Understanding Number Analogy Questions

Number analogy questions test your ability to find the relationship between a given pair of numbers and apply that same relationship to find a matching pair from the options. These relationships can involve mathematical operations, digit manipulation, or position changes of digits.

Analyzing the Given Number Pair: 416 ∶ 614

Let's carefully examine the two numbers in the given pair: 416 and 614.

• The first number is 416. Its digits are 4, 1, and 6.
• The second number is 614. Its digits are 6, 1, and 4.

We observe that the two numbers use the exact same digits, but they are in a different order. Let's see how the positions of the digits have changed.

• In 416, the digits are in the order: First digit (4), Second digit (1), Third digit (6).
• In 614, the digits are in the order: First digit (6), Second digit (1), Third digit (4).

Comparing the positions:

• The original first digit (4) has moved to the third position in the second number.
• The original second digit (1) has stayed in the second position.
• The original third digit (6) has moved to the first position in the second number.

So, if we represent the first number as a three-digit number 'abc', where 'a' is the hundreds digit, 'b' is the tens digit, and 'c' is the units digit, the second number is formed by rearranging the digits to 'cba'. In this case, for 416 (a=4, b=1, c=6), the transformation results in 614 (c=6, b=1, a=4).

The identified pattern is swapping the first and third digits while keeping the middle digit unchanged.

Applying the Pattern to the Options

Now, we will apply this 'cba' pattern to the first number in each option pair to see which second number matches the one provided in the option.

Option 1: 384 ∶ 843

• First number: 384
• Digits: a=3, b=8, c=4
• Applying the pattern 'cba': The new number would be 483.
• The second number in the option is 843.
• Since 483 is not equal to 843, this option does not follow the same pattern.

Option 2: 286 ∶ 682

• First number: 286
• Digits: a=2, b=8, c=6
• Applying the pattern 'cba': The new number would be 682.
• The second number in the option is 682.
• Since 682 is equal to 682, this option follows the same pattern.

Option 3: 483 ∶ 843

• First number: 483
• Digits: a=4, b=8, c=3
• Applying the pattern 'cba': The new number would be 384.
• The second number in the option is 843.
• Since 384 is not equal to 843, this option does not follow the same pattern.

Option 4: 592 ∶ 925

• First number: 592
• Digits: a=5, b=9, c=2
• Applying the pattern 'cba': The new number would be 295.
• The second number in the option is 925.
• Since 295 is not equal to 925, this option does not follow the same pattern.

Based on our analysis, only Option 2, 286 ∶ 682, exhibits the same relationship as the given pair 416 ∶ 614, where the first and third digits are swapped.

Conclusion

The relationship between 416 and 614 is that the second number is formed by swapping the first and third digits of the first number. Option 2, 286 ∶ 682, follows this exact pattern because swapping the first (2) and third (6) digits of 286 results in 682.

Revision Table: Key Concepts in Number Analogy

Additional Information: Solving Analogy Questions

To effectively solve analogy questions, consider these strategies:

• Identify the Relationship: Carefully analyze the first pair to find the exact relationship. It could be arithmetic, positional, alphabetical (for letter analogies), or based on categories.
• Test Options: Apply the identified relationship to the first element of each option pair.
• Verify the Match: Check if the result of applying the relationship matches the second element of the option pair.
• Consider Multiple Relationships: If a simple relationship isn't obvious, look for more complex patterns involving digits or combined operations.
• Eliminate Options: Rule out options that clearly do not fit the pattern.

Practicing different types of analogy questions helps in quickly recognizing common patterns and developing problem-solving skills.