# SOLVE CUBE QUESTIONS IN CAT EASILY

# HOW TO SOLVE CUBE QUESTIONS IN CAT

## Do you dread cube questions in CAT? Find out why they are important and learn how to master them. Find out about IIM Skills online CAT coaching.

In this article, we will learn about tricks to solve cube questions in CAT. But first, let’s learn why it is important and where it fits in the big picture.

MBA is one of the most popular degrees in the whole world. There are many reasons for that.

An MBA from a top B-school is not just a degree. It is proof of your expertise and value. It is a symbol that you are part of the tradition of excellence that is your business school.

An MBA enhances your personality from all angles. It makes you more confident and street-smart. You become secure in yourself when you see your projects completing successfully and proving your mettle among the best and the smartest audience.

- You learn to become a team player. You learn to accommodate other members. You learn to delegate and find out that any work that is done by a team is more efficient and of better quality. Especially if the team is well-coordinated and where people have skills complementary to each other.
- With an MBA you can enter any industry that you want to and your opportunities won’t be limited. Sectors like hospitals, hotels, manufacturing industries, media houses, sports, politics, tech companies, start-ups, etc. are after all businesses that require efficient personnel to run it.
- MBA also develops your strategic thinking. With this vision, you can always plan wisely. You start to automatically weigh the pros and cons of any decision, whether in business or in personal life. With this skill, you can make the best short and long term decisions for the best possible outcome. Strategic and logical thinking is important in solving cube questions in CAT.
- This is an important quality for managers in any business. With the landscape changing faster than ever, with new trends and technological breakthroughs, it is important to make the right choices now to reap the fruits in the future.
- Another advantage of doing an MBA which is as important in personal life as it is professional is communication skills. Management teaches you how to convey your ideas and thoughts effectively. Your smartness and intelligence are of no use if you cannot explain it to others. You have to learn how to persuade and convince people. All these skills are necessary for real life too.
- MBA also involves doing lots of projects, assignments, tests, etc. under tight deadlines. The 2-year program is packed with activities and there is no time to waste. You learn the most essential skill of time management. You become much more efficient and productive with time.
- Perhaps the greatest asset that a business school provides you is a great network. Your worth is associated with the kind of people you surround yourself with. Many experts think that college is the best place to build a network. The batchmates you meet today are someday going to sit at important positions in business, politics, media and so on.
- A management college provides you an asset of a lifetime. You meet renowned economists, policymakers and business leaders that come as professors and lecturers. There is no better place to network.
- Doing an MBA also broadens your mindset. In an internship, you get to see and learn what a day in a real job looks like. You get hands-on experience in dealing with clients, making strategy, handling day-to-day tasks and so on. A good management college will get you an internship in the best companies in India and as well as abroad. Some MBA programs also give you a chance to study a semester overseas.
- You learn the impact of your position. How the decisions you make are going to affect thousands of people. For example, correct business advice from a management consultant can save a company from being declayellow bankrupt. This, in turn, many jobs and so many families from being incomeless for months. That is the kind of impact you will have.
- In the materialistic sense, a good college provides you more value. You can negotiate salaries to suit your needs. You will have the possibility of working for so many companies. Your options will be vast.
- The best colleges also get you high pay packages. You can afford a better lifestyle and a high standard of living. You will also get more respect in society as well as the business world.
- Another unseen advantage of an MBA is innovative thinking. As a manager, you will encounter many problems. To solve them, you will need to think outside the box. Because there will be problems that no one has ever come across before. Your solutions have the opportunity to set a precedent for later managers.

## Why CAT?

A good percentile in CAT is the ticket to a management college in India. CAT is designed to test the candidates in specific areas and analyze how suitable and effective they will be as managers and CEOs. Almost all business schools in India take admissions based on your CAT score. If you want to be an MBA, CAT is what you should focus on.

CAT is an online test. The paper has 3 different sections of

- Quantitative Ability (QA)
- Data Interpretation(DI) & Logical Reasoning (LR)
- Verbal Ability (VA) & Reading Comprehension (RC)

The Quantitative Aptitude(QA) section has problems in basic math, based on 10 + 2 level. Questions come from various topics such as Arithmetic, Geometry, Algebra, trigonometry, statistics, profit-loss and simple and compound interest. The problems usually look for the application of basic math for finding solutions to real-world problems.

In the Data Interpretation and Logical Reasoning (DI-LR), questions come in sets that are based on a group of data. The data given could be in graphs, charts, or tables. DILR for CAT tests how the candidate makes use of given data to solve the problems. DILR problems test the ability to use logic and evaluate situations. Logical thinking is also important in solving cube questions in CAT.

The Verbal Ability (VA) section consists of questions on standard English language and rules of grammar. VA problems test the candidate’s ability to arrange paragraphs, judging the tone of statements, completing the sentences, etc.

Each correct answer gets 3 marks for the candidate. A wrong choice deducts 1 point. The test has many sets of question papers, therefore, all the scores are neutralized later.

To be eligible for getting a seat in any college, a candidate must hold or expect their bachelor’s degree before the time of admission.

A good score in CAT doesn’t guarantee a seat, but it is a necessity for a seat in the best management colleges in India. To get to the top b-schools, you also need to pass their group discussions and personal interview stages.

CAT is like a gateway to the top B-schools. We have already seen why you need to be in the best business school.

A great CAT score basically increases the possibility of a great learning environment. You get a great corporate network for a lifetime. You get to meet industry leaders and renowned policymakers and economists. You get a great start to your career. The best business schools also boast records of 100% placements. That’s how valuable a good CAT score is.

## How can you improve logical thinking

### What is logical thinking?

Logical thinking is the process of analyzing a situation from all sides and reaching a sensible solution. It is very similar to critical thinking. But logical thinking involves looking at issues objectively and making rational conclusions.

When you use the information available to brainstorm a problem, you are practicing your logical skills. Logical thinking is important in solving cube questions in CAT.

We will now learn why logical thinking helps you become more efficient with tips on how can you improve your logical thinking skills.

### Why are logical thinking skills essential?

Logical thinking is important in solving cube questions in CAT. But logical thinking skills are essential as they help you reason through significant decisions, solve problems, generate creative solutions and set targets—all of which are key to the development of your career.

You will come across many issues and challenges, no matter whether you are a fresher or a senior employee. The stronger you build your logical thinking skills, the easier it would be to reach a solution that would benefit you as well the company.

### HOW TO BUILD LOGICAL REASONING ABILITY

There are many ways to strengthen logical reasoning in your daily work. We know that logical thinking is important in solving cube questions in CAT. Here are a few tricks and tips to develop your skills:

**Develop a few creative hobbies:**Creative activities like drawing, writing, painting, and playing music can stimulate the creative part of the brain and promotes logical thinking. Creative activities naturally develop problem-solving skills that help us become a better problem-solver. Creative activities also help reduce stress. When stress levels are low, you have an easier time focusing and reaching solutions. We deal with stress in many different ways, but developing our creative thinking is productive and can improve both your personal and professional life.**Practice questioning everything:**One of the best ways to strengthen your logical thinking skills is to ask questions about things you typically accept as fact. Regularly asking questions helps you see the bigger picture, allowing you to find out of the box solutions. Asking questions can also often lead to new findings of facts you did not consider before, which may increase your curiosity. You can use this technique anywhere. Just look around you and try to find out why something is the way it is. Can it be made any better? Consider a new department at your office you are not really familiar with and make a list of questions that will help you understand its purpose for the company. For example, if you work in the sales department and want to know more about the legal department, consider asking someone in that department for a short informational interview to learn more about their role and day-to-day tasks. This will help you see the bigger picture and where everyone fits in the puzzle.**Socialize with others**. Building relationships with different people broadens your perspective. It helps you understand different kinds of people. It gives you more chances to develop your logical reasoning skills. When you learn about someone better and their perspective, it may help you approach problems at work in a new and different way. There are many ways in which you can develop relationships, like participating in new and enjoyable activities or simply eating in a group in the office. The more you handle issues at the workplace, the easier you will be able to rise in your career.**Learn a new skill**. Learning a new ability can also help you develop logical reasoning skills. When you take every chance to learn as much as possible, you can apply the same approach to your job. Learning a new instrument, for example, stimulates the prefrontal cortex in the brain that is responsible for deep thought and awareness. The logical thinking skills we develop in this way can help focus on our work more, developing our ability to solve more problems more easily.**Try to anticipate the results of your decisions**. It is useful to consider the impact of your decisions in the future. The closer you pay attention to the pros and cons of your decisions, the more your vision will develop. Logical reasoning skills can be easily mastered with daily practice. When you do these exercises every day, you will make this approach a habit for making decisions at work with a logical point of view.

### HOW TO SOLVE CUBE QUESTIONS IN CAT?

**Cube questions in CAT are one of the most commonly asked puzzle problems in CAT.** These puzzles or problems make us think visually, which makes it a little difficult for many.

We will learn the basic concepts of the cube problems and a few more things that we would be using in most of the cube related puzzles.

cube questions in CAT are common in a number of ways. Contrary to selection or arrangement puzzles, where the main pattern stays similar. We will show some of the common types of problems and the right approach to solve such problems.

We will find what happens to the cube when it is cut in specific ways, the shape of that cube afterward, and how many new parts are formed as a result.

Referring to the basics first, a cube is three dimensional solid with 6 equal sides

Basic facts about the cube

A cube has a total 6 sides

A cube has a total 12 edges

A cube has a total of 8 vertices

Let’s make a cut in the cube that is parallel to the base of the cube. We get two new solids. If we make another similar cut, we get three solids. For n number of cuts, all parallel to the base, the total number of new solids we get is (n+1).

CUBE QUESTIONS IN CAT IN LOGICAL REASONING

Let’s say the base is parallel to the x-axis. If we make one cut parallel to the x-axis and another cut perpendicular to the first cut and parallel to the y axis, the second cut will divide each of the two new pieces we get from the first cut into two more pieces. We get a total of 4 new parts of the first big cube. Similarly, making another cut parallel to the previous cuts (z-axis) will further divide these 4 pieces into two pieces each, thus making the total 8 new pieces.

When we start to evaluate this, we find that when we made A mutually parallel cuts along the x-axis, B mutually parallel cuts along the y axis and C mutually parallel cuts along z axis we get (A+1)*(B+1)*(C+1) new pieces of the cube we had in the first place.

Total number of solids obtained with A cuts along the x-axis, B cuts along the y-axis and C cuts along z axis =

** (A+1)*(B+1)*(C+1)**

All these new solid pieces are not necessarily cubes themselves. But they are all cuboids. It should be remembeyellow that every cube is a cuboid but not every cuboid is a cube.

All the pieces are cubes when A=B=C and all the cuts are at equal distances.

This is the case when the number of cuts is given in the question. Sometimes, we are provided with the sum of X + Y + Z instead of individual values.

### Minimum number of pieces in any number of cuts

When we already know the total number of cuts, you have to consider that the cuts could be along any axis. For example, if we make a total of 10 cuts, all 10 can be along the x-axis, or 5 along the x-axis and 5 along the y-axis, etc. For a given number of cuts, we can have a number of combinations.

We get the minimum number of pieces when all the cuts are made on the same axis. If we make all 10 cuts along the x-axis, a total of 11 new cuboids are formed. All other combinations will result in more than 13 pieces. Let’s say, 11 cuts along the x-axis and 1 cut along y. The total number of pieces formed is (11+1)*(1+1) = 24.

### Maximum number of pieces in any number of cuts

In order to get the maximum number of pieces with a given number of cuts, divide the total cuts equally among the three axis. If we divide 9 cuts equally among the three axis, we get 3 cuts in each axis making (3+1)*(3+1)*(3+1) = 64 pieces in total. But what if the total number of cuts cannot be divided equally among the three axis. For a number like 14, we cannot distribute the cuts equally among all the three axis, since the number of cuts cannot be a fraction.

In such a case, for getting the maximum number of total pieces, we need to reduce the difference between the number of cuts as much as possible, between the axes. For 14 cuts, we can divide it as A = 5, B = 5, C = 4.

Any other combination of numbers will result in a lower number of cuboids. If we evaluate, we find that in the case of an equal number of cuts, when the difference between the numbers of cuts along different axes is 0, that case forms the maximum number of new cuboids.

### NUMBER OF CUTS FROM TOTAL NUMBER OF PIECES GIVEN

The cube question in CAT can also ask the total pieces formed after a specific number of cuts. We need to find the number of cuts in different axis based upon the question.

Suppose, a cube is cut to make 10 new pieces. Now 10 = (A+1)*(B+1)*(C+1). Now 10 is to be represented as the product of 3 numbers or factors. We can have, 10 = 1*10*1 or 1*5*2.

We already know that factorising the total number of pieces into equal factors gives us the minimum numbers of cuts. If the number is not divisible by 3, then we should minimize the difference between the factors. In the case of 10 pieces, 1*5*2 gives the least difference between factors.

If all the cuts are made along the same axis, we get the maximum number of cuts. For instance, for 10 pieces, factors should be 1*10*1 that means the cuts parallel to the x-axis are 9 and no cut is made along any other two axes.

### Painting the cubes

Painting the cubes is the most common question in CAT. For example, a cube is painted purple, then it is cut into 64 pieces by 3 cuts along every axis. So there are 4 different rows of 16 pieces (small cubes) each. We can draw the following conclusions

A number of cubes with 3 sides painted purple= all the corner cubes which is equal to 8 cubes.

Number of cubes with exactly 2 sides painted = (n-2)*(number of edges) = (4-2)*(12) = 24.

Number of cubes with exactly 1 side painted purple= cubes on the sides (except on the edge and the corner) = (n – 2)2*6=24

Number of cubes with 0 sides painted purple= (n-2)3 = 8

The number of cubes that remain unaffected with the painting is those, which are not on the outer side. In other words, if we remove the outer painted shell then the inner structure is what we desire or we reduce the dimension of the cube by 2 units (remove a painted layer from all the sides or sides) to get an inner cube of side dimension = n-2 units.

### If the number of cuts are not equal, let’s say if X =5, Y = 6, Z = 7, then:

A number of cubes with 3 sides painted purple= all the corner cubes which is equal to 8 cubes.

Number of cubes with exactly 2 sides painted = (X-2)*4 + (Y-2)*4 + (Z-2)*4 {since 4 edges will have each of (X-2),(Y-2),(Z-2)}= 12 + 16 + 20 = 48.

Number of cubes with exactly 1 side painted purple= cubes on the sides (except on the edge and the corner) = 2*[(X-2)(Y-2) + (Y-2)(Z-2) + (X-2)(Z-2)] = 2*(12 + 20 +15) = 94

Number of cubes with 0 sides painted purple= the inner cuboid = (X-2)*(Y-2)*(Z-2)= 3*4*5 = 60

### If cubes are painted with different colors

The cube question can also paint sides with a different color. Let us say the three pairs of adjacent sides are painted with yellow, purple and orange respectively. The cube is cut into 64 identical cubes with an identical number of cuts along the three axis.

### The following observations can be made:

Cubes with all the three sides colored = 2 cubes diagonally opposite to each other.

Cubes with only same color on two sides = three edges without corner cubes = 3*(a-2) = 6

Total cubes on the edges = 4*a + 8*(a-2) = 32

Number of cubes with only 2 color sides = total cubes on edges – same color on two sides cubes – all three color side cubes = (3) – (2) = 32 – 6 – 2 = 24

From the above observation, we can say cubes with only yellow and orange sides or only purple and orange = 24/3 = 8

Number of cubes with exactly one side yellow = cubes on the two sides of the painted yellow side = 2*(a-2)2 = 8

Number of cubes with sides only yellow = (2)/3 + (6) = (a-2) + 2*(a-2)2 = 10

Number of cubes with exactly one side painted = 6 sides with (n-2)2 cubes painted on one side = 6*(n-2)2 = 150.

Number of cubes with exactly two sides painted with different colors = 9 edges with (n-2) cubes = 9*(n-2) = 18

It is a useful approach to make the cube diagram on the paper while solving the cube questions in CAT. Cube is a 3-D figure and becomes challenging while solving without a figure, hence it is highly recommended that you make a cube figure while solving the cube questions in CAT.

Visualizing cubes and colors helps us develop logical reasoning for CAT and visualizing skills. It is important to solve cube questions in CAT as it is common in the exam.