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Digit Sum Analogy

Digit Sum Analogy problems involve number pairs where the second number is the sum of the digits of the first number. For example, in the pair 45:9 (4+5=9). You may also encounter digital root (repeated sum until single digit) or sum of digits with additional operations. These problems test digit manipulation skills.

10Worksheets
200+Practice Questions
IntermediateDifficulty
2-3 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Digit Sum Analogy

Digit Sum Analogy problems involve number pairs where the second number is the sum of the digits of the first number. For example, in the pair 45:9 (4+5=9). You may also encounter digital root (repeated sum until single digit) or sum of digits with additional operations. These problems test digit manipulation skills.

Prerequisites

Digit sum calculation Understanding of digital root Basic addition Number digit extraction
Why This Matters: Digit Sum Analogy problems appear in 1-2 questions in SSC CGL and Banking PO exams. They test digit manipulation and mental math skills.

How to Solve Digit Sum Analogy Problems

1

Step 1: Identify the two numbers in the given analogy pair (A:B)

2

Step 2: Calculate the sum of digits of A: S = sum of digits of A

3

Step 3: Check if B equals S (or S with additional operation)

4

Step 4: For digital root, repeatedly sum digits until single digit

5

Step 5: Apply the same operation to the second pair's first number

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Step 6: Verify the pattern with all given examples

7

Step 7: Present the answer

Pro Strategy: Always calculate the digit sum of the first number. For digital root, continue summing until a single digit. Check if the result matches the second number.

Example Problem

Example: 456 : 15 :: 789 : ? Solution: Step 1: First pair: 456 and 15 Step 2: Sum of digits of 456 = 4+5+6 = 15 Step 3: Relationship: Second number = sum of digits of first Step 4: Apply to 789: 7+8+9 = 24 Answer: 24

Pro Tips & Tricks

  • Digit sum = sum of all digits in the number
  • Digital root = digit sum reduced to single digit (e.g., 456 → 4+5+6=15 → 1+5=6)
  • Digital root is also called the repeated digit sum
  • For numbers with zeros, digit sum unaffected (0 adds nothing)
  • The digit sum of a number is congruent to the number modulo 9
  • Watch for patterns where digit sum is then multiplied or added to a constant

Shortcut Methods to Solve Faster

Digit sum = sum(int(d) for d in str(A))
Digital root = digit sum mod 9 (0 becomes 9 if number > 0)
For large numbers, add digits in groups for faster calculation
If B = digit sum of A, then answer = digit sum of C

Common Mistakes to Avoid

Forgetting to sum all digits (missing zeros is okay)
Using digital root when plain digit sum is needed
Not handling multi-digit sums correctly
Confusing digit sum with product of digits

Exam Importance

Digit Sum Analogy is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
1-2 questions
BANKING PO
1-2 questions
RAILWAYS RRB
1-2 questions
CAT
0-1 questions
INSURANCE
1-2 questions

Ready to Master Digit Sum Analogy?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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