Solving Number Analogy Problems

Number analogy questions require you to find the relationship between the numbers in a given set and then identify an option set that shares the same relationship. Let's break down how to solve this specific problem.

Analyzing the Given Number Set (131, 142, 153)

First, we need to carefully examine the relationship between the numbers in the provided set: (131, 142, 153).

• Look at the difference between the first and second number.
• Look at the difference between the second and third number.

Let's calculate these differences:

• Difference between 142 and 131: $142 - 131 = 11$
• Difference between 153 and 142: $153 - 142 = 11$

The pattern in the given set is that each subsequent number is obtained by adding 11 to the previous number. This is an arithmetic progression with a common difference of 11.

Checking the Options for the Same Relationship

Now, we will check each option set to see which one follows the exact same rule: the difference between consecutive numbers must be 11.

Option 1: (161, 172, 195)

• Difference between 172 and 161: $172 - 161 = 11$
• Difference between 195 and 172: $195 - 172 = 23$

The differences are 11 and 23. This does not match the pattern of adding 11 consistently.

Option 2: (119, 130, 141)

• Difference between 130 and 119: $130 - 119 = 11$
• Difference between 141 and 130: $141 - 130 = 11$

The differences are 11 and 11. This exactly matches the pattern found in the given set (131, 142, 153).

Option 3: (149, 160, 193)

• Difference between 160 and 149: $160 - 149 = 11$
• Difference between 193 and 160: $193 - 160 = 33$

The differences are 11 and 33. This does not match the pattern of adding 11 consistently.

Option 4: (127, 149, 160)

• Difference between 149 and 127: $149 - 127 = 22$
• Difference between 160 and 149: $160 - 149 = 11$

The differences are 22 and 11. This does not match the pattern of adding 11 consistently.

Conclusion

Only Option 2, the set (119, 130, 141), shows the same relationship as the given set (131, 142, 153), which is a common difference of 11 between consecutive numbers.

Revision Table: Key Concepts

Additional Information: Types of Number Relationships

Number analogy problems can involve various types of relationships beyond simple addition or subtraction. Understanding these can help solve different problems:

• Arithmetic Operations: Addition, subtraction, multiplication, division.
• Differences: Constant difference, difference increasing/decreasing by a constant, differences forming another pattern.
• Squares and Cubes: Numbers being squares or cubes, or related by adding/subtracting squares/cubes.
• Prime Numbers: The numbers being prime or related to prime numbers.
• Digit Operations: Sum of digits, product of digits, reversing digits.
• Combinations of Operations: A mix of the above.

Practicing identifying these patterns is key to mastering number analogy and number series questions.