Cause and Effect; Puzzles and Arrangements; Ranking and Ordering; Mathematical Operations

Cause and Effect

12.1 Concept

Two statements given. Determine if:

• Statement I is cause, Statement II is effect

Statement II is cause, Statement I is effect

• Both are effects of a common cause
• Both are independent causes
• Both are effects of independent causes

12.2 Tips

• Cause comes BEFORE the effect in time
• Look for a logical causal chain
• "Because of..." / "As a result..." are temporal clues
• Statistical data as cause → concrete event as effect

Puzzles and Arrangements

13.1 Scheduling / Timetable Puzzles

People/items assigned to positions, days or times.

Approach:

1. List all items and positions
2. Apply definite clues first (absolute positions)
3. Apply relative clues to narrow down
4. Use elimination

13.2 Floor-based Puzzles

People in different floors of a building.

Common constraints:

• "A is above B" → A's floor number > B's floor number
• "A is immediately above B" → A's floor = B's floor + 1
• "Two floors between A and B" → floor numbers differ by 2

13.3 Box / Container Arrangement

Items arranged in stacks or containers.

Key terms:

• "Just above" → immediately next above
• "Somewhere above" → any floor above
• "Between X and Y" → in between their floors

13.4 Day-based Puzzles

Activities/meetings assigned to days of the week.

Approach:

• List 7 days in order
• Apply definite assignments first
• Use "before/after/between" clues to restrict options

Ranking and Ordering

14.1 Core Formulas

Type 1 — Finding Total Count:

Total = (Rank from top + Rank from bottom) - 1

Example: Arush is 7th from top and 26th from bottom:

• Total = (7 + 26) - 1 = 32 students

Type 2 — Finding Rank from Other End:

Rank from top = Total - Rank from bottom + 1 Rank from bottom = Total - Rank from top + 1

Example: Anita is 12th in a class of 46:

• Rank from last = (46 - 12) + 1 = 35th

Type 3 — Person Changes Position:

Total = (New position of first person + Old position of second person) - 1

Example: Sheena is 8th from left, Heena is 17th from right. They swap. Sheena becomes 14th from left:

• Total = (14 + 17) - 1 = 30 girls

Type 4 — Finding New Rank After Swap:

New position of second person = (Difference of two positions of first person) + Old position of second

Example: Dipa is 5th from left, Vinay is 6th from right. After swap, Dipa is 13th from left:

• New Vinay position from right = (13 - 5) + 6 = 14th from right

14.2 Between Two People

Number of persons between A and B in a row:

• If A is at position m from one end and B at position n from same end (m < n):
• Persons between = n - m - 1

14.3 Extended Ranking Problems

When rank from each end is given for the same person:

• Check for consistency: rank from top + rank from bottom = Total + 1

When two people's ranks are given and they swap:

• Carefully distinguish between "rank from left/right" and "rank from top/bottom"
• Always state clearly what each rank refers to

14.4 Row/Column Arrangements

In a classroom with rows and columns:

• Position from front: row number
• Position from right: column number
• "In 3rd row from front and 4th from right" → (row 3, column 4)
• If class has R rows and C columns: position from back = R - (front row) + 1

Mathematical Operations

15.1 Concept

Standard mathematical symbols (+, -, ×, ÷) are replaced by other symbols. First decode the symbols, then apply.

Example:

• "P means ÷, Q means ×, R means +, S means -"
• Solve: 20 P 5 Q 4 R 10 S 6
• = 20 ÷ 5 × 4 + 10 - 6
• = 4 × 4 + 10 - 6
• = 16 + 10 - 6 = 20

15.2 Interchange of Signs

Given: "If + and - are interchanged and × and ÷ are interchanged, find value of..."

Replace each sign with its pair

• Solve using standard BODMAS

15.3 Balanced Equation

Find the operator that makes the equation true:

• 6 ? 4 = 10 → "+" works
• 5 ? 4 = 20 → "×" works