either (A) or (B) Conversely, if (C) turns out too small, then either (D) or (E) must be correct Of course, you might also be able

to eliminate an answer choice right away by sizing up the questions (a previous strategy)

Always Check Your Work

Always check your work Here are three suggestions for doing so:

Do a reality check Ask yourself whether your solution makes sense based upon

what the question asks (This check is especially appropriate for word problems.)

For questions where you solve algebraic equations, plug your solution into the

equation(s) to make sure it works

Confirm your calculations (except for the simplest no-brainers) with your

calcula-tor It’s amazingly easy to accidentally push the wrong button

Checking your calculations is especially crucial for questions asking for an approximation

Why? If your solution doesn’t precisely match one of the five answer choices, you might

conclude that you should just pick the choice that’s closest to your solution—a big mistake if

you miscalculated!

QUESTION 1

A reality check on this question will tell you that answer choice (C), 11.5, seems about right,

but that most of the other choices don’t

Read the Question One Last Time Before Moving On

Among GMAT test takers, simple carelessness in reading a Problem Solving question is by far

the most likely cause of an incorrect answer So even if your solution is among the choices and

you’re confident your calculations are accurate, don’t move on quite yet Read the question

again Make sure you answered the precise question asked For example, does the question

ask for:

• Arithmetic mean or median?

• A circumference or an area?

• A sum or a difference?

• A perimeter or a length of one side only?

• An aggregate rate or a single rate?

• Total time or average time?

Also check to make sure you:

• Used the same numbers provided in the question

• Didn’t inadvertently switch any numbers or other expressions

• Didn’t use raw numbers where percentages were provided or vice-versa

QUESTION 1

The question asked for the amount of juice remaining, not the amount Susan drank Also, a careless test taker might subtract 10 ounces instead of 10%

QUESTION 2

A careless test taker might inadvertently switch the numbers 19 and 21

QUESTION 3

The question asks for an answer in cents, not dollars

SUMMING IT UP

• For success in the GMAT Problem Solving questions, follow the 5-step approach in this

chapter: size up the question, appraise the answer choices, check for shortcuts to finding

the answer, set up the problem and solve it, and verify your response before moving to the

next question

• Problem Solving questions are designed to “reward” you for recognizing easier or more

intuitive ways of finding the correct answer, so be on the alert for possible shortcuts

• Don’t look for easy solutions to complex problems, however Those that involve algebraic

formulas generally aren’t solved by adding or subtracting a few numbers

• Always check your calculations Careless mistakes are the leading cause of incorrect

responses on the GMAT Quantitative section

• Problem Solving questions list numerical choices in ascending order of value So if you

have to work backward, start from the middle choice (C) If it turns out to be too great,

you know the correct answer must be choice (A) or (B); if it turns out to be too small, you

can focus on choice (D) or (E) as the correct answer

and Analysis

OVERVIEW

• The 5-step plan for data sufficiency problems

• Data sufficiency strategies

• Keys to successful GMAT data sufficiency

• The 5-step plan for data analysis problems

• Keys to successful GMAT data analysis

• Summing it up

In this chapter, you’ll learn these basics:

• A step-by-step approach to handling all Data Sufficiency and Analysis questions

• Keys for successfully tackling Data Sufficiency and Analysis questions The Data Sufficiency format is unique to the GMAT; you won’t find it on any

other standardized test Each Data Sufficiency consists of a question followed

by two statements—labeled (1) and (2) Your task is to analyze each of the two

statements to determine whether it provides sufficient data to answer the

question and, if neither suffices alone, whether both statements together

suffice These are your answer choices:

(A) Statement (1) ALONE is sufficient, but statement (2) alone is

not sufficient to answer the question asked;

(B) Statement (2) ALONE is sufficient, but statement (1) alone is

not sufficient to answer the question asked;

(C) BOTH statements (1) and (2) TOGETHER are sufficient to

answer the question asked, but NEITHER statement ALONE

is sufficient;

(D) EACH statement ALONE is sufficient to answer the question

asked;

(E) Statements (1) and (2) TOGETHER are NOT sufficient to

an-swer the question asked, and additional data specific to the problem are needed

.chapter

You’ll also learn several more advanced techniques for achieving your highest possible score

on the Quantitative section of the GMAT These include:

• Applying the basic techniques to more challenging Data Sufficiency questions

• Learning additional ways to apply techniques to certain types of Data Sufficiency questions, with example questions for practice

• Learning a step-by-step approach to handling any Data Analysis question

• Learning how to tackle Data Analysis questions

• Further exploring some of the strategies listed above by applying them to GMAT-style questions that are more challenging

THE 5-STEP PLAN FOR DATA SUFFICIENCY PROBLEMS

The first task in this chapter is to learn the five basic steps for handling any GMAT Data Sufficiency problem:

Size up the question Size up the two statements and look for a shortcut Consider Statement (1) alone

Consider Statement (2) alone

If neither statement alone answers the question, consider both together Later in this chapter, we’ll apply this 5-step approach to four sample Data Sufficiency questions

Step One: Size Up the Question

As with Problem Solving questions, assess what specific mathematical area is being tested (e.g., what mathematical rules and formulas come into play) By determining what you’re up against, you’re well on your way to dealing with the question Data Sufficiency questions, just like Problem Solving questions, vary widely in difficulty level Try to get a feel for your limitations in handling complex questions Determine how much time you’re willing to spend

on the question, if any

Step Two: Size Up the Two Statements and Look for a Shortcut

Before you plunge into a full-blown analysis of statement (1), read both statements and ask yourself:

• Do the statements provide essentially the same information? If so, the answer is probably either choice (D) (“Each statement ALONE is sufficient to answer the question asked”) or choice (E) (“Statements 1 and 2 TOGETHER are NOT sufficient

to answer the question asked, and additional data specific to the problem