id stringlengths 12 47 | source_name stringclasses 4
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GMAT Club Math Book 2024 v8_p97_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 97 | 97 | statistics | Properties
;
only if all elements in a set is equal;
Let standard deviation of be and mean of the set be :
Standard deviation of is . Decrease/increase in all elements of a set by a
constant percentage will decrease/increase standard deviation of the set by the same
percentage.
Standard deviation of is . Decrease/incr... |
GMAT Club Math Book 2024 v8_p98_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 98 | 98 | statistics | if a new element is added to set and standard deviation of a new set is
, then:
1) if
2) if
3) if
4) is the lowest if
Tips and Tricks
GMAC in majority of problems doesn't ask you to calculate standard deviation. Instead it
tests your intuitive understanding of the concept. In 90% cases it is a faster way to use
jus... |
GMAT Club Math Book 2024 v8_p99_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 99 | 99 | statistics | means that all elements strictly related to each other. If we shift the set by adding or
subtracting any integer, does it change standard deviation (average deviation of elements
from the mean)? No. One thing we should know is the number of elements in the set,
because the more elements we have the broader they are dis... |
GMAT Club Math Book 2024 v8_p100_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 100 | 100 | general | covers 68% of data
covers 95% of data
covers 99% of data
m − σ < x < m + σ
m − 2σ < x < m + 2σ
m − 3σ < x < m + 3σ
GMAT Club Math Book
100 |
GMAT Club Math Book 2024 v8_p101_c1 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 101 | 101 | statistics | Practice Questions
Easy:
1. https://gmatclub.com/forum/the-data-set ... 76313.html
2. https://gmatclub.com/forum/which-of-the ... 31485.html
3. https://gmatclub.com/forum/a-certain-ch ... 43982.html
4. https://gmatclub.com/forum/if-d-is-the- ... 93979.html
5. https://gmatclub.com/forum/for-a-certai ... 28661.html
6. ht... |
GMAT Club Math Book 2024 v8_p101_c2 | GMAT Club Math Book 2024 v8 | GMAT Club Math Book 2024 v8.pdf | pdf | 101 | 101 | word_problems | forum/if-j-k-m-n-a ... 72294.html
9. https://gmatclub.com/forum/which-of-the ... 90680.html
10. https://gmatclub.com/forum/the-list-abo ... 93102.html
Page 1 of 1 All times are UTC - 8 hours [ DST ]
GMAT Club Math Book
101 |
book 2_p3_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 3 | 3 | word_problems | MANHATTAN PREP
GMAT Advanced Quant
GMAT STRATEGY GUIDE
This supplemental guide provides in-depth and comprehensive
explanations of the advanced math skills necessary for the highest-level
performance on the GMAT.
GMAT® is a registered trademark of the Graduate Management
Admissions Council™. Manhattan Prep is neither e... |
book 2_p4_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 4 | 4 | general | Table of Contents |
book 2_p5_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 5 | 5 | strategy | GMAT Advanced Quant
Cover
Title Page
Copyright
Instructional Guide Series
Letter
Introduction
In This Chapter...
A Qualified Welcome
Who Should Use This Book
Try It Yourself
The Purpose of This Book
An Illustration
Learning How to Think
Plan of This Book
Solutions to Try-It Problems
Part 1: Problem Solving and Data Suf... |
book 2_p6_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 6 | 6 | algebra | Principle #2: Never Rephrase Yes/No as Value
Principle #3: Work from Facts to Question
Principle #4: Be a Contrarian
Principle #5: Assume Nothing
Problem Set
Solutions
Chapter 4: Data Sufficiency: Strategies & Tactics
In This Chapter...
Chapter 4 Data Sufficiency: Strategies & Tactics
Advanced Strategies
Advanced Guess... |
book 2_p7_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 7 | 7 | sequences_patterns | Rubber Band Geometry
Baseline Calculations for Averages
Number Line Techniques for Statistics Problems
Problem Set
Solutions
Chapter 8: Hybrid Problems
In This Chapter...
Pop Quiz!
Hybrid Problems
Identify and Sequence the Parts
Where to Start
Minor Hybrids
Problem Set
Solutions
Part 3: Practice
Chapter 9 Workout Sets
... |
book 2_p8_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 8 | 8 | general | Workout Set 7 Solutions
Workout Set 8
Workout Set 8 Answer Key
Workout Set 8 Solutions
Workout Set 9
Workout Set 9: Answer Key
Workout Set 9 Solutions
Workout Set 10
Workout Set 10 Answer Key
Workout Set 10 Solutions
Workout Set 11
Workout Set 11 Answer Key
Workout Set 11 Solutions
Workout Set 12
Workout Set 12 Answer ... |
book 2_p9_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 9 | 9 | coordinate_geometry | Acknowledgements
A great number of people were involved in the creation of the book you are holding.
Our Manhattan Prep resources are based on the continuing experiences of our instructors and
students. The overall vision for this edition was developed by Chelsey Cooley, who determined
what new areas to cover and who w... |
book 2_p10_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 10 | 10 | word_problems | GMAT® STRATEGY GUIDES
GMAT All the Quant
GMAT All the Verbal
GMAT Integrated Reasoning and Essay
STRATEGY GUIDE SUPPLEMENTS
Math Verbal
GMAT Foundations of Math
GMAT Advanced Quant
GMAT Foundations of Verbal |
book 2_p11_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 11 | 11 | word_problems | January 7, 2020
Dear Student,
Thank you for picking up a copy of Advanced Quant. I hope this book
provides just the guidance you need to get the most out of your GMAT
studies.
At Manhattan Prep, we continually aspire to provide the best instructors
and resources possible. If you have any questions or feedback, please d... |
book 2_p12_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 12 | 12 | word_problems | particular thanks to instructors Stacey Koprince and Ben Ku for their
content contributions.
Finally, we are indebted to all of the Manhattan Prep students who have
given us excellent feedback over the years. This book wouldn’t be half of
what it is without their voice.
And now that you are one of our students too, ple... |
book 2_p13_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 13 | 13 | general | Introduction |
book 2_p14_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 14 | 14 | fractions_decimals_percents | In This Chapter...
A Qualified Welcome
Who Should Use This Book
Try It Yourself
The Purpose of This Book
An Illustration
Learning How to Think
Plan of This Book
Solutions to Try-It Problems |
book 2_p15_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 15 | 15 | coordinate_geometry | Introduction
A Qualified Welcome
Welcome to GMAT Advanced Quant! In this venue, we decided to be a
little nerdy and call the introduction Chapter 0. A er all, the point (0, 0) in
the coordinate plane is called the origin, isn’t it? (That’s the first and last
math joke in this book.)
Unfortunately, we have to qualify ou... |
book 2_p16_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 16 | 16 | fractions_decimals_percents | Who Should Use This Book
You should use this book if you meet the following conditions:
If you match this description, then please turn the page.
You have achieved a scaled score of at least 47 (out of 51) on the Quant
section of either the Manhattan Prep practice test or the official practice
computer-adaptive test (CA... |
book 2_p17_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 17 | 17 | fractions_decimals_percents | If you don’t match this description, then you will probably find this book
too difficult at this stage of your preparation.
For now, you are better off working on topic-focused material, as found in
the All the Quant guide, and ensuring that you have mastered that material
before you return to this book. |
book 2_p18_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 18 | 18 | general | Try It Yourself
Throughout the chapters of this guide, you’ll see Try-It problems—
problems designed to test your skills on certain aspects of GMAT problems.
Take a look at the following three Try-It problems, which are very difficult.
They are at least as hard as any real GMAT problem—probably even harder.
Go ahead and... |
book 2_p19_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 19 | 19 | coordinate_geometry | Try-It #0-2
Arrow
, which is a line segment exactly 5 units long with an
arrowhead at A, is constructed in the xy-plane. The x- and y-
coordinates of A and B are integers that satisfy the inequalities 0 ≤
x ≤ 9 and 0 ≤ y ≤ 9. How many different arrows with these -
properties can be constructed?
Try-It #0-3
In the dia... |
book 2_p20_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 20 | 20 | general | (Note: This problem does not require any non-GMAT math, such as
trigonometry.) |
book 2_p21_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 21 | 21 | number_theory | The Purpose of This Book
This book is designed to prepare you for the most difficult math problems
on the GMAT.
So…what is a difficult math problem, from the point of view of the GMAT?
A difficult math problem is one that most GMAT test-takers get wrong
under exam conditions. In fact, this is essentially how the GMAT meas... |
book 2_p22_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 22 | 22 | word_problems | Complex structures
Complex structures are essentially disguises for simpler content.
These disguises may be difficult to pierce. The path to the answer is
twisted or clouded somehow.
To solve problems that have simple content but complex structures,
you need approaches that are both more general and more
creative. This ... |
book 2_p23_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 23 | 23 | sequences_patterns | An Illustration
Give this problem a whirl. Don’t go on until you have spent a few minutes
on it—or until you have figured it out.
Try-It #0-4
What should the next number in this sequence be?
1 2 9 64 __
Note: This problem is not exactly GMAT-like, because there is no
mathematically definite rule. However, you’ll know w... |
book 2_p24_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 24 | 24 | fractions_decimals_percents | You might even say that you need two types of brain.
The top-down brain is your conscious self. If you imagine the contents of
your head as a big corporation, then your top-down brain is the CEO,
responding to input, making decisions, and issuing orders. In cognitive
science, the top-down brain is called the executive ... |
book 2_p25_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 25 | 25 | sequences_patterns | Each of your brains needs the other one to solve difficult problems.
Your top-down brain needs your bottom-up brain to notice patterns, sniff
out valuable leads, and make quick, intuitive leaps and connections.
But your bottom-up brain is inarticulate and distractible. Only your top-
down brain can build plans, pose expl... |
book 2_p26_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 26 | 26 | word_problems | You may never have thought explicitly about steps 1 and 2 before. It may
have been easy or even automatic for you to Understand easier problems
and to Plan your approach to them. As a result, you may tend to dive right
into the Solve stage. This is a bad strategy. Mathematicians know that the
real math on hard problems... |
book 2_p27_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 27 | 27 | number_theory | solved it). The top-down brain is labeled TD; the bottom-up brain is labeled
BU.
1 2 9 64 __ TD: “Okay, let’s Understand this thing. At a glance, they’ve
given me an increasing list of numbers, and they want me to
find the number that “should” go in the blank, whatever
“should” means. What’s a good Plan? Hmm. No idea. ... |
book 2_p28_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 28 | 28 | sequences_patterns | BU notices no real pattern. There’s 2−3−2 twice as you go
across, but so what? And the 1 is weird by itself.
1 2 9 64 __ TD: “No good leads there. Hmm...time to go back to the
original and try taking differences.”
BU notices no pattern. The numbers look even uglier.
1 2 9 64 __ TD: “Hmm. No good. Go back to original num... |
book 2_p29_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 29 | 29 | number_theory | it’s 4 to the third power. That fits.”
BU is thrilled: 1, 2, 3, 4 below and 1, 2, 3 up top.
10 21 32 43 __ TD: “Extend le . It’s 10. Confirmed. The bases are 1, 2, 3, 4, etc.,
and the powers are 0, 1, 2, 3, etc.”
BU is content.
10 21 32 43 54 TD: “So the answer is 54, which is 252, or 625.”
Your own process was almost ... |
book 2_p30_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 30 | 30 | number_theory | factors because they weren’t that useful here? Of course not! A computer
can rapidly and easily apply a complicated algorithm with hundreds of
steps, but humans can’t. (If you are an engineer or programmer, maybe
you wish you could program your own brain, but so far, that’s not
possible!)
What humans are good at, thoug... |
book 2_p31_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 31 | 31 | general | Organize your approach:
choose a solution path.
Solve Work the problem!
You’ll get lots of practice using the UPS process throughout this guide. |
book 2_p32_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 32 | 32 | word_problems | Learning How to Think
This book is intended to make you smarter.
It is also intended to make you scrappier.
That description encompasses two main ideas: employing GMAT strategies
as well as textbook solution methods and knowing when to let go.
If you have traditionally been good at paper-based standardized tests, then
... |
book 2_p33_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 33 | 33 | word_problems | GMAT problems o en have back doors—ways to solve that don’t involve
crazy computation or genius-level insights. Remember that in theory,
GMAT problems can all be solved in two minutes. By searching for the back
door, you might avoid all the bear traps that the problem writer set out by
the front door!
In addition to le... |
book 2_p34_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 34 | 34 | word_problems | whether you have the presence of mind to recognize a bad opportunity
and the discipline to let it go.
Show the GMAT that you know how to manage your scarce resources (time
and mental energy) and that you can recognize and cut off a bad
opportunity. |
book 2_p35_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 35 | 35 | word_problems | Plan of This Book
The rest of this book has three parts:
Part One: Problem Solving and Data Sufficiency
Strategies
Chapter 1: Problem Solving: Advanced
Principles
Chapter 2: Problem Solving: Strategies &
Tactics
Chapter 3: Data Sufficiency: Principles
Chapter 4: Data Sufficiency: Strategies &
Tactics
Part Two: Strategies ... |
book 2_p36_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 36 | 36 | statistics | that apply across several topics but are more specific than the approaches
in Part I.
Each of the eight chapters in Part I and Part II contains the following:
Many of these problems will be GMAT-like in format, but many will not.
Part III contains sets of GMAT-like Workout problems, designed to exercise
your skills as ... |
book 2_p37_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 37 | 37 | general | Solutions to Try-It Problems
If you haven’t tried to solve the first three Try-It problems in the Try It
Yourself section at the beginning of this chapter, then go back and try them
now. Think about how to get your top-down brain and your bottom-up
brain to work together like a detective and a bloodhound. Come back
whe... |
book 2_p38_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 38 | 38 | sets_probability_counting | SOLUTION TO TRY-IT #0-1
… jar is filled with red, white, and blue tokens …
chance of randomly selecting …
TD: “I need to Understand this
problem first. There’s a jar, and it’s
got red, white, and blue tokens in it.”
BU notices “chance” and
“randomly.” That’s probability.
TD: “All right, this is a probability
problem. N... |
book 2_p39_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 39 | 39 | algebra | TD: “Let’s Reflect for a moment to
figure out a Plan. How can I
approach this? How about algebra—
if I name the number of each color,
then I can represent each fact and
also what I’m looking for. Okay, I use
R, W, and B. Make probability
fractions. Multiply red and white
fractions. Simplify algebraically.”
BU is now un... |
book 2_p40_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 40 | 40 | algebra | In the very first equation above, each fraction on the
le is less than 1, so their product is even smaller.
The denominators of the three fractions are all the
same.
So the numerator of the product (B) must be smaller
than either of the other numerators
(R and W ).
BU notices fractions less than 1. All
positive.
TD: “... |
book 2_p41_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 41 | 41 | sets_probability_counting | Let R = 6 and W = 9.
(C) is out too. Try the next
possibility.”
BU doesn’t like breaking the
symmetry between R and W. They
seem to be alike.
TD: “Does it matter whether R = 6
and W = 9 or the other way around?
No, it doesn’t. One is 6, the other is 9.
Plug in and go.”
TD: “This works. The answer is 3 + 6
+ 9 = 18.”
T... |
book 2_p42_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 42 | 42 | sets_probability_counting | A jar is filled with red, white, and blue
tokens …
BU is alert—what about 0?
TD: “What about 0? Hmm…the wording at the
beginning assumes that there actually are tokens
of each color. So there can’t be 0 tokens of any
kind.”
(A) 9 (B) 12 (C) 15 (D) 18 (E) 21 TD: “Now let’s look at the answer choices.”
BU notices that th... |
book 2_p43_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 43 | 43 | general | Select a white:
, which is not “select a
blue”
(A) 9 (B) 12 (C) 15 (D) 18 (E) 21
(C) 15
TD: “That doesn’t work either. Knock out (B). Keep
going.”
BU notices 15 has a few options.
Select a red:
Select a white:
, which is not "select a
blue"
,
which is not "select a blue"
(A) 9 (B) 12 (C) 15 (D) 18 (E) 21
(D) 18
, ... |
book 2_p44_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 44 | 44 | coordinate_geometry | Many people find this second approach less stressful and more efficient
than the textbook approach. In fact, there is no way to find the correct
answer by pure algebra. Ultimately, you have to test suitable numbers.
Try-It #0-2
Arrow
, which is a line segment exactly 5 units long with an
arrowhead at A, is constructed... |
book 2_p45_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 45 | 45 | number_theory | properties can be constructed? Reread the question.”
BU wonders which properties.
… exactly 5 units long with an arrowhead
at A … the x- and y-coordinates of A and B
are to be integers that satisfy the
inequalities 0 ≤ x ≤ 9 and 0 ≤ y ≤ 9.
TD: “What are the properties of the arrows
supposed to be again? Each arrow is 5... |
book 2_p46_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 46 | 46 | geometry | There are 10 identical columns: x = 0
through x = 9. 5 × 10 = 50 possible positions
for the arrow pointing straight up.
50 × 2 = 100 possible positions for the
arrow if it points straight up or to the right.
TD: “Great. I’ve Solved one part. Other
possibilities?”
BU notices the square is the same vertically as
horizont... |
book 2_p47_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 47 | 47 | geometry | TD: “3−4−5 triangles. Yes. Put the arrow as the
hypotenuse of a 3−4−5 triangle. How can this be
done? Try to place the arrow. Remember the
reversal. Looks like there are four ways if I go 3
up and 4 across: up right, up le , down right,
down le .”
BU is happy. This is the trick.
Four up, three across:
TD: “Likewise, t... |
book 2_p48_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 48 | 48 | geometry | Try-It #0-3
In the diagram to the right, the value of x is closest to which of the
following?
SOLUTION TO TRY-IT #0-3
TD: “Okay, let’s Understand this. Redraw the
figure. The problem wants the value of x. Now…
how about a Plan?”
BU notices this is an isosceles triangle, because
there are two sides labeled x. How about ... |
book 2_p49_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 49 | 49 | geometry | TD: “Hmm...here’s a Plan: add a perpendicular
line to make right triangles. Drop the line from
the top point. I'll label corners while I'm at it.
Now fill in angles.”
BU notices 45−45−90 and is happy.
TD: “Use the 45−45−90 to write expressions for
its sides. Then
can be split up into two
pieces, and I can set up the ... |
book 2_p50_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 50 | 50 | algebra | BU has no idea how to take the square root of
this.
TD: “Neither do I. Let’s try estimating. If x2 is
about 3.5, then the square root must be a bit
less than 2 (since the square root of 4 is 2). 182 is
324 and 192 is 361, so the answer is around 1.8
or 1.9.”
TD: “Answer (A) is about 3.5; that matches the
squared value,... |
book 2_p51_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 51 | 51 | geometry | Alternatively, the question stem asks for an approximate answer, so you
can also try estimating from the start. Draw the triangle carefully and start
with the same perpendicular line as before. This line is a little shorter than
the side of length
(which is about 1.4). Call the two shorter legs 1.2
and calculate the ... |
book 2_p52_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 52 | 52 | word_problems | PART ONE
Problem Solving and Data
Sufficiency Strategies
In This Part
Chapter 1: Problem Solving: Advanced Principles
Chapter 2: Problem Solving: Strategies & Tactic
Chapter 3: Data Sufficiency: Principles
Chapter 4: Data Sufficiency: Strategies & Tactics |
book 2_p53_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 53 | 53 | strategy | CHAPTER 1
Problem Solving: Advanced
Principles |
book 2_p54_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 54 | 54 | strategy | In This Chapter...
Principle #1: Understand the Basics
Principle #2: Build a Plan
Principle #3: Solve—and Put Pen to Paper
Principle #4: Review Your Work |
book 2_p55_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 55 | 55 | strategy | Chapter 1
Problem Solving: Advanced
Principles
Chapters 1 and 2 of this book focus on the more fundamental of the two
types of GMAT math questions: Problem Solving (PS). Some of the content
applies to any kind of math problem, including Data Sufficiency (DS).
However, Chapters 3 and 4 deal specifically with DS issues.
T... |
book 2_p56_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 56 | 56 | word_problems | Principle #1: Understand the Basics
Take time to think and plan before you start solving a difficult problem. If
Quant is your strength, you may want to dive straight into every problem
as soon as you see it, without pausing to consider all of the angles. There
are two good reasons to slow down:
To remind yourself to sl... |
book 2_p57_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 57 | 57 | word_problems | You don’t need to meticulously go through every one of these questions
whenever you solve a problem. (However, that’s a good thing to do when
you review a problem!) They’re here to help you consider how you might
read more productively.
As you read the problem, jot down any given numbers or formulas on your
scrap pape... |
book 2_p58_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 58 | 58 | number_theory | Try-It #1-1
x = 910 − 317 and
is an integer. If n is a positive integer that has
exactly two factors, how many different values for n are possible?
Glance. This is a PS problem. The answers are numbers but in written form;
this format is reserved for problems that ask for the number of numbers or
number of possibili... |
book 2_p59_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 59 | 59 | number_theory | What do I
know?
x = 910 − 317
That is, x = a specific large integer, expressed in terms of powers of 9 and 3.
is an integer.
That is, x is divisible by n, or n is a factor of x.
Finally, n is a positive integer that has exactly two factors.
Prime numbers have exactly two factors. So I can rephrase the information: n i... |
book 2_p61_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 61 | 61 | statistics | Principle #2: Build a Plan
Next, think about how you will solve the problem:
Reflect. Here are some Pólya questions that help you think about what you
know and come up with a plan:
Is a good
approach
already
obvious?
From your answers above, you may already see a way to reach the answer. If
you can envision the rough o... |
book 2_p62_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 62 | 62 | number_theory | Organize. For the Try-It #1-1 problem, some of the information is already
rephrased (reorganized). Go further now, combining information and
simplifying the question:
Given: n is a prime number AND n is a factor of x.
Combined: n is a prime factor of x.
Question: How many different values for n are possible?
Combi... |
book 2_p63_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 63 | 63 | number_theory | Principle #3: Solve—and Put Pen to
Paper
The third step is to do the work: solve.
You’ll want to execute that solution in an error-free way—it would be terrible to
get all the thinking correct, then make a careless computational mistake. That’s
why we say you should put pen to paper.
In the expression 910 − 317, the 3 ... |
book 2_p64_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 64 | 64 | sequences_patterns | Think back to those killer Try-It problems in the introduction. Those are not the
kinds of problems you can figure out just by looking at them.
When you get stuck on a tough problem, take action. Do not just stare, hoping
that you suddenly get it.
Instead, ask yourself the Pólya questions again and write down whatever ... |
book 2_p65_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 65 | 65 | sequences_patterns | Every GMAT Quant problem has a two-minutes-or-faster solution path, which
may depend upon a pattern that you’ll need to extrapolate. You’ll know a
pattern is needed when a problem asks something that would be impossible to
calculate (without a calculator) in two minutes. When this happens, write out
the first five to e... |
book 2_p66_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 66 | 66 | sequences_patterns | etc.
The terms of the sequence are
. . . . Three terms
repeat in this cyclical pattern forever; every third term is the same. Note: If you
don’t spot a pattern within the first five to eight terms, stop using this approach
and see whether there’s another way (including guessing!).
The problem asks for the sum, so fin... |
book 2_p67_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 67 | 67 | sequences_patterns | The correct answer is (C).
It is almost impossible to stare at the recursive definition of this sequence and
discern the resulting pattern.
The best way to identify the pattern is to calculate a few values of the sequence
and look for the pattern. You will learn more about pattern recognition in
Chapter 5.
2. DRAW IT O... |
book 2_p68_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 68 | 68 | word_problems | Represent Truck A and Truck B as of 1:00 p.m. How does the
distance between Truck A and Truck B change as time goes
by?
Try another point in time. Since the answers are all a
matter of minutes a er 1:00 p.m., try a convenient
increment of a few minutes. A er 10 minutes, each truck
will have traveled 5 miles (30 miles p... |
book 2_p69_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 69 | 69 | algebra | Therefore, y could equal
6 or 8 miles. In other
words, the trucks will be
exactly 10 miles apart at
1:12 p.m. and at 1:16
p.m. Either way, the
correct answer is (B).
Notice how instrumental
these diagrams were for
the solution process. You
may already accept that Geometry problems require diagrams. However, many
other ... |
book 2_p70_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 70 | 70 | number_theory | Try-It #1-4
If x and y are positive integers and
is the square of an odd
integer, what is the smallest possible value of xy ?
As you read, jot down the given information.
Note that you might not immediately write down the square of an odd integer
info if you still have to puzzle out what it means:
What does the squar... |
book 2_p71_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 71 | 71 | algebra | Are there any patterns or commonalities? All of the numbers are odd. All of the
numbers are perfect squares. Therefore,
is an odd perfect square.
Add that to your notes.
The question asks for the smallest possible value of xy. What do you need to
figure out in order to find that?
If the
expression is distracting yo... |
book 2_p72_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 72 | 72 | number_theory | In other words, y2 must cancel out all the even factors in
1,620. The y2 must contain at least two 2’s, so y itself has to
contain at least one 2.
Okay, that takes care of y: at minimum, y must be 2. If so,
then the expression becomes
.
Now, what about x? If you’re not sure, return to your simpler problem thinking.
S... |
book 2_p73_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 73 | 73 | sequences_patterns | Then, see whether you can adjust the solution to the simpler problem in order
to solve the original.
To recap, put your work on paper. Don’t try to solve hard problems in your head.
Instead, do the following:
In general, jot down intermediate results as you go. You may see them in a new
light and consider how they fit ... |
book 2_p74_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 74 | 74 | word_problems | Principle #4: Review Your Work
When you are done with a test or practice set, you are not really done.
When you first do a problem under timed conditions, your brain is too busy
solving the problem to effectively learn and remember. What you learn
from a new problem comes a er you’ve finished it and picked your answer,
... |
book 2_p75_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 75 | 75 | general | What could I take from this problem to help me solve other problems in
the future? |
book 2_p76_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 76 | 76 | sets_probability_counting | When you do the following problem set, apply the first three principles
from this chapter to each problem: Understand, Plan, and Solve. Then,
review each problem in depth. As you review, do two things:
The solutions include our own responses to these two tasks. Yours might
look different, and that's fine.
Problem Set
Id... |
book 2_p77_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 77 | 77 | sequences_patterns | (A)
(B)
(C)
(D)
(E)
2. If x is a positive integer, what is the units digit of (24)5 + 2x(36)6(17)3 ?
2(A)
3(B)
4(C)
6(D)
8(E)
3. A baker makes a combination of chocolate chip cookies and peanut
butter cookies for a school bake sale. His recipes only allow him to
make chocolate chip cookies in batches of 7 and peanut ... |
book 2_p78_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 78 | 78 | algebra | 7(A)
14(B)
21(C)
28(D)
35(E)
4. A rectangular solid is changed such that the width and length are
each increased by 1 inch and the height is decreased by 9 inches.
Despite these changes, the new rectangular solid has the same
volume as the original rectangular solid. If the width and length of
the original rectangular ... |
book 2_p79_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 79 | 79 | general | −7(A)
7(B)
10(C)
12(D)
14(E) |
book 2_p80_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 80 | 80 | number_theory | Solutions
Each solution addresses the two steps from the instructions:
Identify exactly what the problem is asking for, and what that means in
the simplest possible terms.
1)
Note at least one general takeaway that might useful on other problems
in the future.
2)
1. (C)
1. What it’s asking: The problem is asking for t... |
book 2_p81_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 81 | 81 | number_theory | The real question:
Plan: 210 to primes → build full list of factors from prime components →
distinguish between multiples of 42 and non-multiples → count factors →
compute probability.
Alternatively, you could list all the factors of 210 using factor pairs.
1 210
2 105
3 70
5 42
6 35
7 30
10 21
14 15 |
book 2_p82_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 82 | 82 | number_theory | There are 16 factors of 210, and two of them (42 and 210) are multiples
of 42.
You can also count the factors using 210’s prime factorization: (2)(3)(5)
(7) = (21)(31)(51)(71).
Here’s a shortcut to determine the number of distinct factors of 210. Add
1 to the power of each prime factor and multiply:
There are 16 differe... |
book 2_p83_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 83 | 83 | sequences_patterns | the factor-counting shortcut, but only if you do know how to deal with
the multiples of 42.
2. (A) 2:
1. What it’s asking: The problem asks for the units digit. Because the
problem talks about a product, you care only about the units digits, not
the overall values. Furthermore, the problem provides crazy numbers;
you a... |
book 2_p84_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 84 | 84 | number_theory | 3. (E) 35:
1. What it’s asking: The problem asks for the minimum number of
chocolate chip cookies.
Given: The baker only makes chocolate chip (C) or peanut butter (P) cookies. He can only
make chocolate chip cookies in batches of 7 and peanut butter cookies in batches
of 6. He makes exactly 95 cookies total.
What jumps... |
book 2_p85_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 85 | 85 | algebra | 7C 6P = 95 − 7C Is 6P a multiple of 6?
(i.e., Is P an integer?)
28 67 N
35 60 Y
Use the answer choices to calculate the value of 6P. Cross off an answer
choice if 6P is not a multiple of 6. The first answer choice that works is
the last one. The correct answer is (E).
2. At least one takeaway: The two competing constrai... |
book 2_p86_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 86 | 86 | algebra | The width, w, appears in all three constraint equations, so solve for the
other variables in terms of w and substitute into the longest constraint:
Substitute:
Since w can’t be zero, you can divide it
out safely.
Solve for all variables:
The correct answer is (E).
At least one takeaway: The question is complex enough t... |
book 2_p87_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 87 | 87 | algebra | Notice that, though the initial volume formula seemed long and
annoying, the calculations canceled out nicely in the end. This is
common on the GMAT—common enough, in fact, to suspect that you
may be doing something wrong if the algebra becomes very messy.
5. (D) 12:
The question implies that there may be multiple solu... |
book 2_p88_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 88 | 88 | algebra | Sum of the different solutions: 5 + 4 + 3 = 12. The correct answer is (D).
Approach #2: simplify the equation and use theory to finish it off. Isolate
the absolute value:
Think it through. You square a number and get the absolute value of
that same number (not squared!). Only a few numbers can make that
true: 1 squared e... |
book 2_p89_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 89 | 89 | word_problems | CHAPTER 2
Problem Solving: Strategies &
Tactics |
book 2_p90_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 90 | 90 | word_problems | In This Chapter...
Advanced Strategies
Advanced Guessing Tactics |
book 2_p91_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 91 | 91 | word_problems | Chapter 2
Problem Solving: Strategies & Tactics
Sometimes you will encounter a Problem Solving (PS) problem that you
can’t answer—either because its content is difficult or obscure or because
you don’t have enough time to solve completely in two minutes.
This chapter describes a series of different methods you might try ... |
book 2_p92_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 92 | 92 | strategy | The rest of the chapter is devoted to four specialized tactics that can knock
out answer choices or provide clues about how to approach the problem
more effectively:
One of the most productive strategies on the GMAT is to pick good
numbers and plug them into unknowns. Try this when the concepts are
especially complex or... |
book 2_p93_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 93 | 93 | word_problems | PS Tactic 1: Look for Answer Pairs
Some PS questions have answer choices that pair with each other in
some way. The correct answer may be part of one of these pairs.
PS Tactic 2: Apply Cutoffs
Sometimes a back-of-the-envelope estimation can help you eliminate
any answer choice above or below a certain cutoff.
PS Tactic 3... |
book 2_p94_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 94 | 94 | algebra | Advanced Strategies
1. CHOOSE SMART NUMBERS
Some types of problems allow you to pick real numbers and solve the
problem arithmetically rather than algebraically. For instance, almost any
Problem Solving problem that has variables in the answer choices gives you
this opportunity. Likewise, you can o en pick a smart numb... |
book 2_p95_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 95 | 95 | algebra | Andra, Elif, and Grady each invested in a certain stock. Andra
invested q dollars, which was 40% more than Elif invested. If Elif
invested 25% less than Grady invested, what was the total amount
invested by all three, in terms of q ?
This problem can be solved algebraically: write a couple of equations and
solve for al... |
book 2_p96_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 96 | 96 | strategy | Andra invests 40% more than Elif. For just these two, it would be easier to pick
a number for Elif and then calculate Andra’s amount.
Elif invests 25% less than Grady. For these two, it is easier to start with Grady
and then calculate Elif. As a result, start with Grady, then find Elif, then find
Andra.
If Grady invest... |
book 2_p97_c1 | Manhattan Prep GMAT Advanced Quant | book 2.pdf | pdf | 97 | 97 | word_problems | have been to figure out Elif’s amount. It is not the case that Elif would be $60,
or 40% less than Andra.
Rather, Andra is 40% more than Elif: 1.4e = $100, so
. Elif would
actually equal approximately $71.42857. Nobody’s going to want to go down
that path! At this stage, you have two choices: you can go back and pick... |
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