Understanding Number Analogy and Finding the Pattern

This question is a number analogy problem where we need to find the relationship between the first pair of numbers (154 and 10) and apply the same relationship to the third number (261) to find the missing fourth number.

Let's analyze the relationship between the numbers 154 and 10.

Analyzing the Relationship between 154 and 10

We need to discover a mathematical operation or pattern that transforms 154 into 10. Let's try some common approaches for number analogies:

• Checking for simple arithmetic operations (addition, subtraction, multiplication, division).
• Looking for patterns based on the digits of the number.

Consider the digits of 154: 1, 5, and 4.

• Sum of the digits: \(1 + 5 + 4 = 10\).

This result matches the second number, 10. This suggests that the relationship might be that the second number is the sum of the digits of the first number.

Applying the Pattern to 261

Now, let's apply the discovered pattern to the third number, 261. The pattern is to sum the digits of the number.

The digits of 261 are 2, 6, and 1.

Sum of the digits: \(2 + 6 + 1 = 9\).

So, the missing number in the analogy 261 : ? should be 9.

Verification with Options

Let's check the given options:

1. 10
2. 9
3. 7
4. 8

Our calculated value, 9, is present in the options.

Step-by-Step Solution for Number Analogy

Here's a breakdown of the steps taken:

1. Identify the first pair of numbers in the analogy: 154 : 10.
2. Analyze the relationship between 154 and 10. We found that the sum of the digits of 154 (\(1+5+4\)) equals 10.
3. Identify the third number in the analogy: 261.
4. Apply the same relationship (sum of digits) to the third number. Calculate the sum of the digits of 261 (\(2+6+1\)).
5. The result is 9.
6. Match the result with the given options to find the correct answer.

The relationship established is:

\(\text{First Number} \rightarrow \text{Sum of its digits} \rightarrow \text{Second Number}\)

Applying this:

• \(154 \rightarrow 1 + 5 + 4 = 10\) (Correct for the first pair)
• \(261 \rightarrow 2 + 6 + 1 = 9\) (Applying to the third number)

Thus, the missing number is 9.

Revision Table: Number Analogy Concepts

Additional Information on Quantitative Reasoning

Number analogy questions are a common type of quantitative reasoning or logical reasoning problem. They test your ability to find patterns and relationships between numbers based on various mathematical operations, digit manipulations, or sequences.

Common patterns in number analogies include:

• Arithmetic operations (addition, subtraction, multiplication, division).
• Squaring or cubing numbers.
• Relationships based on digits (sum, product, difference, arrangement).
• Prime numbers, composite numbers, odd/even numbers.
• Sequential patterns.

Practicing different types of number analogy problems helps improve pattern recognition skills, which are useful in various aptitude tests.