Mental Reasoning 10 – Problem Solving Technique and Step-by-Step Solutions for Competitive Exams SSC, BSSC, Bank, Railways

Mental Reasoning 10 – Problem Solving Technique and Step-by-Step Solutions for Competitive Exams SSC, BSSC, Bank, Railways

Problem Solving Techniques in Mental Reasoning, is a key topic in competitive exams like SSC, Banking, Railways, BPSC, Defence, and State PSCs. I’ll cover all probable types, the methods to approach them, examples, and step-by-step techniques.

Mental Reasoning: Problem Solving Techniques

Introduction / परिचय

Problem solving in reasoning is the skill to analyze, simplify, and logically solve puzzles, statements, numerical problems, or word problems.

Competitive Exam Context:

• Often appears in aptitude/mental ability sections.
• Tests logical thinking, speed, and accuracy.
• Requires combining analytical, mathematical, and reasoning skills.

हिंदी में:

• यह आपकी तार्किक सोच और विश्लेषण क्षमता को परखता है।
• इसमें विभिन्न प्रकार के पजल, गणितीय, तार्किक और शब्द आधारित समस्याएँ शामिल होती हैं।

Steps to Approach a Problem

1. Read carefully / ध्यान से पढ़ें: Understand exactly what is given.
2. Identify type / प्रकार पहचानें: Number puzzle, coding-decoding, series, seating, inequality, syllogism, blood relation, direction sense, age, calendar, clock, etc.
3. Extract data / तथ्य निकालें: List known facts, variables, relationships.
4. Choose technique / तकनीक चुनें: Use table, diagram, Venn diagram, equation, backward reasoning, or elimination.
5. Solve logically / तार्किक हल करें: Step by step, avoid assumptions.
6. Verify / जाँच करें: Check answer fits all conditions.

Most Common Types of Problem-Solving Questions in Competitive Exams

Here is a comprehensive list of probable types:

Problem-Solving Techniques for Each Type

1. Number / Alphabet Series

• Look for differences, sums, products, squares, cubes, alternating patterns.
• Check alphabetic positions, skip counts.
• Use tables to track progression.

Example:
Series: 2, 6, 12, 20, ?
Step: Differences: 4, 6, 8 → Next diff = 10 → 20+10=30

2. Coding & Decoding

• Identify pattern: letter shift, reverse, position, arithmetic on numbers.
• Make coding table for clarity.

Example:
If CAT → DBU (shift +1 each letter), DOG → ? → EPH

3. Blood Relations

• Convert statements into a family tree diagram.
• Use symbols: M = Mother, F = Father, B = Brother, S = Sister.

Example:
“P is brother of Q. Q is mother of R. How is P related to R?”
Solution: P = maternal uncle → Answer.

4. Direction Sense

• Draw diagram for each movement.
• Consider turns clockwise/counterclockwise and relative position.

Example:
“John walks 5 km North, 3 km East, 2 km South. Distance from start?” → Apply Pythagoras.

5. Seating Arrangements

• Use table / circle diagram.
• Mark fixed positions first, then relative positions.
• Check all given conditions.

6. Inequalities

• Use symbolic comparison: A>B≥C
• Combine statements carefully.
• Always check dominant sign (> / < stronger than ≥ / ≤)

7. Syllogisms

• Use Venn diagrams for “All, Some, No”.
• Apply logical deduction to see which conclusion follows.

8. Calendars & Clocks

• Calculate day of the week using known formula.
• Clock problems → angles of hands:
  • Hour hand: ( H \times 30 + \frac{M}{2} )
  • Minute hand: ( M \times 6 )
  • Angle = |Hour angle − Minute angle|

9. Age Problems

• Use equations, “current age”, “after n years”, “ratio” formulas.
• Always assign variables clearly.

Example:
A is twice as old as B. 5 years ago, A was 3 times B. Find current ages.

10. Data Sufficiency / Complex Puzzles

• List given facts in tabular/diagram format.
• Check if all conditions satisfied before concluding.
• Apply elimination method.

11. Profit-Loss / Simple Math Logic

• Use shortcut formulas and mental math tricks:
  • Profit % = (Profit / Cost Price) × 100
  • Loss % = (Loss / Cost Price) × 100
  • Shortcut for successive %: ( \frac{p_1 + p_2 + p_1p_2/100}{?} )

12. Analogy & Classification

• Identify common feature or pattern.
• Odd one out → eliminate the one breaking the pattern.

13. Logical Sequence

• Arrange steps or events logically.
• Use flow diagram to simplify.

14. Coded Directions / Symbols

• Create mapping table for symbols → actions → directions.
• Track each move step by step.

Key Problem-Solving Tips (English + Hindi)