The Graduate Management Admission Test (GMAT) is a standardized exam used by many business schools to evaluate applicants for admission into MBA and other graduate management programs. The test assesses analytical, writing, quantitative, verbal, and reading skills in English, and is designed to measure potential success in business school and beyond.
THIS BLOG INCLUDES:
1. Complete Guide to GMAT Integrated Reasoning
2. The Best Approach to GMAT IR Questions for Your Prep
3. An Example of a 750+ level GMAT Geometry Question
4. GMAT Algebra: Questions, Contents, Preparation Tips, and More
5. Tips and Tricks to Crack GMAT Algebra Questions
6. GMAT Data Sufficiency questions: Do you need to do Math?
7. How to Deal With the GMAT Questions Involving Fractions?
8. Ratios and Proportions on the GMAT
9. All You Need to Know About GMAT Analytical Writing
10. Guide to GMAT Inequalities
11. Fun Way to Crack Complex Work-Rate Questions on the GMAT Without Getting Intimidated
The Integrated Reasoning (IR) section on the GMAT was introduced in 2012. This section tests what the B-Schools authorities think is necessary for the students to succeed in the MBA – the ability to analyze data. Managers have to filter through a plentitude of data in various forms to make decisions and incorporate the refined data to find solutions. This is exactly the skill that IR tests the GMAT test-taker.
IR is a 30-minute section. It consists of 12 questions each of which may have many parts. The scores in this section range from 1-8. According to the GMAT Syllabus 2023, this section comprises data in the form of passages, tables, or graphs. There are four types of questions in this section:
The IR section tests some of your Critical Reasoning and Quantitative skills. So, when you are preparing for those two sections, you are laying the foundation for the IR section too. Once you have moved on, you cannot go back to the previous questions.
Though it is not very clear how the colleges accept the IR scores, there are certain things the applicant needs to keep at the back of his/her mind.
No GMAT Prep is complete without preparing for the IR. While selecting the resources for IR prep, remember to keep in mind that the questions should be similar to actual questions.
GMAT Online Prep will be one of the best options because after all GMAT is an online exam. You are going to see the data on the screen and analyze it.
On the GMAT, Integrated Reasoning (IR) is a non-adaptive section with various question types that test your ability to deal with real-world problems, an ability greatly valued by business schools and in a modern workplace.
Knowing is half winning — this means that the better your acquaintance with the question types, the better will be your ability to answer them easily and accurately. According to the GMAC, IR is 50% verbal and 50% quantitative. So you need both verbal and quantitative reasoning skills to answer IR questions well. You may not need to learn anything new, but being familiar\ with the question types and having a strategy in place will help.
In the IR Section, you get 12 questions and have 30 minutes to answer them. There are four types of Integrated Reasoning questions: (1) Two-Part Analysis, (2) Multi-Source Reasoning, (3) Graphic Interpretation, and (4) Table Analysis. Many of these, particularly the last three types, contain questions requiring multiple responses — and all responses must be right for you to get any marks for that question. This is the only section that allows you to use a calculator, but you cannot use your own calculator; you have to use the on-screen calculator, which provides very basic functionality. You should get used to using the calculator while taking practice tests or doing online IR drills.
Two-Part Analysis questions come with two questions based on a given set of data or information. The answer choices are presented in a table format, with one column for each question. The subject matter may relate to Verbal or Quant.
Multi-Source Reasoning questions come with two or more tabs providing information from different sources. You will not be able to see all the information in one go. Therefore, it becomes important to read the question first and decide which tab to refer to. These questions often involve more reading of verbal content than the other three types.
The Graphic Interpretation questions test the ability to interpret data critically, sifting through the given information, synthesizing it, and using it as required. These questions require you to handle data in charts and graphs and are more about quantitative skills. The answer options come in the drop-down format.
Table Analysis questions come with the information given in a “sortable” table. You should focus on what you need to answer the questions. Often the crucial point is whether to sort or not to sort.
Here are a few things you should take care of. As you may have realized already, the manner in which the questions are presented is pretty tricky.
Overall, Integrated Reasoning should not cause too much concern as it is based on what you have already learned in the Quant and Verbal sections. Do not get overwhelmed by the amount of data and apparent complexity presented by the questions. The questions are usually more straightforward than you think — and, perhaps, realize later.
Getting a GMAT score that is above 700 is what most students who take the exam aspire for. Only 12% of those who take the GMAT test get a score that is above 700 and even fewer get a score above 750. A 750+ level question is generally considered to be difficult and can only be solved by a select few. However, this is not true. Even a 750+ level question can be solved if you have a good grasp of the basic concepts. Here is an example of a 750+ level GMAT geometry question that you can encounter in the GMAT question paper.
A right-angled triangle PQR exists on the xy-plane. The right angle is at the vertex P, and the side PR is parallel to the x-axis. The x and y coordinates of each of the vertices, P, Q, and R have to satisfy the following inequalities:
-3 <= x <= 6
5 <= y <= 15
How many different triangles can you construct that satisfies both of the aforementioned conditions?
Option D: 9,900
As per the question, the total number of possibilities for the x and y coordinates of each vertex are:
Possibilities for x = 10
Possibilities for y = 11
There is a right angle at P and PR is parallel to the x-axis. This implies that the side PQ will be perpendicular to the x-axis, which in turn implies that PQ will be parallel to the y-axis.
Since PR is parallel to the x-axis, the value for the y coordinate for both P and R will remain the same. Similarly, since PQ is parallel to the y-axis, the x coordinate for P and Q will remain the same.
Possibilities of x and y coordinates for P = (10 values for x)(11 values for y) = 10*11 = 110.
This is because it isn’t stated where P should be apart from the range of x and y.
Once you select a coordinate for P, there are (10 – 1) = 9 possibilities for the x coordinate of R. The y coordinate of R will remain the same as that of P.
Once you select a coordinate for P, there are (11 – 1) = 10 possibilities for the y coordinate of Q. The x coordinate of Q will remain the same as that of P.
The total number of triangles that upon meeting the specified conditions that can be constructed are = (110)(9)(10) = 9900.
The problem uses both combinatorics and geometry.
Scoring above 750 requires some serious planning and practice. It is suggested that you start your GMAT preparation with the quant section. Start by understanding the basic concepts and proceed on to solving practice questions. As seen from the above example, the question is pretty simple once you understand how to approach it. It only used the basic concepts but combined two topics. You can take GMAT mock tests to get a better idea of the GMAT format and to develop strategies you can use in the actual test. This will definitely help you improve your GMAT score.
The dispersion of numbers or values in a list is known as the standard deviation. The standard deviation is more significant when the data is more scattered and away from the mean.
The Greek letter sigma (σ) usually represents standard deviation and is calculated using the formula.
Where X represents each value in the list, x̄ represents the mean of the values in the list, and n is the number of values in the list.
To understand how standard deviation may be tested on the GMAT, here is an example, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22
List M (not shown) consists of 8 different integers, each of which is in the list shown. What is the standard deviation of the numbers in list M?
(1) The average (arithmetic mean) of the numbers in list M is equal to the average of the numbers in the list shown.
(2) List M does not contain 22.
We are given ten different numbers, 8 of which are in List M. The question asked is: what is the standard deviation of the numbers in list M?
We know that we can find the standard deviation of a set of numbers if we know the names. Thus the question turns out to be: which eight numbers are in the list or which two numbers are not in the list?
Let’s consider Statement (1): The average (arithmetic mean) of the numbers in list M is equal to the percentage of the numbers in the record shown. It follows that the percentage of the two numbers excluded should be the same as the average of the numbers in the list displayed.
The average of the numbers in the list shown is 13, and, therefore, the sum of the two numbers excluded should be 26. You find that the numbers could be 4 and 22, or they could be 12 and 14, or even they could be any three other pairs of that sort (6 and 20, 8 and 18, or 10 and 12).
On observation, one sees that the numbers 2 and 22 are far away from the mean; whereas, 12 and 14 are close to the way. This shows that as we move on to exclude different pairs of numbers, the standard deviations obtained will be different.
In order to solve the question correctly, it is essential to look at the second Statement.
Let’s consider Statement (2): List M does not contain 22. This doesn’t tell us which eight numbers are there in List M. The information provided in Statement (2) alone is also not sufficient for answering the question.
On combining the information provided in both statements, we know for sure that the two numbers that are not in List M are 4 and 22. Hence, to answer the question, using both statements is essential.
The correct answer is C.
Note: Did you notice that in the list shown, the ten numbers are evenly spaced? If you did, it must have been easy for you to find the average and figure out the pairs of numbers that add up to 26.
Observations: Note that to solve the question, we did not have to calculate the standard deviation. It was enough to know that (i) the standard deviation depends on every number/value in a list and (ii) the standard deviation depends on the extent of dispersion of the numbers/values in the list.
(i) Standard deviation can’t be negative; the minimum possible standard deviation of the numbers/values in any list is 0 — when all the numbers/values are the same.
(ii) If every number/value in a list is increased or decreased by a fixed amount, the standard deviation remains unchanged.
Conclusion: The more closely packed the values around the mean, the smaller the standard deviation. The higher the standard deviation, the farther away are the values from the mean.
The GMAT Quantitative section tests Arithmetic, Algebra, Geometry, and Word Problems. Algebra is one of the essential parts of mathematics and is tested in different ways on the GMAT as it helps business schools to get students with good levels of aptitude skills. Solving GMAT questions involving algebraic analysis and quantitative reasoning is considered challenging by most of the aspirants, especially when these questions come in the form of Data Sufficiency. This is mostly due to a lack of knowledge of algebraic concepts. In this blog, you will get a detailed overview of Algebraic concepts tested on the GMAT exam.
You will see approximately 5-8 algebra questions in Problem-solving and Data Sufficiency formats combined. According to the GMAC, the following algebraic concepts are tested on the GMAT: Algebraic Expressions and Equations, Linear Equations, Factoring, Quadratic Equations, Inequalities, Functions, Formulas, and Measurement Conversion. It is vital to know all the important algebraic terminologies for a better understanding of the algebraic concepts tested on the GMAT.
Make sure that you know all the following algebraic terminologies before you move on to the next part:
|Variables||A symbol that is used in mathematical or logical expressions to represent a variable quantity||x, y, z, etc.|
|Constants||A number representing a quantity assumed to have a fixed value in a specified mathematical context||5 is a constant in the polynomial expression 3x2 + 5|
|Terms||A single mathematical expression. It may be a single number (positive or negative), a single variable (a letter), or several variables multiplied but never added or subtracted||3x2 and 5 are terms in the polynomial expression 3x2 + 6|
|Degree||The highest power of a term or variable||2 is a degree of the polynomial expression 3x2 + 6|
|Coefficient||The number in front of a term||3 is a coefficient of the term 3x2 in the polynomial expression 3x2 + 5|
|Algebraic Expression||A symbol or a combination of symbols used in algebra, containing one or more numbers, variables, and arithmetic operations||2(3x – 7y)|
|Monomial||An algebraic expression consisting of one term||2x, 3x2, etc.|
|Binomial||An algebraic expression consisting of the sum or the difference of two terms||2x + 3y|
|Polynomial||An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s)||4x3 – 4xy + 7y3|
|Exponent||A quantity representing the power to which a given number or expression is to be raised, is usually, expressed as a raised symbol beside the number or expression||ab, 23, or 5x|
|Absolute Values||The absolute value of a number may be thought of as its distance from zero. The absolute value or modulus of a real number x is denoted by |x|. It implies that the result will remain non-negative no matter whether x is positive or negative.|||5| = 5
|-5| = 5
|0| = 0
|GMAT Algebra Concepts||Description||Examples|
|Algebraic Equation||A mathematical equation in which two expressions are set equal to each other||2(3x – 7y) = 10|
|Algebraic Inequalities||A relation that makes a non-equal comparison between two mathematical expressions.||2x – 3 > 7y
5x2 + 2x £ 20
|Linear Equations||An equation between two variables that gives a straight line when plotted on a graph. It is represented by y = mx + b||y = 2x + 3
2x – 3y = 5
|Quadratic Equations||A polynomial equation with the highest degree of 2. It is represented by ax2+ bx + c = 0||2x2+ 5x + 3 = 0|
|Functions||An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). This relationship is commonly symbolized as y= f(x)—which is called “for x”—and y and x are related such that for every x, there is a unique value of y. That is, f(x) cannot have more than one value for the same x.||If f(x) = 2x, then f(4) = 2 × 4 = 8|
|Sequences||A sequence is a list of numbers in a particular order. The numbers in a sequence are called the terms of the sequence. The order of the terms in the sequence matters||2, 5, 8, 11, …
3, 6, 12, 24, …
1, , , , …
|Absolute Value Equations||Are equations where the variable is within an absolute value operator|||x – 2|= 7|
The questions seen in the GMAT Quantitative section are similar to what one has once witnessed during high school. Having said that it is important to note that solving the GMAT questions is not the same as taking the high school GMAT math exam as approximately half of the questions come in the Data Sufficiency format which is very new for most of the GMAT aspirants.
Also, if you will solve the questions in the same conservative way as you used to during your school, you will end up wasting a lot of time resulting in an unfished section leading to a poor score. Thus, it is vital to understand the tips and tricks which are developed specifically for dealing with GMAT Quantitative questions. Some of these are as follows:
Don’t get intimidated by Algebra questions on the GMAT exam. This is something that you have already worked through in high school. You just need to approach them differently when you see them on the GMAT. Follow the above-mentioned tips religiously and see an instant change in your scores. If you still have any doubts, feel free to talk to one of our GMAT Math experts today!
GMAT Data Sufficiency is a question type asked in the Quantitative section of the GMAT. The format of such questions remains the same such as in a question you will be given two mathematical statements. Then considering the given statements you have to decide whether the information given in the statement is enough to answer a question or not. Remember you don’t need to give an answer to the actual question. You just have to decide whether either statement (or both statements) gives data that is sufficient for finding an answer.
Remember, on every standardized test you have taken you must have faced multiple-choice math problems. This is just the same! The Data Sufficiency section tests your managerial skills. You have 62 minutes for solving 31 questions. You will see about 14 to 15 DS questions in the Quantitative section.
Data Sufficiency questions are always the trickiest of the Math questions on the GMAT. But it may be interesting to know that in order to solve many of the Data Sufficiency questions on the GMAT you may not really need to do any math.
Let’s take a few examples to understand how we can answer Data Sufficiency questions without really doing any Math. What you need is just mathematical reasoning.
As we say at Manya-The Princeton Review, the task is to evaluate, not to calculate!
GMAC rightly says that the “Quantitative section measures your ability to analyze data and draw conclusions using reasoning skills” – not your ability to calculate. This is all the more true in respect of Data Sufficiency questions. Problem-solving questions may, however, be a different ball game.
We generally see a lot of questions involving fractions and percentages on the GMAT. The fact is that sometimes you will try a method to solve a question and that method does not work out to be the best way. Don’t give up! Try solving with another method. Of course, the best thing is to select the correct method from the word go, but really: This won’t work all the time on a test day for all the Quant questions. Be ready to change the track when required..!
Let’s just take a look at these below-given examples and try to solve them creatively rather than getting stuck with the most usual ways.
A certain high school band consists of only fourth graders and fifth graders, of the members are fourth grader, and the remaining are fifth graders. If of the fourth graders play guitar and of the fifth graders play guitar, what fraction of all the members are not the guitarist?
The usual way to solve this GMAT question
The more usual way of doing this problem is to solve algebraically. The students start this question by taking a variable for the ‘unknown’ quantity i.e the total number of members in the band.
So, we’ll first see the algebraic way. Our first task: assigning a variable for the total number of members in the band.
Let it be x,
Then, no. of juniors = 3/5 x,
No. of juniors, who play guitar = (1/4)∗(3/5)x=3/20x
And, no. of seniors = 2/5x
No. of seniors, who play guitar = (2/3)×(2/5)x=4/15x
the Total number of guitarists = 3/20x+4/15x=25/60x
Therefore, a fraction of guitarists = 25/60=5/12
But, the question asked about a fraction of members who are not guitarist,
Hence, the answer is C.
The creative way to solve this GMAT question
The more creative way to solve this question is arithmetical. In this case, we take the help of real numbers to solve this question. Solving this problem like a real-world problem will definitely save time and effort.
What should be a good number here to start? Let me tell you whenever there are fractions given, an easy number to start is simply the product of all the denominators of the fractions involved. In this case, there are 3, 4, and 5 in the denominator so, I am starting by taking their product i.e. 60.
So, let us assume the total number of students is 60
# of juniors is 3/5×60=36
no. of juniors, who play guitar = 1/4×36=9
# of seniors is 60 – 36 = 24 and no. of seniors, who play guitar = 2/3×24=16
So, total members who play guitar is 16 + 9 = 25 and total members who don’t play guitar is 60 – 25 = 35
Therefore, a fraction of the members who do not play guitar is 35/60=7/12
Hence, the answer is C
The key take away from the above question:
1. The GMAC is least bothered about how you solve the question neither should you. Always involve creative thinking while solving.
2. Practice makes a man perfect. Practice enough “wordy” problems. By doing so you will feel comfortable in –
We all have studied Ratios and Proportions in school and now the same is going to be tested on the GMAT as well. In schools, we were quite comfortable with them, but not on the GMAT; because they come in various forms, they have a tendency to give test-takers trouble by making them waste time unnecessarily.
Before moving to the forms of questions we see on the GMAT, let’s recall what we learned in school.
A Ratio is the comparison of two or more quantities. It can be represented by words, fractions, or colons. For example: “For example: “The ratio of apple pies to cherry pies is 3 to 7” or “The ratio of apple pies to cherry pies is 3:7”
A proportion is different from a ratio. While a ratio is represented by a single fraction, a proportion is represented by an equation. For example, 3/4 is a fraction, whereas 3/4 = 6/8 is a proportion.
Let’s look at a few questions involving ratios and proportions and how we tackle them on the GMAT.
1. In class A, girls and boys are in a ratio of 3 to 4, and in class B, girls, and boys are in a ratio of 4 to 5. If both classes are combined, the ratio of girls to boys is 18 to 23. How many boys are there in class A?
We are not going to solve this question in a conventional way i.e. by making equations rather we are going to solve it in a very interesting way. If you look at the question carefully, the first statement tells you that in class A, the ratio of boys to girls is 3 to 4 which means that the number of boys in class A should be a multiple of 4 and in the answer choices there is only one option which is a multiple of 4 i.e. option (B). Therefore, the answer to the question is (B).
2. A department manager distributed a number of pens, pencils, and pads among the staff in the department, with each staff member receiving x pens, y pencils, and z pads. How many staff members were in the department? (GMAC OG)
(1) The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.
(2) The manager distributed a total of 18 pens, 27 pencils, and 36 pads.
We know that each staff member received x pens, y pencils, and z pads.
Questions ask for the total number of staff members in the department.
In order to answer the question, we need either x, y, or z and their total number. For example, if each staff member gets 2 pens and a total of 20 pens have been distributed, it means there are 10 staff members.
It gives us only the ratio of x, y, and z. We cannot find out the number of staff members from this information. Therefore, this statement is insufficient.
It gives us the total number of pens, the total number of pencils, and the total number of pads. But, we do not know, x, y, or z. Therefore, this statement is also insufficient.
Even after combining the information from the statements we do not get the value of x, y, or z and hence, the total number of staff members. Thus, it is insufficient and the answer is (E).
In GMAT Analytical Writing, the test will present an argument, generally in the form of a newspaper editorial or a company statement. The structure of this argument allows you to argue for either side, and your choice has no bearing on your final score. You’ll have 30 minutes to read over the prompt and write your essay. Later, your essay will be scored on a scale of 0 to 6 by both a computer and a person; your AWA test score will be the average of these two scores.
Remember that the goal of this work is to assess your GMAT analytical writing abilities.
The AWA test score has no bearing on your GMAT score. Instead, it appears on your score report as a separate category. Although you won’t get a detailed analysis of your marks for each section, the GMAT analytical writing exam looks at your talents in four categories:
Ideas of Good Quality
Style of Writing
Usage and Grammar
You’ll be given a score ranging from 0 to 6 in half-point increments based on your overall performance.
The essay will next be scored by a trained assessor based on the overall development of your ideas and written representation. The GMAT then adds these scores together to give you an overall GMAT AWA score. Don’t panic if there are large differences in scores between the human and computer graders: if the scores differ by more than one point, another human grader is brought in to help set the final score.
Once you understand what to expect on the GMAT analytical writing exam, you may begin implementing methods that will help you maximize your score. Keep returning to these during your GMAT prep to ensure that you stay on track and improve your GMAT analytical writing assessment!
Here are some GMAT AWA tips to help you succeed:
Recognizing assumptions is important for Critical Reasoning questions, and it will also help you counter the prompt argument in your AWA GMAT.
It’s not only a matter of understanding what they’re saying; it’s also a matter of understanding the many options you have for examining the argument. This list of analytical strategies is always offered after the prompt argument. It’s critical to become familiar with this “analytical toolkit” so that you can use it on test day.
GMAT AWA prompt arguments frequently contain one of six types of flaws. Learn to recognize these patterns so that you’ll be prepared on test day.
Some exam takers are aware of this. The first step is to identify counterarguments and defects in the prompt argument. Make a list of all the flaws you can think of. Then choose the 2-4 that are most relevant, as they will be the most convincing talking points. You’re ready to write once you’ve compiled your list of illuminating defects.
Many test-takers find it helpful to follow a basic GMAT AWA template structure and rehearse it ahead of time so that all they have to do on test day is put in the specific details.
First and foremost, change up your sentence structures. Make an effort to use a range of words. Of course, you’ll want to repeat the phrases from the prompt argument. However, in your own analysis, use a variety of descriptive adjectives, never repeating the same one.
All of the above AWA test strategies are crucial to remember for your GMAT analytical writing. But what should you do on test day when you really sit down at the computer? Here’s how to utilize your 30 minutes with the GMAT AWA, with a more thorough GMAT writing template!
You should have read the AWA directions by the time you sit down on test day, so you won’t have to waste time reading them again. Instead, get right to work on AWA brainstorming. List the defects in the argument as you brainstorm, then evaluate those flaws to see which objections are the most powerful.
You don’t have to start from scratch with each GMAT AWA introduction. Begin by stating the source of the passage. After that, concentrate on two main tasks: summarizing the argument and explaining why it is flawed. Keep it short and sweet; three sentences should suffice to establish your main points.
To begin, keep in mind that you should not spend too much time on the conclusion. The body paragraphs are the heart of your essay, and they are what determine your grade. These should be lengthy and comprehensive, but the conclusion should be succinct and to the point. Wrap things up as soon as possible so you can get back to editing and revising your essay.
Don’t go into too much information to make things manageable and concise. You simply need to summaries the argument’s fundamental flaws. It’s sometimes enough to just state that the argument has severe flaws. Ignore the need to restate all of the important points from the body paragraphs. This will merely take up additional space and time.
Finally, suggest a method for achieving the article’s purpose. It is critical to approach the argument analysis as an interested party. You don’t want to be completely pessimistic. For one thing, imagining yourself as a part of the argument will help you create a better analysis, and two, the assignment encourages you to improve the argument. Find some general evidence that will strengthen or irrefutably support your claim. Make a suggestion for a tweak that will put the logic on a firmer basis.
When you first meet the GMAT analytical writing section, it can feel like a slog: it needs intense concentration and analysis, and it’s not something most students have focused on throughout their preparation. However, with a little planning, your GMAT essays can considerably improve your AWA test score, lifting your admissions file to the next level!
By including AWA GMAT writing in your overall GMAT prep plan, you’ll guarantee that this section of the exam doesn’t become a stumbling block for your application—and instead enhances, rather than hinders, your chances of getting into your dream school. Best of luck!
The GMAT exam syllabus for Quant covers topics like Algebra, Arithmetic, Geometry, and word problems.
In the GMAT Quant section, there are two types of questions – Problem-solving and Data sufficiency. The inequalities are mostly tested in Data sufficiency type questions, especially in Yes/No data sufficiency questions. You may get around 3 to 4 questions in a test from inequalities, tested directly or indirectly in a question.
Before getting into GMAT questions we will discuss the basic rules about inequalities. Equalities and inequalities are almost the same except for one important rule about inequalities. To solve equalities, we do the same operations on both sides of the equalities, such as addition, subtraction, multiplication, division, etc. We can do the same in inequalities, but when you multiply and divide by negative numbers we need to flip the inequality sign. Examples of solving equalities and inequalities are given below,
GMAC uses this rule effectively to create traps. Let us look at some examples.
When we try to solve the equation 2x/y = z for x, we can easily solve it as x = y*z/2. Similarly, let’s look at the case of inequalities, 2x/y > z, shall we solve for x as x > y*z/2? Certainly, not, though it appears as if it is correct.
Yes, we have missed the case of multiplying or dividing the inequality by a negative number. Let us look at the step-by-step approach to solving a basic inequality question for a better understanding.
What we did in the first step is correct, because we have divided both sides by a positive value ‘2’. But in the next step, we have divided both sides of the inequality by ‘y’. This step is wrong because we don’t know whether the ‘y’ is positive or negative. If the value of y is negative, we need to flip the inequality sign.
This is the usual mistake that the students do while solving inequality questions. We can easily avoid this mistake by carefully applying the inequality rules while solving through a step-by-step approach. Or we can simply try some numbers that satisfy the inequalities, better to try negative and positive numbers when you have inequalities.
You must have encountered these genuinely long and ugly-looking word problems on Rate and Work while preparing for the GMAT. However, today I am going to show you a unique way of solving this question type in an entirely new and innovative way that will change the way you see and approach Rate and Work questions. Let us start by taking a simpler question:
Three printing presses, R, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take R, working alone at its constant rate, to do the same job?
Tricky, eh! Doing this problem using old school way can be a lot more cumbrous and baffling unless you know all the basic concepts of work rate like the back of your hand. Nevertheless, you can still break through it by assuming a number for work.
Let the work be 20, keeping in mind that we have to deal with 4 and 5 in the question. Since, R, S, and T work together and complete the job in 4 hours, the combined rate of work for R, S, and T will be 20 ÷ 4 = 5. Similarly, S and T worked together on the same job for 5 hours, so the combined rate for S and T will be 20 ÷ 5 = 4. This means that the rate for R should be 5 – 4 = 1 (For your information, rates are additive in work questions). Thus, if R has to do 20 work at the rate of 1, then the time taken will be 20 hours (If confused, use the standard formula, W = R ×T).
The takeaway from this question is that you can actually take a real number for rate questions involving some kind of work and can turn them into a real-life world problem, thus, converting a harder GMAT problem into a simpler one. Let us replicate the same technique on a trickier GMAT problem and make our life easier.
Ross, Harry, and Chris own a farm. Ross, working alone, can plow the farm in 10 hours. Harry and Chris, working independently, can plow the same farm in 6 hours and 5 hours respectively. Ross starts plowing the farm and works on his own for an hour. Harry then joins him and they work together for 2 hours. Finally, Chris joins and decides to help his friends. Harry continues along with Chris in order to finish the rest of the job while Ross takes a rest. What fraction of the farm did Harry plow?
Let us assume the work done to be 60. Therefore, the rate of Ross will be 60 ÷ 10 = 6. Similarly, the rate of Harry and Chris will be 10 and 12 respectively. Now, we know the individual rate of all three friends. Let us take care of the situation now. Ross starts plowing the farm and worked for an hour. Since his rate is 6 and W = R ×T, so work done is 6. In the next situation, Harry joins Ross, which means their combined rate is 16 (Yes! Don’t be surprised. Rates can be combined). So, work done is 16 ×2 = 32. Now, count the remaining amount of work. 60 – 6 – 32 = 22. In the end, Chris and Harry work together in order to finish the job. Their combined rate is 22. We know that W = R ×T ⇒ 22 = 22 ×T ⇒T = 1.
We are not over yet! The question is to find out the fraction of the farm that Harry plowed. Harry worked for 3 hours in total. Since, W = R ×T = 10 ×3 = 30. Therefore, a fraction of the work done by Harry is 30/60 = ½
The moral of the story is that there are ways to crack questions that sound or seem hard to us by turning them into a real-life world problem. In addition, no matter how GMAC test writers try to throw complex questions at us, do not get panic. Instead, take a deep breath and think of the strategies that you have practiced multiple times and can crack even the toughest problem within no time. Remember that GMAT questions are never as hard as they appear to be in the first go.
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