RAS Reasoning, Mental Ability and Basic Numeracy — Study Material
Structured preparation resources for India's competitive examinations.
Reasoning and numeracy improve through deliberate practice, not by reading solutions passively. The official RPSC Prelims syllabus lists deductive, inductive and abductive reasoning; statement-based logic; sequences and coding; relations and directions; diagrams and arrangements; and specified areas of arithmetic and data analysis.
1. Deductive, inductive and abductive reasoning
Deduction asks what must follow if the premises are true. Induction identifies a pattern from examples but does not guarantee that every future case will follow it. Abduction looks for the most plausible explanation of an observation. In questions, distinguish a conclusion that is logically necessary from one that merely sounds likely.
2. Statements and assumptions, arguments, conclusions and courses of action
An assumption is an unstated idea on which an argument depends. A conclusion must follow from the given information, not outside knowledge. A course of action should address the stated problem, be feasible and avoid creating a larger problem. Read the exact wording and avoid adding facts that the question does not supply.
Method: underline the claim, identify the supporting reason, test each option against the text and eliminate choices that are too broad, irrelevant or based on an unstated premise.
3. Analytical and critical reasoning
Separate facts, opinions, evidence and inference. Check whether evidence is relevant and sufficient, whether a comparison is fair, and whether a conclusion confuses correlation with cause. In assumption questions, test what must be true for the argument to work; in inference questions, select only what the information supports.
4. Number and letter sequences; coding and decoding
Look for common patterns: constant addition or subtraction, multiplication, alternating operations, squares or cubes, position-based letter changes, or two interleaved sequences. Test a candidate rule against every term rather than fitting the first two numbers only. For letter codes, write alphabet positions if needed and check direction and wrap-around carefully.
5. Relations and direction sense
For family relations, draw a small tree and mark gender only when the information gives it. For direction questions, establish a north-facing reference, then track each turn and movement. Do not rely on mental rotation when a sketch can prevent an error.
6. Logical Venn diagrams, ranking and seating arrangements
Venn diagrams represent inclusion and overlap. Read quantifiers carefully: “all”, “some” and “none” are not interchangeable. For ranking, record positions from the same end before combining statements. For seating arrangements, fix the direction and viewpoint stated in the question, list each constraint and place only what is certain before making a case split.
7. Shapes and their sub-sections
Revise visual patterns, rotations, reflections, embedded figures and counting of components. Count systematically by size or orientation so that the same shape is not counted twice. If a diagram is crowded, mark each candidate lightly and cross it off after counting.
8. Ratio, proportion, partnership, profit and loss
A ratio compares quantities in the same units. In direct proportion, both quantities change in the same direction by the same factor; in inverse proportion, one increases as the other decreases under a fixed-product condition. Partnership problems generally allocate profit in proportion to capital multiplied by time. Profit percentage is normally calculated on cost price, while discount percentage is calculated on marked price unless the question defines otherwise.
Example: If cost price is ₹800 and selling price is ₹920, profit is ₹120 and profit percentage is 120 ÷ 800 × 100 = 15%.
9. Simple and compound interest
Simple interest is calculated on the original principal: SI = P × R × T ÷ 100 when the rate is annual and time is in years. Compound interest adds interest to the balance at each compounding interval. Check whether the question specifies annual, half-yearly or another compounding period.
Example: At 10% simple interest for 2 years on ₹1,000, interest is ₹200. With annual compounding at 10%, the amount after two years is ₹1,210 and compound interest is ₹210.
10. Perimeter and area of plane figures
Perimeter measures boundary length; area measures the surface enclosed. Revise the formulas for rectangles, squares, triangles, parallelograms and circles, and keep units consistent. A common error is to report square units for perimeter or linear units for area.
11. Tables, bar diagrams, line graphs and pie charts
Read the title, unit, period and scale before calculating. In a pie chart, a sector’s percentage is its angle divided by 360 degrees; conversely, angle = share × 360 degrees. For comparisons, identify whether the question asks for absolute difference, percentage difference, share or growth rate.
12. Arithmetic, geometric and harmonic mean; median and mode
The arithmetic mean is total divided by count. The median is the middle value after sorting, and the mode is the most frequent value. The geometric mean is useful for multiplicative growth rates, while the harmonic mean is used in certain rate and ratio settings. Do not choose an average formula until you understand what the data represent.
13. Permutation, combination and probability
Permutations count arrangements where order matters; combinations count selections where order does not matter. For simple probability, when outcomes are equally likely, probability equals favourable outcomes divided by total possible outcomes. State assumptions clearly: not all real-world outcomes are equally likely.
Practice set
- A price rises from ₹400 to ₹460. Find the percentage increase.
- Two partners invest ₹20,000 and ₹30,000 for the same period. In what ratio should profit be shared?
- The average of six values is 14. What is their total?
- A fair die is rolled once. What is the probability of obtaining an even number?
Answers with working
- Increase ₹60; 60/400 × 100 = 15%.
- Capital ratio 20,000:30,000 = 2:3.
- 6 × 14 = 84.
- Three even outcomes out of six, so 3/6 = 1/2.