Introduction
Numerical or Arithmetic Analogies test your ability to recognize mathematical relationships between numbers. These questions check how well you can identify patterns such as addition, multiplication, squares, cubes, or ratios. It is one of the most common reasoning patterns in competitive exams.
Pattern: Numerical / Arithmetic Analogy
Pattern
The key idea is to identify the mathematical operation or relation connecting the first pair of numbers and apply the same to find the missing number in the second pair.
Step-by-Step Example
Question
2 : 8 :: 3 : ______
(A) 9 (B) 12 (C) 15 (D) 27
Solution
-
Step 1: Identify the relationship between the first pair.
2 is related to 8 through a cube: 2³ = 8. -
Step 2: Apply the same relationship to the second pair.
3³ = 27. -
Final Answer:
27 → Option D -
Quick Check:
2 : 8 (cube relation) → 3 : 27 (same cube relation) ✅
Quick Variations
1. Simple arithmetic (addition, subtraction, multiplication, division).
2. Power or root relationships (square, cube, square root).
3. Combined operations (e.g., multiply then add).
4. Ratio or proportion-based patterns (e.g., 2 : 4 :: 3 : 6).
5. Digit-based operations (sum, difference, reversal).
Trick to Always Use
- Step 1 → Check simple operations first: +, -, ×, ÷.
- Step 2 → If not direct, test for squares, cubes, or multiples.
- Step 3 → Ensure the same rule fits both pairs exactly before answering.
Summary
Summary
- Look for clear arithmetic or geometric patterns connecting the numbers.
- Apply the same mathematical operation consistently to the second pair.
- Test cube/square relationships if simple operations don’t work.
- Double-check that the rule applies in both directions before finalizing your answer.
Example to remember:
2 : 8 :: 3 : 27 (Each number is cubed.)
Hint: Check for square or cube relations first when numbers are small and perfect powers.
Common Mistakes: Choosing 20 by multiplying instead of squaring.