Understanding Number Analogy Questions

Number analogy questions test your ability to find the relationship between a pair of numbers and apply that same relationship to another number. The relationship can involve mathematical operations, digit manipulation, positional changes, or other patterns.

Analyzing the Given Number Analogy: 9783 : 3879 :: 1958 : ?

We are given the pair 9783 and 3879, and we need to find the number that relates to 1958 in the same way. Let's look closely at the first pair of numbers.

• The first number is 9783. Its digits are 9, 7, 8, and 3.
• The second number is 3879. Its digits are 3, 8, 7, and 9.

We can see that the second number uses the exact same digits as the first number. This suggests a rearrangement or positional change of the digits.

Identifying the Relationship or Pattern

Let's examine the position of each digit in the first number (9783) and where it appears in the second number (3879).

Consider the digits from left to right (thousands, hundreds, tens, units).

The pattern observed is that the digit from the 4th position of the first number moves to the 1st position of the second number, the digit from the 3rd position moves to the 2nd position, the digit from the 2nd position moves to the 3rd position, and the digit from the 1st position moves to the 4th position.

We can represent this positional shift as: P1 P2 P3 P4 becomes P4 P3 P2 P1.

Applying the Pattern to the Third Number (1958)

Now, let's apply this same rule to the third number, 1958.

• The third number is 1958.
• Its digits are: P1=1, P2=9, P3=5, P4=8.

Applying the transformation P4 P3 P2 P1:

• The digit from the 4th position (8) moves to the 1st position.
• The digit from the 3rd position (5) moves to the 2nd position.
• The digit from the 2nd position (9) moves to the 3rd position.
• The digit from the 1st position (1) moves to the 4th position.

This results in the digits in the order 8 5 9 1.

The fourth number is 8591.

Checking the Options

Let's compare our result (8591) with the given options:

1. 9518
2. 9851
3. 8591
4. 5891

Our calculated number, 8591, matches Option 3.

Conclusion

The relationship between 9783 and 3879 is a specific rearrangement of their digits based on their original positions. Applying this same rearrangement rule (P1 P2 P3 P4 becomes P4 P3 P2 P1) to the number 1958 gives us 8591. This corresponds to Option 3.

Revision Table: Key Learnings

Additional Information: Types of Number Analogies

Number analogies can involve various relationships. Besides digit rearrangement, common types include:

• Mathematical Operations: Addition, subtraction, multiplication, division, squares, cubes, roots, etc., applied to the number itself or its digits.
• Digit Properties: Sum of digits, product of digits, even/odd digits, prime digits.
• Sequence Patterns: Applying a step-by-step rule to transform the first number into the second.
• Combinations: A mix of the above.

Practicing different types helps in quickly identifying the pattern during exams.