Arithmetical reasoning and figural classification questions are asked in almost every SSC and Railway related competitive exams - be it SSC CGL, SSC CHSL, SSC JE, HSSC Patwari, HSSC Canal Patwari, HSSC Sachiv, HSSC Clerk, Delhi Police, RRB Group D, RRB JE, RRB NTPC, RRB ALP, SSC MTS, SSC CPO, SSC Steno, SSC Constable or any other related competition in government sector in India.
Arithmetical reasoning consists of a numeral or a word problem to be solved using basic arithmetic. These questions encircle a variety of concepts to solve using basic mathematics like ages and weights, number system, ratio and proportion, profit, loss and discounts, time and distance, sequences and patterns, fractions and percentages, time and work, simple and compound interest, HCF and LCM, pipes and cisterns, games and tournaments, probability, square roots etc.
Figural classification questions are the means to judge a candidate’s non-verbal capabilities, keen observance and general intelligence quotient. In such types of questions, mainly a group of figures except one belongs to a particular pattern, whereas the ignored one is the odd one out not resembling that pattern and the candidate has to identify this odd patterned option. As an example, to one such figural classification question
In figure (c) only, two out of the four elements are opening in the same direction. Hence the answer would be (c). Figural questions practice may come handy in the data interpretation section also.
Important arithmetical reasoning and figural topics
Topic | Explanation |
Natural numbers | Counting numbers 1, 2, 3, 4, 5, ... are called natural numbers |
Whole numbers | All counting numbers together with zero form the set of whole numbers. Thus, (i) 0 is the only whole number which is not a natural number. (ii) Every natural number is a whole number. |
Even numbers | A number divisible by 2 is called an even number, e.g., 2, 4, 6, 8, 10, etc. |
Odd numbers | A number not divisible by 2 is called an odd number. e.g., 1, 3, 5, 7, 9, 11, etc |
Prime numbers | A number greater than 1 is called a prime number, if it has exactly two factors, namely 1 and the number itself. |
Composite numbers | Numbers greater than 1 which are not prime, are known as composite numbers, e.g., 4, 6, 8, 9, 10, 12. |
Co-primes | Two numbers a and b are said to be co-primes, if their H.C.F. is 1. e.g., (2, 3), (4, 5), (7, 9), (8, 11), etc. are co-primes |
Distributive law | (i) a * (b + c) = a * b + a * c, and (ii) a * (b-c) = a * b - a * c |
Euclidean algorithm | If we divide a given number by another number, then: Dividend = (Divisor x Quotient) + Remainder |
Basic and important formulae | |
Arithmetic progression | If every upcoming term of a progression differs from its previous term by a constant value, then it is called an AP. |
Geometrical progression | A GP is where every term holds a constant ratio with its previous term |
Highest Common Factor | The H.C.F. of two or more than two numbers is the greatest number that divides each of them exactly |
Least Common Multiple | The least number which is exactly divisible by each one of the given numbers is called their L.C.M. |
Laws of Indices, and Law of Surds | |
Ratio | The ratio of two quantities a and b in the same units is the fraction a/b and we write it as a:b |
Proportion | The equality of two ratios is called proportion. If a: b = c: d, we write, a: b:: c : d and we say that a, b, c, d are in proportion |
Direct proportion | Two quantities are said to be directly proportional if on the increase (or decrease) of the one, the other increases (or decreases) to the same |
Inverse proportion | Two quantities are said to be inversely proportional if on the increase of the one, the other decreases to the same extent and vice-versa. |
Time and distance | Speed=distance/time, Time=distance/speed, and distance=time*speed. |
Tips to solve/prepare arithmetical reasoning and figural classification questions
- The most important tip for solving the arithmetical reasoning and figural classification questions is Time Management, and that comes from one thing only- Practice. Practice as many questions as you can. Keep a time track too.
- Go on solving the numerical problems, rather than mugging the theory.
- Learn short-cut methods, but do not jump the steps for solving arithmetical reasoning questions.
- Keep the thumb-rules handy. This will help to lower the attempt time and ensure the answer's accuracy.
Importance of arithmetical reasoning and figural classification in SSC and Railway exams
- If to analyse SSC-CGL previous three years papers, an average of 48% (12 out of 25) of questions in Quantitative Aptitude section which carries 50 maximum marks, comes from arithmetical reasoning part only.
- SSC-CGL apart, in almost every exam, a candidate could find the arithmetical reasoning and figural classification questions in abundance.
- If practised properly, these questions may save the overall time to attempt the paper and thus, one could have more time for other questions.
- Other forms of linear algebra and mathematical questions could be practised and solved in an easier way by practising the arithmetical reasoning and figural classification questions.
Most recommended books for arithmetical reasoning and figural classification (verbal and non-verbal reasoning)
S.No. | Book Name | Author |
1. | Verbal & Non-Verbal Reasoning | R. S. Aggarwal |
2. | Verbal & Non-Verbal Reasoning (Hindi) | Kiran Publication |
3. | Fast Track Objective (arithmetic reasoning) | Arihant Publication |
4. | For Notes, Study Material and Online Quiz (thousands of questions to practice are available) | Gradeup |
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Frequently Asked Questions (FAQs)
1- How to solve the arithmetic problems related to ages? Provide an example.
Problems on age could also be solved by formulating the subjective question into mathematical equations. As an example, let us solve a related problem:
Rajeev's age after 15 years will be 5 times his age 5 years back. What is the present age of Rajeev?
The present problem could be solved as: Let Rajeev's present age be x years. Then,
Rajeev's age after 15 years = (x + 15) years.
Rajeev's age 5 years back = (x - 5) years.
Therefore, x + 15 = 5 (x - 5), or x + 15 = 5x – 25, or 4x = 40, or x = 10.
Hence, Rajeev's present age = 10 years.
2- Provide the solution for this figural problem?
As all other figures can be rotated into each other, the only odd one out is an option (c).
3- Find the remainder when 231 is divided by 5?
As 210 = 1024. Unit digit of 210 x 210 x 210 is 4 [as 4 x 4 x 4 gives unit digit 4].
Therefore, Unit digit of number 231 is 8. Now, 8 when divided by 5, gives 3 as remainder. Hence, 231 when divided by 5, gives 3 as remainder.
4- What will be the product of all the numbers on a telephone?
One of the numbers on the telephone will be zero which gives us the product of all the numbers as zero.
5- What could be the proportionate image at “?” ?
Answer will be (C), as following the symmetry the image at (C) will be proportional.