Solving Number Analogy Questions

This question asks us to find a missing number in a sequence based on the relationship between given pairs of numbers. We are given three pairs: 5 ∶ 31, 7 ∶ ?, and 9 ∶ 87. The relationship between the first two numbers should be the same as the relationship between the next two numbers and the last two numbers.

Analyzing the Relationship between Numbers

Let's look at the relationship in the known pairs:

• Pair 1: 5 and 31
• Pair 3: 9 and 87

We need to find a pattern or rule that connects the first number to the second number in these pairs.

Identifying the Pattern

Let the first number in a pair be \(n\). We are looking for a relationship \(n \rightarrow \text{related number}\).

Consider Pair 1: \(n=5\). The related number is 31. Possible relationships could involve squaring, multiplication, addition, or a combination.

• If we square the first number: \(5^2 = 25\). To get 31, we need to add \(31 - 25 = 6\). So, the rule might be \(n^2 + 6\).

Let's test this potential rule with Pair 3: \(n=9\). The related number is 87. Using the proposed rule \(n^2 + 6\):

• Calculate \(9^2\): \(9 \times 9 = 81\).
• Add 6: \(81 + 6 = 87\).

This matches the second number in Pair 3 (87). The rule \(n^2 + 6\) seems consistent for both known pairs.

Applying the Pattern to Find the Missing Number

Now we apply the identified rule \(n^2 + 6\) to the third pair, 7 ∶ ?. Here, the first number is \(n=7\).

• Calculate \(7^2\): \(7 \times 7 = 49\).
• Add 6: \(49 + 6 = 55\).

So, the missing number is 55.

Verifying the Solution with Options

The calculated missing number is 55. Let's check the given options:

Our calculated value, 55, matches Option 3.

Conclusion: The Missing Number

The relationship is defined by taking the first number (\(n\)), squaring it, and adding 6 (\(n^2 + 6\)). Applying this to the number 7 gives \(7^2 + 6 = 49 + 6 = 55\).

Revision Table: Number Analogy Pattern

Additional Information: Solving Analogy Questions

Number analogy questions test your ability to find patterns and relationships between numbers. Common patterns include:

• Arithmetic operations (addition, subtraction, multiplication, division)
• Squaring or cubing numbers
• Prime numbers
• Composite numbers
• Squares or cubes of numbers plus/minus a constant
• Multiplying by a constant and adding/subtracting
• Patterns based on digits of the number

To solve these, look for simple relationships first and then move to more complex ones. Testing the potential pattern with all given pairs is crucial to ensure consistency.