Understanding Numerical Reasoning

Understanding Numerical Reasoning Tests

Understanding Numerical Reasoning Tests

Numerical reasoning tests are not meant to test your mathematical skills. For that purpose, there are quantitative aptitude tests. These tests measure a candidate’s ability to analyze, interpret and draw logical conclusions that are based on the numerical data given. Thus, understanding numerical reasoning tests is important

In today’s world, all organisations are privy to huge amount of data that, if analyzed properly, can help achieve better business goals. Thus, companies are looking for people who have good analytical skills and ability to analyze data—both numerical and subjective.

In such Tests, candidates are provided with information in the form of graphs and tables that project different situations. Each situation is followed by a number of questions relating to the information given. The candidates are required to decide the correct answer to each question solely on the basis of the given numerical information.

A crucial point to be noted here is that these tests have time limits and are designed in such a way that only about two to three per cent of the test-takers can correctly answer all the questions in the given time.

Since these are not maths test, calculators are allowed to be used. However, it is advised to check before taking the exam if use of calculator is allowed.

Numerical Reasoning Tests are used by recruiting agencies/employees to find if the candidate is:

  • capable of efficiently and effectively identifying critical business-related issues based on logically drawn conclusions from the given numerical data;
  • capable of efficiently monitoring performance and progress based on numerical metrics;
  • capable of clearly presenting issues in forms of charts and tables to the higher management and clients.

The level of these exams is set on the basis of benchmarks set for different jobs. For example, candidates applying for a post-graduate role are expected to have stronger numerical capabilities than those applying for a graduate job. Similarly, level of such Tests will be easier for marketing executive jobs vis-à-vis Engineering or managerial jobs.

The level of difficulty is generally defined using three dimensions – amount of data (some questions only offer the data you need to get to the answer, but others have much more data that is used to distract your attention and consume time), time limitation (a test at a higher level of difficulty will allow you less time for each test question) and complexity of data (number of transformations or calculations you need to do to find the answer).

The only way to prepare for such Tests is to practice, practice, and more practice. Your being good at maths will be an advantage but you will still encounter a number of hurdles that you would be able to tackle only if you have practiced well.

To practice, you can take online tests on offer as also use various reasoning test books.

In most cases, there is no ‘passing’ marks for such tests. A candidate’s result is calculated relative to that of other people in similar roles. This means that even if you correctly answered most of the questions, your result may still be lower than that of other people in similar roles. For example, a candidate correctly answers 24 of 30 questions. However, other people in similar roles, on average, answer correctly 26 of 30 questions. This means that your ‘good result’ is actually a ‘bad result’ because it’s lower than the average result.

Point to remember: Such tests are not something that you can learn by reading a book or simply taking tuition classes. To master these tests requires a combination of practice, concentration and knowledge of test-taking strategies.

how to solve test of reasoning
How to Solve Reasoning Questions Exam Preparation Tips" >

How to Solve Reasoning Questions Exam Preparation Tips

Tips on How to Solve Reasoning Questions

The Reasoning Ability section is one of the most crucial parts of any competitive exam. You need to be aware of the different types of reasoning questions that are asked, as also practice to develop the ability to solve them as quickly as you can.

Test of Reasoning questions can be broadly classified in following head:

  1. Analytical Reasoning: A number of clues are given based on on which you have to answer a set of questions. To solve such questions make a table of the clues and then answer based on your analysis.
  2. Logical Reasoning: In such questions, either a large table is given or some clues are given in the form of a riddle. You have to arrive on your answers after figuring out the elements of the riddle or table.
  3. Mathematical Reasoning: You are required to do some simple maths to solve such questions. For example finding the missing number based on some mathematical equation on which the given series has been made; or finding how many triangles can exist of a particular perimeter, and so on.
  4. Games: These type of questions are mostly been asked in CAT and other Management Entrance Tests. On basis of a given data you have to find out either the odd or matches played/lost. Such questions require processing of lots of data.
  5. Puzzles: Such questions are generally long and require more than a minute to solve. A number of conditions are given that give limitations to the answers. Sometimes there might be just one question to be answered, which makes it a tie consuming exercise. You need to practice a lot of puzzles from books and on internet to train yourself to solve such questions in shortest possible time.
  6. Miscellaneous Reasoning: This is a combination of data and reasoning and the questions cannot be solved by conventional methods of data interpretation. The charts need to be interpreted using logic.


The questions can be easy to extremely difficult. A systematic arrangement of facts and step-by-step approach is required. Generally, a large number of statements are given and you have to process all the statements to come to the answer. The task becomes easy if you are able to spot the crucial statements first and proceed to others thereafter. Following steps will be useful while attempting such questions:

  1. Read the given information and decide how best the information can be arranged.
  2. Arrange the information in tables, charts or maps.
  3. Look for the crucial statements fist that give the maximum information.
  4. Use arrows, crosses and other notations for different elements.
  5. Do not proceed sequentially.
  6. Tackle one or two variables at a time, completely ignoring the other variables.

Here is a sample question to help you to understand better:


Directions: Answer the following questions based on statements given below:

(i) There are three houses on each side of the road

(ii) These six houses are labelled as P, Q, R, S, T and U

(iii) These houses are of different colours, namely, Red, Blue, Green, Orange, Yellow and White

(iv) These houses are of different heights

(v) T, the tallest house, is exactly opposite the Red coloured house.

(vi) The shortest house is exactly opposite the Green coloured house.

(vii) U, the Orange coloured house is located between P and S

(viii) R, the Yellow coloured house is exactly opposite P.

(ix) Q, the Green coloured house is exactly opposite U

(x) P, the White coloured house is taller than R, but shorter than S and Q

  1. What is the colour of the tallest house?
    (a) Red  (b) Blue  (c) Green  (d) Yellow  (e) None of these
  2. What is the colour of the house diagonally opposite the Yellow coloured house?
    (a) White  (b) Blue  (c) Green  (d) Red  (e) None of these
  3. Which is the second tallest house?
    (a) Red  (b) Blue  (c) Green  (d) Yellow  (e) None of these


How to attempt:

At first glance the question looks difficult: ten statements have to be read and arranged. There are three variables: colour, height, order. If you will start looking at all variables at once you will definitely get confused. The second trap is to process the information sequentially, that is, reading each statement and writing it down in the arrangement. This will end up in a big mess by the time we are at the half way mark of our processing of the data.

Instead, scan all the statements quickly and see which statements give the maximum information. In this question the crucial statement is number (vii). Immediately we know that the three houses on one side are P,U and S. Combining it with statements (viii) and (ix) we have the order of the houses as follows:

P R (Yellow)
U (Orange) Q (Green)

​Note that the above diagram is obtained just by processing three statements and gives us a lot of clarity. Also note, that at this stage we are completely ignoring the third variable, height. Now we can use the information from the other statements. From (v) we see that T is the tallest house. From (x) we see that P is White. Since the tallest house is opposite the Red house, the only colour left for T is Blue, and that is the answer to the first question. For the second question we see that R, the Yellow coloured house, is opposite S. We are already given the colour of S, that is Red. So, we are able to answer two of the three questions simply by using the colour information. For the third question, we will need to use the third variable, height. The crucial statement for height is (x). From this we get: S, Q > P > R. Since T is the tallest, we can write: T > S, Q > P > R. To find the second tallest house we need to know the heights of U, S and T. Scan the ten statements again and we see that no such information is given. So, the answer to the third question is: None of these (e). The trick is to maintain clarity and not get bogged down by excess information. Always assess one or two variable at a time and you will never go wrong or get confused.


Directions: Answer on the basis of the information given below:K, L, M, N, P, Q, R, S, U and W are the only ten members in a department. There is a proposal to form a team from within the members of the department, subject to the following conditions:

  • A team must include exactly one among P, R and S
  • A team must include either M or Q but not both
  • If a team includes K, then it must also include L, and vice versa
  • If a team includes one among S, U and W then it also must include the other two.
  • L and N cannot be members of the same team.
  • L and U cannot be members of the same team.

The size of the team is defined as the number of members in the team.

  1. Who cannot be a member of a team of size 3.
    (a)(b) M   (c) N   (d) P    (e) Q
  2. Who can be a member of a team of size 5?
    (a)(b) L   (c) M   (d) P    (e) R
  3. What would be the size of the largest possible team?
    (a)(b) 7   (c) 6   (d) 5    (e) Cannot be defined
  4. What would be the size of a team that include K?
    (a) 2 or 3  (b) 2 or 4   (c) 3 or 4   (d) Only 2    (e) Only 4
  5. In how many ways a team can be constituted so that the team includes N?
    (a) (b) 3   (c) 4   (d) 5    (e) 6

How to attempt:

The method to be used here will be different from what we used in Set 1. Order is not required in this case. Different teams are possible so we cannot make a table. Each question has to be tackled separately, using the clues given.

The first two statements are crucial as they tell us that one member must be chosen from each of PRS and MQ.

Approaching the first question, we have to make a team of three, with two members already from the above two groups. We see that L cannot be there because if L is selected then K also has to be there. This will lead to a four-member team. Hence, L cannot be part of any three-member team.

For the second question, if we choose K then L has to be there, then we have to take one from M or Q, and one from P or Q or S making it four members. Problem is choosing the fifth. N is ruled out because of the second last statement and U cannot be part of the five-member team because of the fourth statement. By this logic K and L are ruled out as they cannot be part of any five-member team. Taking M, we can take other members as S, U, W and one of P/R/S. Hence (c) is the correct answer.

Solving question 2 helps us to solve Question 3 also. We already know that five-ember team is possible. Since K and L cannot be part of a five-member team, by the same logic, they cannot join the six-member team also. Thus, there is no member who can be added to the make a six-member team. Thus maximum team size possible is five.

Question 4 can be solved using the previous information. If K,L are chosen then maximum team size can be 4.

For Question 5 we find that analyzing the information we used for previous questions we find that if N is taken, L cannot be taken. If we take U we have team consisting of SUWNM or SUWNQ. If U is not taken we have NMP/NMR and NQP/NQR. Thus we have six different ways in which we can make a team that includes N.


The challenge before you is to process large amount of information in shortest possible time. This looks to be a daunting task, but learning to break the information in parts can make it easy and manageable. The technique can be learned by practice, and more practice.

CLICK HERE to take a Test of Reasoning Practice test and assess your capability to attempt Reasoning questions. We will be posting more practice tests in coming months. So keep coming back for more!