Logical Reasoning and General Mental Ability

Syllogisms

• Use Venn diagrams. Draw the minimum overlap that the statements require, then test each conclusion.
• Rules:
  • "All A are B" → "Some B are A" (conversion).
  • "Some A are B" → "Some B are A".
  • "No A is B" → "No B is A".
  • Two "some" statements give no definite conclusion.
• "Either–or" cases: when two conclusions are complementary (some A are B / no A is B) and neither definitely follows, "either I or II follows".

Coding–decoding

• Letter shift: +1, −1, or reverse (A↔Z). Know the positions: A=1 ... Z=26; reverse position = 27 − n.
• Number coding and substitution coding ("sky is called sea").
• Memory aid: EJOTY (E=5, J=10, O=15, T=20, Y=25).

Blood relations

• Draw a family tree: males as squares, females as circles; = for married; vertical lines for generations.
• Decode statements step by step, starting from the end ("only daughter of my mother" = me).

Direction sense

• Draw a compass. Right turn = clockwise 90°; left turn = anticlockwise.
• Pythagoras gives the shortest distance. For example, 3 km east and 4 km north = 5 km north-east.
• Shadows: in the morning the Sun is in the east, so shadows fall west. In the evening, shadows fall east.

Arrangements and puzzles

• Linear arrangement: fix the most certain clue first. Draw positions 1 to n; "facing north" means your right is their right.
• Circular arrangement: facing the centre, right = anticlockwise.
• Scheduling and floor puzzles: make a table; mark definite placements and eliminate.
• If the clues cannot fix a position, the answer is "cannot be determined". Do not force an answer.

Series and odd-one-out

• Number series: look at differences (and differences of differences), products, squares and cubes (n², n³, n² + 1), primes and alternating patterns.
• Letter series: positions and skips.
• Odd one out: squares, primes, even/odd, or meaning (fruits vs vegetables).

Calendars and clocks

• Odd days:
  • an ordinary year has 1 odd day and a leap year has 2;
  • 100 years = 5 odd days, 200 = 3, 300 = 1, 400 = 0.
• Leap year: divisible by 4. A century year must be divisible by 400 (2000 was a leap year; 1900 was not).
• Clock angle θ = |30H − 5.5M| (in degrees). The hands overlap 11 times in 12 hours and 22 times in a day. They are at right angles 44 times a day.

Statements and conclusions, assumptions and arguments

• Conclusion: must follow only from the statement.
• Assumption: what the speaker takes for granted.
• Strong argument: relevant, important and backed by facts. Weak argument: emotional, trivial, or based on assumption.
• Course of action: practical, solves or reduces the problem, and is not extreme.

Practice routine

• 20 reasoning questions a day, timed (under a minute each for simple types).
• After each test, note the type of question you got wrong and practise that type for two days.

Exam tip: BPSC's GS paper has about 10–15 mental ability questions mixing reasoning and arithmetic. They are the easiest marks in the paper if you practise daily. UPSC CSAT has 15–20 reasoning questions.