Understanding Number Analogy and Reasoning

Number analogy questions test your ability to find a logical relationship between a pair of numbers and apply that same relationship to find a missing number in another pair. The key is to identify the underlying pattern connecting the numbers.

Analyzing the Given Number Analogy Pairs

We are given two completed pairs and one incomplete pair:

• 56 : 11
• 34 : 7
• ? : 13

We need to find the relationship between the numbers in the first two pairs and apply it to the third pair to find the missing number.

Pattern Identification in the First Pair (56 : 11)

Let's examine the relationship between 56 and 11. We can look at basic arithmetic operations, digit manipulation, etc.

Consider the digits of the first number, 56. The digits are 5 and 6.

Let's try adding the digits:

\(5 + 6 = 11\)

This matches the second number in the pair (11). This suggests a possible pattern: the second number is the sum of the digits of the first number.

Verifying the Pattern with the Second Pair (34 : 7)

Let's test if this pattern holds for the second pair, 34 : 7.

Consider the digits of the first number, 34. The digits are 3 and 4.

Let's add the digits:

\(3 + 4 = 7\)

This also matches the second number in this pair (7). The pattern holds true for both given pairs.

Applying the Pattern to Find the Missing Number

The established pattern is: The second number is the sum of the digits of the first number.

We need to apply this pattern to the third pair: ? : 13.

Here, the second number is 13. Following the pattern in reverse, the missing first number should be a number whose digits sum up to 13.

Let the missing number be X. We are looking for X such that the sum of its digits equals 13.

Checking the Options

Let's examine the given options and check which one fits this criterion:

From the analysis, only the number 76 has digits (7 and 6) that sum up to 13.

Conclusion

The pattern observed is that the second number is the sum of the digits of the first number. Applying this pattern to the pair ? : 13, we find that the missing number must have digits that sum to 13. Among the given options, only 76 satisfies this condition (7 + 6 = 13).

Therefore, the missing number in the analogy ? : 13 is 76.

Revision Table: Key Concepts in Number Analogies

Additional Information on Number Reasoning

Number reasoning questions are a common part of many competitive exams. They assess your ability to think logically and identify numerical patterns quickly. Common patterns include:

• Adding, subtracting, multiplying, or dividing by a constant number.
• Adding, subtracting, multiplying, or dividing by a variable number (e.g., increasing difference).
• Squares, cubes, or other powers of numbers.
• Operations on the digits of the numbers (sum, product, difference).
• Relationships between numbers based on prime numbers, composite numbers, odd/even numbers.
• Combinations of these patterns.

Practicing a variety of number analogy and series problems helps in recognizing these patterns faster during an exam.