CAT Numerical Reasoning: Formulas, Preparation Tips, and Sample Questions

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CAT Numerical Reasoning: The CAT Exam Numerical Reasoning section is a critical component that tests candidates’ mathematical skills and ability to interpret data accurately. This section includes questions that assess problem-solving abilities through topics such as arithmetic, algebra, geometry, and data interpretation. Excelling in this part of the CAT exam requires a solid understanding of mathematical concepts and the ability to apply them to solve complex problems efficiently. Proper preparation and practice in numerical reasoning are essential for achieving a high score and gaining admission to top management institutes. In this blog, we will break down difficult problems, share useful tips, and provide practice questions to evaluate yourself. 

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What is CAT Numerical Reasoning?

Numerical reasoning is created to test students’ maths skills and manages to concentrate on various specific areas. It involves understanding and interpreting data, performing calculations, and making logical decisions based on numerical information. In tests like the CAT (Common Admission Test), numerical reasoning questions assess your skills in areas such as Arthematic, Algebra, Geometry, Statistics, and Problem-Solving.

Also Read: Everything about CAT exam: CAT syllabus, fees, dates

CAT Numerical Reasoning Test Formulas

Here are some formulas you need to know for CAT Numerical Reasoning. Understand these formulas and use them while solving questions:


The average, or ‘mean’, is noticed by adding the values in the dataset and dividing the total by the number of values.

Average= Sum of Value of Items / Number of Items

Reverse Percentages

Reverse percentages are used to find the original amount before a percentage increase or decrease is applied. Here’s how you can think about it:

Original Value = New Value / (1+Increase)
Original Value = New Value / (1-Increase)


Percentage means ‘per 100’. When we calculate the percentages by dividing the value by the total and multiplying the answer by 100.

Percentage = (Value/Total) * 100

Hopefully, this is easy for you, the real difficulty with percentages arises when we must work out percentage changes and increases/decreases.

Percentage Change (Increase)

Percentage Increase = [(New Number-Original Number)/Original Number] * 100

Percentage Change (Decrease)

Percentage Increase = [(New Number-Original Number)/Original Number] * 100

Weighted Average

A weighted average is a type of average where some values contribute more to the final result than others. Here is the formula that students can refer to:

Weighted Average = Sum of Weighted Values/Number of Values
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CAT Numerical Reasoning Preparation Tips

When preparing for CAT numerical reasoning, it is important for the candidate to look into all the preparation tips which will help one to crack the CAT exam.

Focus on Relevant Math Skills

If you’re finding math exams challenging, don’t worry. Numerical reasoning tests evaluate a different set of skills. These tests involve basic numerical operations, including:

  • Averages
  • Division
  • Addition
  • Percentages
  • Multiplication
  • Subtraction
  • Ratios

Start by Understanding the Question

Differences in test scores often arise not just from numerical reasoning ability but from understanding the question correctly. The first step is to identify what the question is asking. Instead of getting overwhelmed by all the numbers and graphs, read the question carefully to determine which numbers are relevant. This approach is especially crucial for questions with numerous figures.

Choose an Optimal Test Environment

Even if you excel in math or numerical reasoning, a distracting environment can hinder your performance. Ensure you are well-prepared and familiar with the test format. Take the test in a quiet, distraction-free setting to perform at your best.

Remove Stress to Work Concentration

If students are feeling stressed out, then it is an appropriate idea to take deep breaths prior there test start. This will help with fighting nervousness as well as building focus towards their studies. Students should utilise their anxious energy and work it into the test! Therefore sometimes it is a high sense of anxious concentration can help students to focus during a test.

Be Aware of The Amount of Time

Numerical reasoning tests will be far different so pay attention to the number of questions that students have to answer, as well as calculate how much time you have per question, and overall. Some questions will require longer to finish than others, and that is why students need to calculate how long it generally takes them to answer a numerical reasoning question.

Get Familiar With Tables and Reading Graphs 

The foremost aspect of taking a numerical reasoning test is to fast and accurately digest and analyse presented data in graphs and tables. Speed is an important element in good mock test-taking methods, interpreting graphs and tables quickly is the best place to improve your speed.

CAT Numerical Reasoning Sample Questions

Find below questions on CAT Numerical Reasoning which will help you get an idea about how the actual paper will look like.

Question 1: The ratio of the ages of two friends A and B is 5:6. If the sum of their ages is 33 years, what are their present ages?

Answer: Let the present ages of A and B be 5x5x5x and 6x6x6x respectively.

According to the problem: 5x+6x=33


x = 3

So, the present ages are: 

Age of A = 5x = 5 × 3 =15 Years

Age of B = 6x = 6 x 3 = 18 Years

So, the present ages of A and B are 15 years and 18 years respectively.

Question 2: If the sum of three consecutive even numbers is 78, find the numbers.

Answer: Let the three consecutive even numbers be xxx, x+2x+2x+2, and x+4x+4x+4.

Their sum is: x+(x+2)+(x+4)=78x + (x + 2) + (x + 4) = 78x+(x+2)+(x+4)=78



x = 24

The three numbers are: 


X + 2 = 26

X + 4 = 28

So, the three consecutive even numbers are 24, 26, and 28.

Question 3: A retailer marks up the price of an item by 25% above its cost price. During a sale, the retailer offers a discount of 20% on the marked price. If the final selling price of the item is $240, what is the original cost price of the item?


Let’s break it down step by step.

Let the cost price be C.

Mark up the price by 25%:
Marked price=C+0.25C=1.25C

Offer a discount of 20% on the marked price:

Final selling price=1.25C−0.20(1.25C) = 1.25C × (1−0.20) = 1.25C×0.80=1.00C

We know the final selling price is $240, so:
1.00C = $240

Solve for C: C = $240

The original cost price of the item is $240.

This question tests your ability to work with percentages and understand the relationships between cost price, marked price, and discounts.

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What do you understand about CAT the numerical reasoning test?

A numerical reasoning test is used to assess a candidate’s ability to handle and interpret numerical data. You will be required to analyse and draw conclusions from the data, which may be presented in the form of tables or graphs. The tests are timed and in a multiple-choice format.

What do understand about numerical aptitude examples?

Numerical aptitude tests usually target the following mathematic skills: 1) Addition 2) Subtraction 3) Multiplication 4) Division 5) Averages 6) Percentages 7) Ratios. Additional advanced calculations, such as percentages, averages and ratios can become simpler with the use of specific formulas.

What are essential numerical skills?

Basic numeracy abilities are the ability to understand basic arithmetical operations examples subtraction, addition, division, and multiplication. For example, you are supposed to have at least basic numeric comprehension if you can answer simple arithmetic problems like 2 + 2 = 4.

This was all about CAT numerical reasoning. For more informative blogs, check out our Management Exams Section, or you can learn more about us by visiting our  Indian exams page of Leverage Edu.

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