## 760+: What GMAT Assassins Do to Score at the Highest Levels

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### 760+: What GMAT Assassins Do to Score at the Highest Levels

by [email protected] » Fri Aug 18, 2017 10:08 am
760+: What GMAT Assassins Do to Score at the Highest Levels

Introduction:

Whether you're just beginning your studies or have been training for the GMAT for some time now, you likely have some idea of what your 'goal score' is. For many GMATers, the goal is 700+. That score is relatively rare territory though - only about 10% of Test Takers ever reach that level (and some of them actually hit that score repeatedly - in an attempt to score higher, so not as many Test Takers score 700+ each year as you might think). Obviously, the numbers become even more rare at higher levels. The 760+ level is essentially the 99th percentile. For simple comparison purposes, for every 1,000 people who take the GMAT this year, only about 10 of them will score 760+ (and some of those Test Takers are GMAT Teachers/Tutors or other industry experts).

The GMAT is a remarkably consistent Exam. It's predictable - and you can train to properly face everything that will appear on Test Day. However, mere knowledge will not be enough to get you to a 760+. The GMAT is NOT an 'IQ test', nor is it a 'math test' or a 'vocab test.' At its core, it's a 'critical thinking test', so to score at the highest levels, you have to look beyond having the necessary knowledge and general math/verbal abilities - and you have to train to 'see' (and respond to) the GMAT a certain way. A degree of flexibility is required on your part; since GMAT questions can almost always be approached in more than one way, you have to learn the various approaches (so that you can choose the most efficient approach for every question that you face).

GMAT Assassins aren't born, they're made,
Rich

Note: If you have any questions about anything in this thread, then you can feel free to contact me directly via email or PM.

Page 1:
08/18/2017 Learning to Solve Quant Questions in More than Just One Way (part 1)
08/20/2017 Learning to Solve Quant Questions in More than Just One Way (3 approaches)
08/28/2017 Finding Patterns in PS Questions When You Don't Immediately See Them
01/02/2018 Test Your Pattern-Finding Skills on These 3 PS Questions
01/10/2018 Solutions: The Patterns Behind those Prior 3 PS Questions
01/19/2018 Acknowledge That "Your Way" is NOT Necessarily the Fastest Way (and Then CHANGE Your Approach)
05/12/2018 Answer to the Prior Question: Long Math Approaches vs. Faster Tactical Approaches
Last edited by [email protected] on Sat May 12, 2018 1:39 pm, edited 7 times in total.
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by [email protected] » Fri Aug 18, 2017 10:10 am
Learning to Solve Quant Questions in More than Just One Way (part 1)

The Quant section of the GMAT is NOT a 'math test' - it's a 'critical thinking test' that uses math as the subject through which you can prove your critical thinking skills. While the Quant section does require that you complete lots of basic calculations as you work through the section, the GMAT will NEVER require that you complete complex calculations to get to the correct answer... so if you CHOOSE to approach questions in that way, then you will likely limit how high you can score. If one of your goals is a Q51, then you would find it really helpful to build up a multitude of Quant skills, instead of focusing on complex, long-winded 'math approaches' that often take longer to implement than other more-strategic options and increase the chances of you making little mistakes along the way.

The GMAC Official Guide is a fantastic book of practice questions - and if you don't have a copy, then you should absolutely purchase one for your studies.

Consider the following question that appears in the Diagnostic Test of the GMAC Official Guide. It's question #8 in the Problem Solving section of the Diagnostic - and has appeared in the last several versions of that book:

If a certain toy store's revenue in November was 2/5 of its revenue in December and its revenue in January was Â¼ of it's revenue in November, then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?

Â¼
Â½
2/3
2
4

This is a fairly mid-level prompt; it's a little wordy but the 'math' behind it isn't too difficult. How would you approach it? Would you use algebra? Do you recognize that there are at least two OTHER ways to get to the correct answer (and one of those approaches requires almost no math...)?

Take a moment to answer this question in whatever way you choose. Write everything down and - in the next post - we'll compare your approach to the three options that I've hinted at.

GMAT Assassins aren't born, they're made,
Rich

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by [email protected] » Sun Aug 20, 2017 10:03 am
Learning to Solve Quant Questions in More than Just One Way (3 approaches)

In the prior post, I hinted that there were (at least) 3 different approaches to solving the included OG Diagnostic question. Here they are:

1st Approach: Algebra

The explanations provided in the Official Guide often focus on the 'math approach' as that is that standard approach taken in most math books. However, that type of approach is often step-heavy and arguably takes the longest to complete.

For this prompt, we can create 3 variables:

N = revenue in November
D = revenue in December
J = revenue in January

With the information in the first half of the prompt, we can create two equations:

N = (2/5)(D)
J = (1/4)(N)

We're then asked to calculate (D) / [(N+J)/2]

With the given equations, we can translate each variable 'in terms of' D and plug in... Again, this is tedious, step-heavy work, but you can view it in the Official Guide if you like.

2nd Approach: TESTing VALUES

Many questions in the Quant section can be solved with a Tactical approach (and part of your training should focus on learning those approaches and when certain Tactics are applicable). Here, we are given no actual values to work with, so we can choose our own.

Based on the fractions involved, the common denominator would be 20, so let's start with D = 20...

IF....
D = 20 then
N = (2/5)(D) = 8
J = (1/4)(N) = 2

Now, we just have to place D = 20, N = 8 and J = 2 into the question....

(20) / [(8 + 2)/2] = (20) / (5) = 4

This is the answer to the question - and you'll get that same result regardless of the values that you choose to TEST (as long as your numbers 'fit' the given equations). This approach has the benefit of being fast and easy (consider the work involved - we're really just adding and multiplying small numbers together). With fewer steps, you're also less likely to make a little mistake along the way.

Certain questions in the Quant section are designed with really fast 'concept shortcuts' in mind. This is done on purpose to reward strong critical thinkers. Business Schools are looking for EXACTLY that type of critical-thinking applicant, but the GMAT has no way to give you extra points for 'being clever' - it can only provide you with potential shortcuts that will save you time and decrease whatever pacing-related anxiety that you might have. As a result of finding these shortcuts, your chances of scoring higher should increase, since you'll have more time to answer the remaining questions than someone who is using lengthy math approaches and losing time as a result.

Here, consider how the given monthly revenues relate to one another....

1 - November's revenue is 2/5 of December's revenue. This means that the December revenue is MORE THAN DOUBLE November's revenue.

2 - January's revenue is Â¼ of November's revenue. Since January's revenue is so much smaller than November's revenue - and we already know that December's revenue is MORE THAN DOUBLE November's revenue, then this means that December's revenue is a LOT greater (FAR MORE than double) than January's revenue.

We're asked to compare December's revenue to the AVERAGE of November's and January's.... Averaging those two smaller numbers will lead to a result that is SMALLER than November's. By extension December's revenue will be far GREATER than double than average. Looking at the answer choices, there's only one answer that fits that description.... 4.

Now, consider how much actual work went into the 2nd and 3rd approaches to this prompt (especially relative to the work that went into the 1st approach). Assuming that you had an equal ability to tackle this question using all 3 approaches, which one would be fastest and easiest to implement? If you're training to be a 760+ Assassin, then you know that it's NOT the 1st approach.

GMAT Assassins aren't born, they're made,
Rich

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by [email protected] » Mon Aug 28, 2017 2:16 pm
Finding Patterns in PS Questions When You Don't Immediately See Them

Since the GMAT is a standardized Test, all of the questions that you'll face are designed around one or more patterns. Sometimes the patterns are obvious - such as math formulas or grammar rules. Sometimes the patterns are more subtle - such as number properties or causality arguments.

With the proper study materials and Study Plan, you can learn all of the necessary patterns and train to properly use them. However, sometimes the patterns are so rare that they're not worth learning in advance and sometimes they are essentially 'hidden', meaning that you won't immediately see the pattern involved. However, the pattern is still there - and correctly answering some of the tougher questions on the GMAT will be considerably easier IF you are comfortable with the idea that you can 'play around' with the prompt a bit and define what the pattern is.

"Playing around" with a GMAT question is essentially about running little 'experiments' on it. In basic terms, you need to ask "what if....?" and then go about determining the result.

For example, here is a question from the PS Forums here. Your immediate task is NOT to calculate the result - it's to figure out the first 4 terms in the sequence and THEN deduce a pattern within those 4 terms....

For every integer K from 1 to 10, inclusive, the Kth term of a certain sequence is given by:

[(-1)^(K+1)] x [1/(2^K)].

If T is the sum of the first 10 terms in the sequence, then T is....

A. Greater than 2
B. Between 1 and 2
C. Between Â½ and 1
D. Between Â¼ and Â½
E. Less than Â¼

So... what have you deduced? The answer appears below:

The first four terms are: +1/2, - 1/4, + 1/8, - 1/16. Thus, the terms 'flip-flop' between positive and negative. In addition, each negative term, when 'paired' with the positive term immediately ahead of it, cuts the positive term in half...

+1/2 - 1/4 = +1/4
+1/8 - 1/16 = +1/16

Now that you recognize this pattern, you should be able to quickly determine that the value of the other three 'pairs' gets progressively smaller: 1/64, 1/256, 1/1024

The question asks for the sum of those first 10 terms, but doesn't provide exact answers - it provides RANGES, so you do NOT have to be exact with your math. What are we really adding to +1/4? A bunch of increasingly shrinking (and significantly smaller) fractions. Thus, the sum has to be....

A little more than Â¼. Final Answer: D

In the next post, I'll list a few additional PS prompts for you to 'play around' with. Remember the immediate goal - decipher the pattern first. Then, use whatever pattern you discover to answer the question.

GMAT assassins aren't born, they're made,
Rich

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by [email protected] » Sat Sep 09, 2017 10:12 am
Test Your Pattern-Finding Skills on These 3 PS Questions

For each of these three prompts, you should attempt to 'play around' with the question to define the pattern(s) involved - using the same approach showcased in the prior post. An explanation for how to approach each prompt in such a way will be provided tomorrow.

1) How many positive integers, from 2 to 100, inclusive, are not divisible by odd integers greater than 1?

A. 5
B. 6
C. 8
D. 10
E. 50

2) There are 20 doors marked with numbers 1 to 20 and there are 20 individuals marked 1 to 20.

An operation on a door is defined as changing the status of the door from open to closed or vice versa. All doors are closed to start with.

One at a time, one randomly picked individual goes and operates the doors. The individual operates only those doors which are a multiple of the number he/she is carrying. For example, the individual marked with the number 5 only operates the doors marked with the following numbers: 5, 10, 15 and 20.

If every individual in the group gets one turn, then how many doors are open at the end?

A. 0
B. 1
C. 2
D. 4
E. 6

3) A test has 200 questions. Each question has 5 options, but only 1 option is correct. If test-takers mark the correct option, then they are awarded 1 point. However, if an answer is incorrectly marked, the test-taker loses 0.25 points. No points are awarded or deducted if a question is not attempted. A certain group of test-takers attempted different numbers of questions, but each test-taker still received the same net score of 40. What is the maximum possible number of such test-takers?

A. 31
B. 33
C. 35
D. 40
E. 42

GMAT assassins aren't born, they're made,
Rich

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by [email protected] » Tue Jan 02, 2018 12:24 pm
Test Your Pattern-Finding Skills on These 3 PS Questions

For each of these three prompts, you should attempt to 'play around' with the question to define the pattern(s) involved - using the same approach showcased in the prior post. An explanation for how to approach each prompt in such a way will be provided in the next post.

1) How many positive integers, from 2 to 100, inclusive, are not divisible by odd integers greater than 1?

A. 5
B. 6
C. 8
D. 10
E. 50

2) There are 20 doors marked with numbers 1 to 20 and there are 20 individuals marked 1 to 20. An operation on a door is defined as changing the status of the door from open to closed or vice versa. All doors are closed to start with. One at a time, one randomly picked individual goes and operates the doors. The individual operates only those doors which are a multiple of the number he/she is carrying. For example, the individual marked with the number 5 only operates the doors marked with the following numbers: 5, 10, 15 and 20.

If every individual in the group gets one turn, then how many doors are open at the end?

A. 0
B. 1
C. 2
D. 4
E. 6

3) A test has 200 questions. Each question has 5 options, but only 1 option is correct. If test-takers mark the correct option, then they are awarded 1 point. However, if an answer is incorrectly marked, the test-taker loses 0.25 points. No points are awarded or deducted if a question is not attempted. A certain group of test-takers attempted different numbers of questions, but each test-taker still received the same net score of 40. What is the maximum possible number of such test-takers?

A. 31
B. 33
C. 35
D. 40
E. 42

GMAT assassins aren't born, they're made,
Rich

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by [email protected] » Wed Jan 10, 2018 5:43 pm
Solutions: The Patterns Behind those Prior 3 PS Questions

While each of these three prompts might look complex, you CAN get to the correct answer by defining the patterns involved.

1) How many positive integers, from 2 to 100, inclusive, are not divisible by odd integers greater than 1?

In this prompt, we're asked to think about the numbers 2 to 100, inclusive. To start, there's NO way that the GMAT would ask us to truly think about each of these numbers individually, so there MUST be a pattern involved.

Now to the specifics: which of these numbers are NOT divisible by an odd integer that is greater than 1???

Let's start at the first number and work our way "up" until the pattern becomes clear:

2 - this is NOT divisible by any odd integers, so this "fits" what we're looking for...
3 - this IS divisible by an odd integer (3), so it's out
4 - this is NOT divisible by any odd integers, so this "fits"
5 - this IS divisible by an odd integer (5), so it's out
6 - this IS divisible by an odd integer (3), so it's out
7 - this IS divisible by an odd integer (7), so it's out
8 - this is NOT divisible by any odd integers, so this "fits"

Now, looking at the numbers that "fit", we have 2, 4 and 8.....that's 2^1, 2^2 and 2^3....that MUST be the pattern involved, so we can use this knowledge against the rest of the question to find the other values that "fit":
2^4 = 16
2^5 = 32
2^6 = 64
2^7 = 128, but that's outside the range that we were given. Thus, there are 6 values that "fit" what we're looking for.

2) There are 20 doors marked with numbers 1 to 20. And there are 20 individuals marked 1 to 20. An operation on a door is defined as changing the status of the door from open to closed or vice versa. All doors are closed to start with. Now one at a time one randomly picked individual goes and operates the doors. The individual however operates only those doors which are a multiple of the number he/she is carrying. For e.g. individual marked with number 5 operates the doors marked with the following numbers: 5, 10, 15 and 20. If every individual in the group gets one turn, then how many doors are open at the end?

It would take a LOT of time to work through all 20 people and all 20 doors, so I'm going to work through the first several so that we can define the pattern involved...

Remember: All the doors start off CLOSED...
Door 1: Only Person 1 touches this door. So it IS OPEN at the end.
Door 2: Person 1 and Person 2 touch this door. So it is closed at the end.
Door 3: Person 1 and Person 3 touch this door. So it is closed at the end.
Door 4: Person 1, 2 and 4 touch this door. So it IS OPEN at the end.

Now, stop and look at the work that we've done so far... Which doors do we know for sure will be open? Door 1 and Door 4. What do those two numbers have in common? They're both PERFECT SQUARES..... Let's see if that pattern continues...

Door 5: Person 1 and 5 touch this door. CLOSED.
Door 6: Person 1, 2, 3 and 6 touch this door. CLOSED.
Door 7: Person 1 and 7. CLOSED.
Door 8: Person 1, 2, 4 and 8. CLOSED
Door 9: Person 1, 3 and 9. OPEN.

Notice how the next door that we know will be open in the end is Door 9. It is ALSO a PERFECT SQUARE. Given the work we've done so far, this MUST be the pattern, so we're ultimately looking for the number of perfect squares from 1 to 20. They are 1, 4, 9 and 16. That's a total of 4 open doors at the end.

3) A test has 200 questions. Each question has 5 options, but only 1 option is correct. If test-takers mark the correct option, then they are awarded 1 point. However, if an answer is incorrectly marked, the test-taker loses 0.25 points. No points are awarded or deducted if a question is not attempted. A certain group of test-takers attempted different numbers of questions, but each test-taker still received the same net score of 40. What is the maximum possible number of such test-takers?

From the answer choices, we can see that there are a lot of different ways to get a total of 160 points (at least 31 ways...), so there's no way that the GMAT would require that we calculate each individual option. There has to be a pattern, so let's start off with the easiest 'ways' to get 160 points and go from there... Remember - a correct answers get you 1 point, an incorrect answer gets you MINUS 1/4 point and a skipped question gets you 0 points. So, how can we get 160 points...

40 correct, 0 incorrect, 160 skipped
41 correct, 4 incorrect, 155 skipped
42 correct, 8 incorrect, 150 skipped
Etc.

To find all of the options, you can either "count up" (40+0 = 40, 41+4 =45, 42+8 = 50, etc.) OR you can "count down" from the number of skipped questions. (160, 155, 150, etc.). With either option, you'll eventually run out of questions, then you'll be done.

Counting down from 160 is probably faster, as long as you don't forget the final option - the one with 0 skipped questions). Here, there are 33 multiples of 5 (including the 0
'option').

As you continue to study, it's important to remember that most GMAT Quant questions are NOT 'testing' your knowledge of advanced math, specialty formulas or complex ideas. The 'math' behind most Quant questions is actually rather straight-forward. As such, to maximize your score, you have to be ready to 'play around' with 'tough-looking' prompts and find the simple math behind them.

GMAT assassins aren't born, they're made,
Rich

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by [email protected] » Fri Jan 19, 2018 7:10 pm
Acknowledge That "Your Way" is NOT Necessarily the Fastest Way (and Then CHANGE Your Approach)

The GMAT is a remarkably consistent and predictable Exam, so improving your performance isn't just about 'fixing' the things that you are doing 'wrong' - it's also in developing the proper skills to improve on work that you can already do.

Consider the following question. For many "math thinkers", the approach would be "system algebra" - write out the appropriate equations and then solve for whatever the question asks for. That approach will absolutely get you to the correct answer here - and I suggest that you try it. Make sure to time yourself though - we need to know how long it would take you to solve this question using an algebraic approach.

Andrew has a certain number of coins in his pocket. He has three times as many dimes as quarters and six times as many nickels as dimes. A nick is worth $0.05, a dime is worth$0.10 and a quarter is worth $0.25. If he has a total of$10.15, then which of the following represents the number of dimes in Andrew's pocket?

9
10
18
20
21

How long did it take you? For most GMATers, this question would require 2-3 minutes of work. If you're really great at algebra, it might take you less time than that.

Now, I bet that I can show you a MUCH faster way to get to the correct answer - and it's an approach that you'll be able to use 2-3 times on the Official GMAT. Tomorrow, I'll show you how it works and how to use it.

GMAT assassins aren't born, they're made,
Rich

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by [email protected] » Sat May 12, 2018 1:38 pm
Answer to the Prior Question: Long Math Approaches vs. Faster Tactical Approaches

In the prior post, I listed the following Quant PS question:

Andrew has a certain number of coins in his pocket. He has three times as many dimes as quarters and six times as many nickels as dimes. A nick is worth $0.05, a dime is worth$0.10 and a quarter is worth $0.25. If he has a total of$10.15, then which of the following represents the number of dimes in Andrew's pocket?

9
10
18
20
21

Many GMATers will approach these types of questions algebraically, even though that type of approach often takes longer than other, faster, more strategic options.

To start, here is how you can solve this algebraically. Let's use the following variables:

N = number of nickels
D = number of dimes
Q = number of quarters

The second sentence allows us to create two equations using the above variables:

D = 3Q
N = 6D

The third and fourth sentences allow us to create a third equation:

(.05)N + (.10)D + (.25)Q = 10.15

Now we have a 'system' of equations - three variables and three unique equations, so we can solve for each of the individual variables. The prompt asks us to determine the number of DIMES, so I'll focus the work on solving for D.

D = 3Q .... Q = D/3
N = 6D

Substituting in for N and Q, we end up with...

(.05)(6D) + (.10)(D) + (.25)(D/3) = 10.15

.3D + .1D + (.25D/3) = 10.15

We can now multiply everything by 3 to get rid of the fraction...

.9D + .3D + .25D = 30.45

1.45D = 30.45

D = 30.45/1.45

D = 21

Now, consider ALL of the work that I just did. Even if you took a slightly different approach to the algebra, how long would all of this work take...? Two minutes? Three minutes? Longer?

Instead, let's use the 'design' of the GMAT to our advantage. Here, the answer choices ARE numbers, and we're asked to solve for just one variable (the number of dimes), so let's TEST THE ANSWERS.

To start, we're told that the number of dimes is 3 TIMES the number of quarters, so the number of dimes MUST be a MULTIPLE OF 3. That helps us to immediately eliminate answers B and D (since 10 and 20 are NOT multiples of 3).

Let's TEST Answer C: 18. If it's the correct answer, then we'll be done. If it's "too high" or "too low", then we'll know exactly which of the remaining two answers is the correct one.

IF... there are 18 dimes
Then there are 6 quarters (since there are three times as many dimes as quarters) and there are 108 nickels (since there are 6 times as many nickels as dimes).

Given the respective values of the three coins, we would have a total of....

(108)(.05) = $5.40 (18)(.10) =$1.80
(6)(.25) = $1.50 Total =$8.70

However, we were told that the actual total value of the coins is $10.15. This total ($8.70) is TOO LOW, which means that we need there to be more nickels, dimes and quarters. There's only one answer left that 'fits' what we're looking for, so that MUST be the correct answer!