Class 7 Logical Reasoning — Full Lesson Notes

Shared Section 1 for both NSO and IMO (Classes 5–10 band use the same reasoning skillset)

At Class 7, the Logical Reasoning section moves from Class 1–4's simple pattern/shape puzzles into real Verbal and Non-Verbal Reasoning — the same 10 skills below cover this section in both the NSO and IMO papers, so master it once and it counts for both exams.

Each topic: What it is → 3 worked examples → How to teach it → Practice problems (with answers).

1. Number & Alphabet Series

What it is: A sequence of numbers or letters that follows a hidden rule (add/subtract/multiply by a fixed amount, or skip a fixed number of alphabet positions). Find the rule from the first 3–4 terms, then extend it.

Examples:

  1. 5, 10, 20, 40, __ → ×2 each time → 80
  2. Z, X, V, T, __ → back 2 letters each time → R
  3. 2, 6, 12, 20, 30, __ → differences increase by 2 (4,6,8,10,12) → 42

How to teach it: Have students write the differences (or the letter-position jumps) underneath the series before guessing the answer — this turns a guessing game into a reliable method.

Practice: (a) 3, 9, 27, 81, __ (b) B, E, H, K, __ (c) 1, 4, 9, 16, __ Answers: (a) 243 ×3 (b) N (+3 each) (c) 25 (perfect squares)

2. Analogy

What it is: "A is to B as C is to __" — find the relationship in the first pair, then apply the same relationship to the second.

Examples:

  1. Doctor : Hospital :: Teacher : __ → School (workplace relationship)
  2. Bird : Nest :: Bee : __ → Hive (home relationship)
  3. Water : Liquid :: Ice : __ → Solid (state-of-matter relationship)

How to teach it: Insist students say the relationship as a full sentence first ("a doctor works in a hospital") before searching for the matching word — this prevents surface-level guessing based on category alone.

Practice: (a) Pen : Write :: Knife : __ (b) Fish : Water :: Bird : __ (c) 4 : 16 :: 5 : __ Answers: (a) Cut (b) Sky/Air (c) 25 (n²)

3. Classification (Odd One Out)

What it is: Given 4 items, three share a property and one doesn't — find the outlier.

Examples:

  1. Apple, Mango, Potato, Banana → Potato (a vegetable; rest are fruits)
  2. Triangle, Square, Sphere, Rectangle → Sphere (3D; rest are 2D shapes)
  3. 8, 27, 64, 90 → 90 (not a perfect cube; 8=2³, 27=3³, 64=4³)

How to teach it: Ask "what category do three of these belong to?" before "which one looks different" — students often pick based on appearance (colour, size) rather than the actual mathematical/scientific property being tested.

Practice: (a) 16, 25, 36, 40 (b) Rose, Lily, Carrot, Sunflower (c) Circle, Square, Cube, Rectangle Answers: (a) 40, not a perfect square (b) Carrot, a vegetable (c) Cube, a 3D solid

4. Coding-Decoding

What it is: Letters are shifted by a fixed rule (e.g., +1 forward through the alphabet). Learn the rule from one example, then apply it to a new word.

Examples:

  1. Rule "+1": CAT → DBU
  2. Rule "+1": FLOWER → GMPXFS
  3. Rule "−1": BUS → ATR

How to teach it: Write the full alphabet in a row with the shifted alphabet directly below it — students can then read off any letter's code instantly rather than counting each time.

Practice: Using "+1", code (a) PEN (b) decode QFU back to English (c) using "−1", code DOG Answers: (a) QFO (b) PET (c) CNF

5. Blood Relations

What it is: Working out family relationships from a chain of clues (e.g., "X is Y's father's only son").

Examples:

  1. "Pointing to a boy, a woman says: this boy's mother is the only daughter of my mother." → The woman is the boy's mother (her mother's only daughter is herself).
  2. "A is B's brother. C is B's mother." → A is C's son.
  3. "D is E's father's father." → D is E's grandfather.

How to teach it: Draw a small family tree diagram for every question rather than solving it purely in your head — visualising the chain avoids mixing up generations.

Practice: (a) "X is Y's son. Y is Z's father." How is X related to Z? (b) "A's mother is B. B's only daughter is C." How is C related to A (if A is female)? (c) "P is Q's brother. R is Q's mother." How is P related to R? Answers: (a) X is Z's grandson (b) They are the same person — C is A herself, assuming A has no sisters (c) P is R's son

6. Direction Sense

What it is: Tracking a person's or object's facing direction or position after a series of turns and moves, using North/South/East/West.

Examples:

  1. Facing North, turn 90° clockwise → now facing East.
  2. Facing South, turn 90° anticlockwise twice (180° total) → now facing North.
  3. Walk 5 km East, then 5 km North: straight-line distance from start ≈ using the two legs as a right triangle (not simple addition — for Class 7, usually just asked "how far East and how far North," i.e., 5 km East and 5 km North of the start).

How to teach it: Draw a compass (N/E/S/W) on paper for every question, physically rotate a pencil or arrow to represent "facing direction," and trace the turns — this avoids the common error of confusing clockwise and anticlockwise.

Practice: (a) Facing West, turn 90° clockwise. Which direction now? (b) Facing East, turn 180°. Which direction now? (c) A man walks 4 km North, then 4 km South. How far is he from his start point? Answers: (a) North (b) West (c) 0 km — he's back where he started

7. Ranking / Ordering

What it is: Finding a position in a line/list, or ordering items by a comparison (taller, older, heavier).

Examples:

  1. Rohan is 15th from the top and 21st from the bottom in a class → total students = 15+21−1 = 35.
  2. A is taller than B. C is shorter than B but taller than D → order: A > B > C > D.
  3. In a race, Ravi finishes 2 positions after Meena, who finishes 3rd → Ravi finishes 5th.

How to teach it: For "Nth from top/bottom" problems, always use the formula total = (rank from top) + (rank from bottom) − 1, and explain why the −1 exists (the person is counted in both ranks) using a small real line-up of students.

Practice: (a) Priya is 10th from the left and 15th from the right. Total students in the row? (b) X > Y, Y > Z, W < Z. Who is the smallest? (c) A runner finishes 4th. Another finisher is exactly 2 places behind. What position is the second runner? Answers: (a) 24 (b) W (c) 6th

8. Calendar

What it is: Working out the day of the week for a given date, using the fact that any date exactly 7 days later/earlier falls on the same day.

Examples:

  1. If 1st January is a Monday, 8th, 15th, and 22nd January are also Mondays.
  2. If 3rd March is a Friday, what day is 17th March? → 17−3=14 days later = exactly 2 weeks → Friday.
  3. If today is Wednesday, what day is it 10 days from now? → 10÷7 = 1 week + 3 days → Wednesday+3 = Saturday.

How to teach it: Always divide the day-gap by 7 first and use only the remainder — this is far faster and more reliable than counting day-by-day for gaps larger than a week.

Practice: (a) If 5th June is a Tuesday, what day is 19th June? (b) If today is Sunday, what day is 16 days from now? (c) If 1st of a month is a Thursday, what day is the 30th? Answers: (a) Tuesday (14 days = 2 weeks later) (b) Tuesday (16÷7=2 weeks+2 days, Sunday+2=Tuesday) (c) 30−1=29 days later; 29÷7=4 weeks+1 day; Thursday+1=Friday

9. Age & Number Puzzles

What it is: Word problems using algebra-style reasoning about ages, or custom symbol operations (e.g., "P # Q means P²−Q²") that must be applied to solve for a value.

Examples:

  1. A father is 4× his son's age. After 5 years, he'll be 3× his son's age. Let son=x: 4x+5=3(x+5) → x=10.
  2. If P # Q means P²−Q², find 5#3 → 25−9=16.
  3. Sam is twice his sister's age (8). In 5 years, Sam will be 16+5=21.

How to teach it: Encourage writing the algebraic equation directly from the sentence, phrase by phrase, rather than trying to solve age puzzles by trial and error — it's much faster and rarely goes wrong once the equation is set up correctly.

Practice: (a) If P $ Q = P×Q+(P−Q), find 6$4. (b) A mother is 3× her daughter's age (currently x). In 10 years she'll be 2× her daughter's age. Find x. (c) Find 4&5 if P&Q=P²+Q. Answers: (a) 26 (24+2) (b) x=10 (c) 21 (16+5)

10. Mirror Images & Embedded Figures

What it is: A mirror image flips a picture left-right (not upside-down). An embedded figure is a small shape hidden inside a larger, busier drawing.

Examples:

  1. The letter "b" mirrored looks like "d."
  2. "AMBULANCE" is printed mirror-reversed on ambulance fronts so it reads correctly in a car's rear-view mirror.
  3. A small triangle hidden within the crossing lines of a larger star is found by tracing each line individually.

How to teach it: Use a real handheld mirror for mirror-image questions, and a highlighter for tracing embedded figures — both topics are learned far faster hands-on than by staring at a still picture.

Practice: (a) What does "3" look like mirrored left-right? (b) Is a mirror image the same as a 180° rotation? (c) What's the best tool for finding a hidden shape in a busy drawing? Answers: (a) A backward "3" (b) No — mirroring flips left-right, rotation turns the whole image (c) A highlighter/coloured pencil to trace candidate lines

Use this alongside the NSO Class 7 Science notes or IMO Class 7 Mathematics notes for the rest of each exam's syllabus.