Solving Number Analogy Reasoning Questions

This question is a type of number analogy where we need to find the relationship between the numbers in the given pairs. The relationship found in the first pair (4284 : 18) and the third pair (1482 : 15) should apply to the second pair (? : 16) to find the missing number.

Identifying the Number Analogy Pattern

Let's examine the first pair: 4284 and 18.

We need to find a connection between 4284 and 18. Let's try performing operations on the digits of 4284:

• Adding the digits: \(4 + 2 + 8 + 4 = 18\)

This calculation gives us 18, which is the second number in the first pair. This looks like a potential pattern: the second number is the sum of the digits of the first number.

Verifying the Pattern with the Third Pair

Now, let's check if this pattern holds true for the third pair: 1482 and 15.

Let's add the digits of 1482:

• Adding the digits: \(1 + 4 + 8 + 2 = 15\)

This calculation gives us 15, which is the second number in the third pair. The pattern (sum of digits) is consistent across both given pairs.

Applying the Pattern to Find the Missing Number

The pattern is: Second Number = Sum of Digits of the First Number.

In the second pair, we have ? : 16. This means the sum of the digits of the missing number (?) must be 16.

We will now check the sum of digits for each of the given options to find the number whose digits add up to 16.

The number from the options whose digits sum up to 16 is 3256.

Conclusion

Based on the identified pattern, the missing number in the analogy ? : 16 is 3256 because the sum of its digits \(3 + 2 + 5 + 6\) equals 16.

The completed analogy is: 4284 : 18 :: 3256 : 16 :: 1482 : 15.

Revision Table: Key Concepts in Number Analogy

Additional Information: Types of Number Patterns in Reasoning

Number analogy and reasoning problems often involve various patterns. Recognizing common types can help solve problems faster. Some common patterns include:

• Arithmetic Operations: Adding, subtracting, multiplying, or dividing the numbers or their digits.
• Squaring or Cubing: Relationship involving squares or cubes of numbers or digits.
• Digit Manipulation: Sum, product, difference, or rearrangement of digits within a number.
• Prime Numbers: Patterns involving prime numbers.
• Sequences: Numbers following a specific mathematical sequence (e.g., arithmetic progression, geometric progression).
• Combinations: A combination of two or more of the above patterns.

Always look for simple patterns first, like sum or product of digits, before considering more complex relationships.