It is important to realize that contributes to tougher feel of the GMAT Quant section is that the GMAT questions often blend multiple topics into one question. While Secondary School exams had the problems on topics separated out, having multiple concepts applied in one question is indeed tougher. Hence, let us take a look at all the topics that are in syllabus for GMAT Math.

Below, we have divided the GMAT Math topics by three categories:

Math topics such as Trigonometry, Calculus and Complex numbers are currently not in scope of the GMAT Math Syllabus. However, for solving a triangle related problem you may use any tool at your disposal including Trigonometry. Similarly you can use any advanced mathematics tool at your disposal to solve a particular problem.Note:

Arithmetic Topics | GMAT Quant Topics |
---|---|

Number Theory | Integers and number properties |

Fractions, Percentage and Decimals | |

Multiples and Factors | |

Exponents and Radicals | |

Remainders and Divisors | |

Ratio and Proportion | |

Permutations & Combinations | |

Probability | |

Absolute Values | How to solve GMAT Modulus / Absolute Value questions & math practice questions |

Set Theory | |

Mixtures & Alligations | How to Solve GMAT Mixtures & Allegations problems |

Statistics | Most important GMAT Statistics Tutorials & Practice Questions |

Pipes & Cisterns | |

Speed, Time & Distance | |

Simple and Compound Interest |

All things considered, Arithmetic makes for the most complex GMAT questions on GMAT Math section. Obviously, Probability and Permutations & Combinations topics are well known to be very complex. However, even simple topics such as integers are full of tricks and concepts that need to be mastered for a good GMAT score.

- (2022) What Are GMAT Quant Topics in Syllabus For The GMAT Test ?
- GMAT Statistics Practice Examples
- Tricky Triangles – daily GMAT practice example – DS

Algebra |
---|

Monomials & Polynomials |

Functions |

Equations |

Quadratic Equations |

Inequalities |

Progressions |

As a matter of fact, Equations and Inequalities seem to be the most popular in GMAT Quant among the Algebra topics. If you are strapped for time during your preparation, you may focus on these topics (amongst the algebra topics) to get the most out of your time. At GMAT By Examples, we have FREE comprehensive guides for the following topics:

- GMAT Inequalities
- GMAT Equations (coming soon)

Geometry | Learn more |
---|---|

Lines and Angles | |

Triangles | GMAT Triangles Properties & Theorems: 23+ Theorems on GMAT Triangles in GMAT Quant syllabus |

Quadrilaterals | |

Circles | GMAT Circles Properties & Theorems: 31+ Theorems on GMAT Circles in-scope for GMAT Quant Preparation |

Solid Geometry – Cubes, Cylinders, Pyramids etc. | A Framework to solve all the “Fitting one container into another” type of GMAT Quant Questions |

Coordinate Geometry | |

Please note that, Geometry is a long topic and the problems usually range from basic to medium complexity. However, you may come across some really tough Geometry problems in your exam. Hence, to save time and not get stuck in Geometry questions, we recommend that you prepare well by remembering as many geometry properties as you can.

For more information on the GMAT syllabus, please visit mba.com.

]]>In GMAT, Statistics is one of the toughest topics to master. And while there are various guides providing theory, theory, theory – not a single guide explains the “**Thought Process**“. In the few examples below we take GMAT Statistics to the next level – ** “Understanding the Thought Process”** – by solving many GMAT Statistics practice examples with the following in mind:

**Step by Step**approach to solving GMAT Statistics Practice examples**Wrong vs Right approach**to solving the Statistics practice questions- Understanding
**Common Mistakes**people make while solving the Statistics questions. **How to get unstuck**when you are stuck and do not know how to proceed.

Step by Step, Wrong & Right approach, Understanding & avoiding common mistakes & knowing how to get unstuck

Thats how you master a topic.

1) The sum of the elements of the series is 35

2) There are 5 elements in the series

Why do people get this question wrong? What is the possible impact on the GMAT Score?

GMAT Preparation Strategy

1) Minimum number in the set is 50

2) The average of the numbers in the set is 50

What if the question had asked “What is the total number of elements in the set?”. In GMAT, simple question can be converted into a 700+ question. You must know the right approach to solve these GMAT Statistics sample questions.

How to Solve GMAT Statistics Sample questions

1) The median of all the scores is 45

2) The range of all the scores is 38

A? B? C? What is the right answer? What is the impact of getting this level of question incorrect in the actual exam?

GMAT By Example

1) 10 is the median of S

2) c is the median of S

GMAT 700+ Level statistics question that most get wrong. Learn from their mistakes and avoid the wrong approach

GMAT By Example

1) The range of the sequence is y

2) The smallest observation in the sequence is 0

Stuck? Let’s focus on how to get

GMAT By Exampleunstuckthrough a solution to GMAT Statistics sample problem.

- Free GMAT Videos: https://bit.ly/GMATExample_U
- Best Online GMAT Course: https://bit.ly/MagooshU
- GMAT Preparation Study Plan: https://bit.ly/GMATStudyPlan2021
- Free GMAT Mock Tests: https://bit.ly/GMATMocks
- Facebook group: https://bit.ly/3jJh4dM

Q. In a triangle two of the sides are 7 and 19. What is the value of the third side?

1) the triangle is an isosceles triangle

2) the third side is a multiple of 7

**Difficulty level**: 600+

**Concepts/Topics tested**: #Geometry, #triangles

**Main/differentiating concept**: Sum of two sides > greater than third side

**Other similar problems on YouTube**:

Looking for a study plan? : GMAT Study Plan 2021

Fine more Triangles GMAT practice example on YouTube: GMAT Triangles

]]>Not a member of GMAT WhatsApp groups? Join now (membership is limited):

Topic | Sub-Topic | Concepts | Relevant links |
---|---|---|---|

Number Theory | HCF / GCD, LCM | Two important concepts are discussed in this example – product of two numbers equals product of HCF and LCM. And GCD (HCF) must be a factor of LCM. Do not miss out on explanation of this tricky problem. | https://youtu.be/xqvuO937wSc |

Number Theory | Even Odd | This gmat example discusses two important concepts: The importance of simplifying the terms for even and odd discussions, and the importance of zero | https://youtu.be/q3l2MFKQSEU |

Number Theory | Greatest Integer | The approach to solve complex greatest integer problems. | : https://youtu.be/rj-XX_9oIAgBeginner level theory: https://youtu.be/7TaEiIRN2IAModerate level theory:Expert level theoryhttps://youtu.be/piKezWYJ3HY Solution:Coming soon |

Inequalities | Absolute value | This classic problem by CrackVerbal through GMATClub demonstrates many concepts of inequalities and absolute value. Solved via three methods. | : https://youtu.be/20jkPQm75AUSolution – Algebra: https://youtu.be/6vRKVrhUHAASolution – Picking values:Solution – Distancehttps://youtu.be/DBxEfmFQN0A |

Inequalities | Absolute value | This is a challenge problem based on the previous GMAT Example we solved (above). Hence, you must use the concepts learnt in previous video to solve this problem. | GMAT Inequalities Challenge Problem |

If you have any questions regarding these GMAT example questions or their solutions, please comment here or contact us. Experts also respond to queries posted in the FaceBook group & WhatsApp groups above.

]]>[su_pullquote]Starting GMAT Prep can be overwhelming with so many books, videos, groups and prep companies all trying to get your attention.[/su_pullquote]

In this article, we will provide a step-by-step Study Plan to get your GMAT Preparation started. The article by default assumes that you are looking to self-prepare at the start of your GMAT Prep.

As you might imagine, this is a generic post applicable to all GMAT Participants. If you are looking have answers for your particular case, please Contact us.

So, here is the 10-step GMAT Study Plan that we will detail in this article:

- #1: Familiarize yourself with the GMAT
- #2: Understand your target GMAT score
- #3: Gather the most essential GMAT resources
- #4: Get ready to track your mistakes – create a log
- #5: Benchmark yourself before you start
- #6: Personalize your prep – identify weak areas
- #7: Personalize your prep – the future weeks
- #8: Commit to the work
- #9: Avoid common GMAT Prep mistakes
- #10: Seek paid help if needed

Firstly, before diving to the deep end, you should take a few days just to familiarize yourself with the GMAT exam. Here are the few resources that will help:

Why? You need to set a goal when you start the prep without which you will not be organized enough. In general, you would need 700+ for top 20 B-schools, 680+ for B-schools ranked 20-40 and about 650 to crack into top 50.

Essentially, if you score well above the average GMAT score for your target schools, you will have better chances of admission.

This is where most GMAT Aspirants make a mistake. They spend so much time collecting every book ever written on GMAT, every video ever made and other materials that they lose sight of their goal and feel overwhelmed.

However, here is the good news – you only need to start with a few basic essential resources to start your GMAT Prep and we have laid them out here. Along with the books, there are some additional resources such as Facebook groups, YouTube Channels, WhatsApp/Telegram groups and GMAT Forums that you should join to keep yourself connected in the GMAT world and follow questions, experiences and the latest in the MBA Admissions process.

GMAT Official guides are the only only books from the official source and contain real GMAT questions for you to practice. Hence, we recommend the Official Guide Bundle with the online question bank (The first in the list below). If you are at an advanced stage of your prep and already scoring close to 650+, we recommend GMAT Advanced Questions book.

Manhattan Prep Guides have for a long while been one of the best source of GMAT Verbal Preparation. Their Sentence Correction, Critical Reasoning and Reading Comprehension books have all helped test takers for past 10+ years. The Mathematics books are decent as well, however the verbal have better ROI. While their “All the GMAT” book bundle comes with 6-Practice tests, it is pricey at $150, therefore, we recommend that you start with either the Verbal bundle “All the Verbal” or just the Sentence Correction book.

If you are already advanced in your prep, then the “GMAT Advanced Quant 250+” is highly recommended.

Facebook has many active GMAT groups, so you can always search for them. However, most groups are filled with spam with minimal admin activity to fight spam. There is just no point overwhelming yourself with all the different Facebook groups out there that will not add any value to your preparation. Hence, we recommend the following groups mostly due to the reduced spam and better quality control:

Some of these groups are new, but we like them because of better spam control.

Similar to facebook groups, there are just wide array of WhatsApp groups, however the activity can be limited while taking up important space on your phone. Hence, we do not recommend participating in more than 2-3 groups because the discussion can be distracting. We recommend the following groups, however please note that the entry to the groups are limited:

YouTube has plenty of videos on different topics related to GMAT that you could look at, however most videos are not in-depth enough to help. In other words, they are built to lure you into some kind of paid service or other. On the other hand, On our YouTube channel we post a lot of free detailed and in-depth videos on a variety of GMAT topics including ways to solve complex GMAT topics.

Please subscribe: GMAT By Example YouTube Channel.

There are two most famous GMAT forums. Again forums can be distracting to your overall prep, however when you are practicing questions, forum and the filters they provide can be a very helpful tool to put your prep into overdrive.

Recently GMATClub Forum has been more active than BeatTheGMAT forum so if you are looking to join just one forum, GMATClub might be the way to go.

Don’t underestimate the power of error log. But, what is an error log?

An error log is a tool that you can use to track all of your mistakes during practice/practice tests and then use it to find trends, weak areas and eventually improve. Most importantly, without an error log, you are just going through the motion of preparation without a clear direction on what to tackle next. For instance, imagine this – “If your strong point is Number Theory and you are solving 75% of your time solving Number Theory problems because everyone on FB, WhatsApp is asking them” – Is that really where you should be spending your time on?

Forums like GMATClub have a built in error log, but let’s be honest, you will often solve GMAT practice problems outside of the forum. So, having an error log at the forum doesn’t always help you. Hence we recommend keeping a nice error log of your own.

What should an error log look like? We are glad you asked:

- Please, join our mailing list to get a FREE GMAT Error log template and a guide to use it. efficiently.

The log should be able to track the following:

- Question: types, topics, difficulty, source
- Kind of mistake: Silly, fundamental, didn’t understand question, spent too much time
- Your notes / assessment

Finally, this is where your GMAT Preparation really starts. If you are just starting, then you need to know where you are starting from and how much work you have to do. We will reference to this as your “benchmark”. Here is the basic formula:

*The improvement you need = GMAT Target Score [Step 2]- Your GMAT Practice test score [Step 5: Benchmark] *

It is also important that you utilize the freely available tests from MBA.com for this attempt as these tests are the closest you will find to the GMAT. Alternatively, you could choose to take one of the other available tests – Free GMAT Practice Tests. For this first attempt **only**, you may skip the AWA/Essay section as we are not really testing your stamina just yet, but your knowledge.

After the test, it is time to input the mistakes in your log. This is the start of your log file, hence, you can be as detailed as you can. As you make a habit of logging the items in your log files, you will eventually get into a cadence of inputting only the most required information. But for now, put as much thought as you can in logging the information. I promise, it will help.

Remember the log file? now is the time to look at the log file and analyze the following:

- Where are you making those mistakes, is there any common thread?
- Are you making too many silly mistakes?
- Do you have a tendency to get easy difficulty questions right, but the harder questions incorrect? (Or vice versa due to overconfidence?)
- Is there a certain topic questions that you get consistently incorrect? (Like probability, statistics, subject verb agreement etc.)

Certainly, this is a crucial step in your GMAT Journey, since without proper analysis, you would be at a loss on where to improve. Let’s assume that at this step, you have identified 5 different areas as weak. However, the next step is to start small and focus on 1-2 areas and spend time on those. Finally, go to revise the fundamentals if you need to to master those 1-2 areas before moving to the rest of the weaknesses in your list.

The below diagram outlines the GMAT Study Plan process. Each pillar can be completed within a week, if you have enough time for your preparation. Essentially, the preparation framework is made of three pillars, Take Test -> Identify Weak Areas -> Practice & repeat.

A very common problem Test Takers have during their GMAT Journey is that they do not persevere. Consequently, a stop-start approach to preparation not only loses all momentum, it also undoes some of the learning you have done as you get our of touch with your plan.

Finally, here are some common GMAT Study Plan mistakes you must avoid at all costs:

**Collecting a lot of material**: Starting to collect all the material you can is just disastrous. Do you think that the rules of even and odd change from one book to another? How about rules of grammar? Collecting every book out there, every tutorial, every video is not healthy and it only serves as a distraction and an overwhelming agent.**Jumping into tests and questions unprepared**: Trust the method described in this post. Jumping directly into questions without having a focus area or without having the right fundamentals is going to be ineffective.**Not focusing on fundamentals first**: Assuming that you are already familiar with the GMAT topics because you did them in high school is a mistake. At least a small brush-up of concepts is likely to get you back in the grove.**Getting distracted by “strategies”**: This one is important. There are many “strategies” to solve certain kinds of questions or to improve speed. However without having a handle on the fundamentals, these strategies will just prove as distraction.**Trying to improve speed**: There is just no time to trying to increase speed if your accuracy is already bad. Increase accuracy first!**Getting bogged down with one area**: There are some areas that you just cannot be a master at. If you get stuck trying to get every question right on these topics you will be preparing for ever.

For read this article for more common GMAT Study Plan Mistakes.

There will be instances when you are not able to improve on your own. Hence, It is perfectly ok to seek a tutor or a course to help supplement your preparation. For example when you:

- Do not have a lot of time before your real exam
- Are unable to improve on your scores
- Scoring well in practice tests but poorly in the real exam
- Are not great at self-pacing yourself

]]>

Disclosure: Some of the links above are affiliate links. This means that, at zero cost to you, GMATByExample will earn an affiliate commission if you click through the link and finalize a purchase. #commissionsearned

Starting to collect all the material you can is disastrous. Do you think that the rules of even and odd change from one book to another? How about rules of grammar? Collecting every book out there, every tutorial, every video is not healthy and it only serves as a distraction. Having so much material also overwhelms you.

Jumping directly into questions without having a focus area or without having the right fundamentals is going to be ineffective. Follow a study plan that provides a healthy dose of fundamentals and a focus on weak areas. Checkout GMAT By Example’s GMAT Study Plan [Coming soon].

It is a mistake to assume that you are already familiar with the GMAT topics because you did them in high school. At least a small brush-up of concepts is likely to get you back in the grove.

There is just no point to trying to increase speed if your accuracy is bad. Increase accuracy first! However, many GMAT Test takers make the mistake of jumping into speed and further compromise their accuracy.

- 18 GMAT Acronyms you must know to start an outstanding GMAT Prep
- Most important and basic things you must know about GMAT Exam
- GMAT Inequalities – One mistake to avoid to improve your GMAT score
- GMAT online test Vs GMAT in-center test differences

Not having an “error log” while preparing for GMAT is like missing out on a huge part of due diligence while buying a new company. It is a strict no-no. Logs serve a dual purpose: a) They help you track and analyze your weaknesses b) They also provide a great revision technique during the last few days before your actual GMAT Test. Need a FREE GMAT Error Log template? Please sign up.

GMAT is a test of “application of fundamentals”. Cramming of questions, answer choices or any such material will never be effective. Focus on understanding and the art of problem solving. However, it is ok to remember formulas well.

Topics like Probability & Permutations/Combinations are really hard to master. Hence, getting bogged down and spending too much time trying to master these topics may be folly. Instead, it may be best to cut your losses and move on to other topics that you can actually make some progress on.

Don’t say we didn’t warn you!

*If you are new to GMAT, please see: Introduction to GMAT Test

]]>Along with the fundamentals, we will give you a **“Secret Framework”** that has helped hundreds of students avoid traps in GMAT Number Theory Problems.

Do not miss the “Secret framework” and the “Secret practice resource” to master the GMAT Number Theory Even & Odd topic.

The below videos covers the most important fundamentals on the operations of even and odd integers. It includes some advanced topics such as simplifying the expression without impacting the even and odd nature of the expression. For example, did you know that (t^{6}−13)^{12 * }(t^{3}+4)^{3} can be re-written as (t-13)(t+4) without impacting the even/odd nature of the term? For more understanding of this, please review the video provided below.

The first video below covers the following topics:

- Operations of even & odd integers
- Addition & Subtraction
- Multiplication
- Division

- Powers of even & odd integers
- Simplifying complex terms for even & odd kind of problems

Most importantly, GMATByExample emphasizes the principle of learning through targeted practice and focused approach. The next video takes you through the Secret Framework to avoid GMAT Number Theory traps. In addition, the video takes you through 5 solved examples to apply that framework.

**Secret Practice Resource**

Finally, 5 examples are simply not enough. Therefore, I have created a practice resource that is guaranteed to help you master the GMAT Number Theory Even & Odd topic. And for a limited time, I am giving it away absolutely free! Hence to take advantage of this offer, please visit this page to sign up: GMAT Number Theory Even & Odd Practice Questions Sign up.

**Please view my YouTube channel for additional videos: GMAT By Example**

Hence, to make it quick and easy to solve these type of problems, we have developed a GMAT Inequalities Comparison Framework. However, the framework does come with a caveat – you must remember the range table or must atleast be able to draw the table quickly. This is certainly possible with a little bit of practice.

Since the details of the basic framework for solving this type of question is covered in the article GMAT Comparisons Framework, in this article, we will skip the basics and solve this question using the framework only.

Let’s start with the question statement and see in which of these ranges would the statement be true:

**Is 1/x ^{4} > 1/x^{2} ?**

As you can see from the ranges, for the question statement to be true, x must lie between -1 and 1. We could have arrived at the same conclusion after algebra, but that would have been time consuming and also prone to mistakes.

So the question statement truly becomes:

**Is 1/x ^{4} > 1/x^{2} ?** is same as

Now look at statement (a)

**a) 1/x > 1/x ^{2}**

Lets look at the ranges where this is true:

As you can see in the diagram, this is only possible when x>1. So given that 1/x > 1/x^{2}, we are given that x>1. Hence x cannot be between -1 and 1. So this answers **a clear “NO”** to the asked question in the question statement.

Hence, statement (a) is SUFFICIENT.

Lets look at statement (b)

**b) x ^{2} > 7**

Using a little bit of algebra, we get

x2 – 7 > 0 => (x-⎷7)(x+⎷7) > 0

This gives us:

either x>⎷7 OR x<-⎷7 . This clearly means that x is NOT in the range -1<x<1. Hence, this gives **a clear “NO”** to the asked question.

Hence, statement (a) is SUFFICIENT.

[Coming Soon][su_quote]Coming soon![/su_quote]

]]>[su_quote] **Are you missing out on free webinars and tutorials? Join our facebook group**: ACE GMAT 700+ now! [/su_quote]

In this article we have listed the following GMAT Practice Tests:

- MBA.com (GMATPrep)
- Manhattan Prep (MPrep)
- Veritas Prep
- Kaplan
- Princeton Review
- GMAT Pill
- Economist
- 800Score
- Manhattan Review
- Experts Global
- Crack GMAT
- Target Test Prep
- Other free tests

- (2022) What Are GMAT Quant Topics in Syllabus For The GMAT Test ?
- GMAT Statistics Practice Examples
- Tricky Triangles – daily GMAT practice example – DS

– | Free | Paid |
---|---|---|

Numbers | 2 Tests | 4 Tests |

Type | Adaptive (CAT) | Adaptive (CAT) |

Closeness to real GMAT | Very close (+/- 30) | Very close (+/- 30) |

Price | $0 | $90 (varies) |

Where to find | MBA.com Practice Test 1&2 | MBA.com Practice Test 3-6 |

[su_pullquote]**Free tutorials, expert answers, 750+ questions, Join on Facebook: ACE GMAT 700+ now! **[/su_pullquote]

** Verdict**: Provided by the same company that administers GMAT – GMAC. Contains real GMAT questions and likely uses the same Computer Adaptive Algorithm that real GMAT uses. It is the best predictor of the actual GMAT score based on knowledge. It is hard to predict impact of test conditions, test day stresses on the scores, and since you take this test at your home, there is a possibility that you score better or worse than your practice test results. Previously called “GMATPrep”. Finally – taking the paid tests is also highly recommended.

[su_quote]Buying the paid MBA.com tests is highly recommended! [/su_quote]

– | Free | Paid |
---|---|---|

Number | 1 Test | 5 Tests |

Type | Adaptive (CAT) | Adaptive (CAT) |

Closeness to real GMAT | Very close (+/- 50) | Very close (+/- 50) |

Price | $0 | $49 (could be free with stipulation) |

Where to find | Free Test | Paid Tests |

** Verdict**: Very strong and accurate set of CATs. Students have consistently reported Manhattan Prep tests as the closest to actual GMAT. Students have often reported Quant to be harder than actual GMAT level, so you may actually do better in Quant in real GMAT test.

– | Free | Paid |
---|---|---|

Number | 1 Test | 6 Tests |

Type | Adaptive (CAT) | Adaptive (CAT) |

Closeness to real GMAT | N/A | N/A |

Price | $0 | $49 (could be free with stipulation) |

Where to find | Free Test | Paid Tests |

** Verdict**: Good interface, good quality questions and an overhauled Adaptive algorithm makes for a promising test. Give it a try.

– | Free | Paid |
---|---|---|

Number | 1 Test | 4 Tests – 8 Tests (limited time access) |

Type | Adaptive (CAT) | Adaptive (CAT) |

Closeness to real GMAT | Decent (+/- 70) | Very close (+/- 70) |

Price | $0 | $149-$199 (additional prices likely in combination with their books and courses) |

Where to find | Free Test | Paid Tests |

** Verdict**: Traditionally Kaplan tests used to grade much harsher compared to GMAT. As a result, the test takers often reported huge difference (as much as +100) between the Kaplan’s practice tests and actual GMAT. However, Kaplan’s tests have been overhauled since then and I do not currently have enough data to provide a better picture. They are a very reputed company and its definitely worth it to try out their free test.

– | Free | Paid |
---|---|---|

Number | 1 Test | NA |

Type | Adaptive (CAT) | – |

Closeness to real GMAT | Decent (+/- 70) | – |

Price | $0 | – |

Where to find | Free Test | – |

** Verdict**: Worth a try. GMAT Test takers haven’t really found this test useful. Still if you are running out of options, this is worth a try.

– | Free | Paid |
---|---|---|

Number | 1 | N/A |

Type | Adaptive (CAT) | – |

Closeness to real GMAT | NA | – |

Price | $0 | – |

Where to find | Free Test | – |

** Verdict**: We are not sure if GMAT Pill free test is a standalone test or part of their course which means they will ask for your credit card to take the free test. Further review required. If you have a feedback, please send us a note.

– | Free | Paid |
---|---|---|

Number | 0 (1 available with stipulation) | NA |

Type | Adaptive (CAT) | – |

Closeness to real GMAT | N/A | – |

Price | $0 | – |

Where to find | Free Trial | – |

** Verdict**: We have heard good things about the test. The problem is you can only access the test after your subscribe for a 7-day trial. While no credit-card is required, its not really free is it? There are no paid tests available as a separate package.

– | Free | Paid |
---|---|---|

Number | 1 Test | 5 Tests |

Type | Adaptive (CAT) | Adaptive (CAT) |

Closeness to real GMAT | N/A | N/A |

Price | $0 | $25 |

Where to find | Free Test | Paid Tests |

** Verdict**: 800Score has been in the GMAT business for a long time. They are however not the most popular platform amongst the students we have spoken to. We do not have a lot of information or feedback on them. But hey! they do offer a free test – so what have you got to loos? Try them out!

– | Free | Paid |
---|---|---|

Number | 1 | 1 or 5 |

Type | Adaptive (CAT) | Adaptive (CAT) |

Closeness to real GMAT | N/A | N/A |

Price | $0 | $15 (for 1), $40 (for 5) |

Where to find | Free Test | Paid Tests |

** Verdict**: Wait – didn’t we already cover Manhattan? We covered “Manhattan Prep”. Manhattan Review is a different company and they have been in the GMAT business for a long time. We do not have a lot of information or feedback on them. But hey! they do offer a free test – so what have you got to loos? Try them out!

– | Free | Paid |
---|---|---|

Number | 1 | 15 |

Type | Non-Adaptive | Non-Adaptive |

Closeness to real GMAT | N/A | N/A |

Price | $0 | $15 |

Where to find | Free Test | Paid Test |

** Verdict**: Waiting on a verdict. We do not have enough information yet.

– | Free | Paid |
---|---|---|

Number | 1 | 5 |

Type | Adaptive (CAT) | Adaptive (CAT) |

Closeness to real GMAT | N/A | N/A |

Price | $0 | $50 |

Where to find | Free Test | Paid Tests |

** Verdict**: Waiting on a verdict. We do not have enough information yet.

– | Free | Paid |
---|---|---|

Number | 1 (Quant Only) | |

Type | Adaptive (CAT) | – |

Closeness to real GMAT | N/A | N/A |

Price | $0 | – |

Where to find | Free Quant Test | – |

** Verdict**: Waiting on a verdict. We do not have enough information yet.

- GMAT Statistics Practice Examples
- GMAT Example Questions & Solutions – June 28 – July 3
- GMAT Number Theory: Even & Odd fundamentals & solved examples

- London Business School Free GMAT Practice (Babson, Hult, Oxford – all of these provide the same interface from economist, so there is no guarantee that the questions will be any different than the Economist practice test listed above)
- Platinum GMAT

I.1 Is |x-y|>|x| ?

(a) |x+y|<|x-y|

(b) x=-7y

If you haven’t already looked at the article on the 3 methods you can use to solve GMAT inequalities and Absolute value questions like these, please read through the article. This GMAT Inequalities Challenge problem was posted in the same article. The GMAT Inequalities article covers all the basics you need to understand to solve questions like this. Hence, in this explanation, we assume that you are already familiar with these methods and we will skip over the basics and focus primarily on two methods:

The “pick a value” method has been left as an exercise for the readers.

Lets unpack the question’s statement first using Algebra.

**Is |x-y| > |x|? **

Since both sides are *non-negative*, let us start by squaring both sides and removing the absolute value.

(x-y)^{2} > x^{2}? **=>** x^{2} + y^{2} – 2xy > x^{2} ? **=>** y^{2} – 2xy > 0 ?

Here, we can try to simplify further, but for now, let us leave it at this. The question essentially becomes

**Is |x-y| > |x|?** is same as **Is y ^{2} – 2xy > 0?**

Now lets take the statements one by one:

Given (a) **|x+y|<|x-y|**

We are given that|x+y|<|x-y| , this tells us a couple of things:

- both LHS and RHS are non-negative, hence as before we can square both sides.
- Both x & y cannot be zero at the same time. Why? If x and y were both zero, we will be “given” 0<0 – which is not possible.

So lets start with squaring the both sides, it is given that:

(x+y)^{2} < (x-y)^{2} => xy < 0

If xy<0, what can we say about the question stem which evaluated to “*Is y ^{2}-2xy > 0*“

Since xy is negative, lets assume xy = -K, where K is positive. So the question becomes

**Is y ^{2} + 2K >0 ?**

Since y^{2} is positive & K is also positive, the answer is a unique YES. So Statement (a) is Sufficient to answer the question.

Statement (a) is SUFFICIENT.

Given (b) **x=-7y**

On a cursory look, we may conclude that x and y are opposite signs. That will be a BIG MISTAKE. In statement (b), we are given x = -7y. This means one of two things:

- Either x and y are of opposite signs OR
- x and y are both zero [It is critical not to miss this possibility]

- if x and y are of opposite signs, then xy < 0 and it is similar situation to the Statement (a). And it will answer “YES” to the asked question
- If x and y are both zero, then the question becomes Is 0 > 0? The answer to this question is a clear “NO”

Hence for Statement (b), there is no unique YES/NO to the asked question. Hence Statement (b) is insufficient. This is a trap in this this GMAT Inequalities Challenge Problem.

Statement (b) is INSUFFICIENT

Hence the answer is A: Only Statement (a) is sufficient to answer the question but not statement (b)

From the distance perspective, lets cover a couple of quick basics here:

- |x-y| means distance from x to y (or from y to x)
- |x| means distance from x to 0 (or from 0 to x)
- |x+y| means distance from x to -y (or from -y to x)

**Is |x-y| > |x|? **

So, the question is asking “is the distance between x and y more than distance between x and 0”.

**Is |x-y| > |x|? **can be rewritten as: *“Is the distance between x & y greater than the distance between x & 0”*

Let’s see this from a number line perspective. Consider x to be greater than 0

The yellow zone indicates all the possible values of y where the distance between y and x is more than the distance between x and 0. How? Take any value of y in the yellow zone. On the positive side of the number line, since y is beyond 2x, the |x-y| value will obviously be more than |x|.

On the negative side of the number line, since x has to go beyond 0 to reach to y, it is obvious that |x-y| will be greater than |x|.

A similar diagram can be drawn for x<0 and you will get a similar result. Few things are clear from this diagram:

- if x and y are opposite signs, |x-y| > |x|
- If x and y are same sign than |x-y| > |x|
**WHEN**|y| > 2|x|

Now let’s look at the question statements.

Given (a) **|x+y|<|x-y|**

Look at the figures below,

From the second diagram we clearly get that the “given” expression of |x-y|>|x+y| is only possible when x and y are opposite signs. So essentially, it is given to us that x and y are opposite signs. From (1) above, if x and y are opposite signs, we get the answer to the question as YES. Hence (a) is SUFFICIENT.

Statement (a) is SUFFICIENT.

Given (b) **x=-7y**

On a cursory look, we may conclude that x and y are opposite signs. That will be a BIG MISTAKE.

Statement (b), we are given x = -7y. This means one of two things:

- Either x and y are of opposite signs OR
- x and y are both zero [It is critical not to miss this possibility]

- if x and y are of opposite signs, then xy < 0 and it is similar situation to the Statement (a). And it will answer “YES” to the asked question
- If x and y are both zero, then the question becomes Is 0 > 0? The answer to this question is a clear “NO”

Hence for Statement (b), there is no unique YES/NO to the asked question. Hence Statement (b) is insufficient.

Statement (b) is INSUFFICIENT

Hence the answer is (A) Only Statement (a) is sufficient to answer the question but not statement (b)

Hopefully, the explanation is detailed enough for you to understand the framework and the solution for this GMAT Inequalities Challenge question. Stay tuned for more questions. Should you have any questions, please feel free to leave a comment or send us an email.

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