Understanding Number Analogy Reasoning

Number analogy questions test your ability to find a relationship between a given pair of numbers and then identify another pair that shares the same relationship. These questions are common in logical reasoning and quantitative aptitude sections of various exams.

Analyzing the Given Number-Pair: 40 : 19

The given number-pair is 40 : 19. We need to find the rule or relationship that connects the first number (40) to the second number (19).

Let's explore possible relationships:

• Is it addition/subtraction? $40 - x = 19 \implies x = 21$. The difference is 21.
• Is it multiplication/division? $40 / y = 19$ (not a whole number). $40 \times z = 19$ (not simple).
• Is it related to division by 2? $40 / 2 = 20$. The second number is 19, which is 1 less than 20.

This suggests a possible rule: The second number is obtained by dividing the first number by 2 and then subtracting 1.

Let's verify this rule with the given pair 40 : 19:

First number $= 40$
Applying the rule: $\frac{40}{2} - 1 = 20 - 1 = 19$
This matches the second number in the pair.

Applying the Rule to the Options

Now, let's apply this rule (divide the first number by 2, then subtract 1) to the first number in each of the given options and see which one results in the second number of that option.

• Option 1: 28 : 13
  First number $= 28$
  Applying the rule: $\frac{28}{2} - 1 = 14 - 1 = 13$
  This result (13) matches the second number in the pair 28 : 13.
• Option 2: 20 : 11
  First number $= 20$
  Applying the rule: $\frac{20}{2} - 1 = 10 - 1 = 9$
  This result (9) does not match the second number (11) in the pair 20 : 11.
• Option 3: 34 : 17
  First number $= 34$
  Applying the rule: $\frac{34}{2} - 1 = 17 - 1 = 16$
  This result (16) does not match the second number (17) in the pair 34 : 17.
• Option 4: 46 : 23
  First number $= 46$
  Applying the rule: $\frac{46}{2} - 1 = 23 - 1 = 22$
  This result (22) does not match the second number (23) in the pair 46 : 23.

Conclusion: Identifying the Matching Number-Pair

Based on the analysis, only Option 1 (28 : 13) follows the same relationship as the given number-pair 40 : 19, where the second number is obtained by dividing the first number by 2 and subtracting 1.

Revision Table: Number Analogy Reasoning Tips

Here are some tips for solving number analogy questions:

Additional Information: Common Number Relationship Types

Number analogies often involve various types of mathematical relationships. Understanding these can help you quickly identify the rule.

• Arithmetic Operations: Addition, subtraction, multiplication, division, or a sequence of these. (e.g., x : x+5, y : y*2)
• Squares and Cubes: The second number is the square or cube of the first, or related to it. (e.g., x : x², y : y³)
• Square Roots and Cube Roots: The second number is the root of the first, or related to it. (e.g., x : $\sqrt{x}$, y : $\sqrt[3]{y}$)
• Combinations: A mix of operations, like the one in this problem (division and subtraction).
• Digit-based Relationships: Operations on the digits of the first number to get the second number (sum of digits, product of digits, etc.).