Position Arithmetic
Position Arithmetic problems involve performing arithmetic operations (addition, subtraction, multiplication, division) on the position numbers of letters. The result may be a new number or a transformed letter. These problems test arithmetic skills applied to alphabet positions.
What You'll Learn
Introduction to Position Arithmetic
Position Arithmetic problems involve performing arithmetic operations (addition, subtraction, multiplication, division) on the position numbers of letters. The result may be a new number or a transformed letter. These problems test arithmetic skills applied to alphabet positions.
Prerequisites
How to Solve Position Arithmetic Problems
Step 1: Convert each letter to its position number (A=1 to Z=26)
Step 2: Apply the specified arithmetic operation to each position
Step 3: For operations that produce numbers >26 or <1, apply modulo 26 (wrap-around)
Step 4: Convert resulting numbers back to letters
Step 5: For sum/product of positions in a word, calculate the total
Step 6: Verify the operation is consistent for all letters
Step 7: Present the coded word or number
Example Problem
Example 1: If each letter is coded as (position × 2), code 'BED'. Solution: Step 1: B=2, E=5, D=4 Step 2: B:2×2=4→D, E:5×2=10→J, D:4×2=8→H Step 3: Coded word = DJH Answer: DJH Example 2: If each letter is coded as (position - 3), code 'CAT'. Solution: C=3→0? 0 mod 26? Usually 0 maps to Z? Actually 3-3=0 → 26→Z, A=1-3=-2+26=24→X, T=20-3=17→Q → ZXQ Answer: ZXQ
Pro Tips & Tricks
- Multiplication by 2: A(1)→B(2), B(2)→D(4), C(3)→F(6), M(13)→Z(26), N(14)→B(2) after wrap
- Addition of constant: A(1)+3=D(4), B(2)+3=E(5)
- Subtraction of constant: A(1)-1=Z(26), B(2)-1=A(1)
- For position × 2, the result is always even (except wrap to odd)
- For position × 3, wrap occurs at 9 (I), 17 (Q), 26 (Z)
- The operations can be chained: ((pos + a) × b) mod 26
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Position Arithmetic. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Position Arithmetic is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Position Arithmetic?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: