Understanding the Number Analogy Question

The question asks us to find the relationship between the first pair of numbers (3978 and 72) and then apply that same relationship to the third number (5172) to find the missing fourth number. This is a classic number analogy problem requiring logical reasoning to identify the pattern.

Identifying the Pattern: 3978 & 72

Let's analyze the first pair: 3978 and 72. We need to find a connection between the number 3978 and the number 72. Let's look at the digits of 3978: 3, 9, 7, and 8.

Let's try performing some operations on these digits or the number itself to see if we can arrive at 72.

Consider the sum of the digits of the first number, 3978:

\(3 + 9 + 7 + 8 = 27\)

Now, let's look at the result, 72. Can we derive 72 from 27? If we reverse the digits of the sum 27 (which are 2 and 7), we get 7 and 2, forming the number 72.

This seems like a potential pattern:

1. Calculate the sum of the digits of the first number.
2. Reverse the digits of the resulting sum to get the second number in the analogy.

Let's confirm if this rule holds for the first pair: The sum of digits of 3978 is 27. Reversing the digits of 27 (2 and 7) gives us 72. This matches the given relationship.

Applying the Pattern to the Second Pair: 5172 & ?

Now that we have identified a potential pattern, let's apply it to the third number, 5172, to find the missing number.

First, calculate the sum of the digits of 5172:

\(5 + 1 + 7 + 2 = 15\)

Next, according to the pattern, we need to reverse the digits of this sum (15). The digits of 15 are 1 and 5.

Reversing the digits 1 and 5 gives us 5 and 1.

This forms the number 51.

Therefore, the number related to 5172 in the same way that 72 is related to 3978 is 51.

Checking the Options

Our calculated result is 51. Let's compare this with the given options:

• Option 1: 98
• Option 2: 51
• Option 3: 27
• Option 4: 66

The calculated number 51 matches Option 2.

Detailed Steps

1. Examine the relationship between 3978 and 72.
2. Calculate the sum of the digits of 3978: \(3+9+7+8 = 27\).
3. Observe that reversing the digits of 27 results in 72.
4. Conclude that the pattern is: Sum of digits of the first number, then reverse the digits of the sum to get the second number.
5. Apply this pattern to the third number, 5172.
6. Calculate the sum of the digits of 5172: \(5+1+7+2 = 15\).
7. Reverse the digits of 15 (1 and 5) to get 51.
8. Identify 51 as the missing number in the analogy.

Conclusion

Following the pattern where the sum of the digits of the first number is calculated and its digits are reversed to get the second number, the number that completes the analogy 5172 ∶ ? is 51.

Revision Table: Number Analogy Analysis

Additional Information: Exploring Number Patterns

Solving number analogy problems often involves looking for patterns related to the digits themselves or simple arithmetic operations. Common patterns include:

• Sum or product of digits.
• Reversing the number or parts of the number.
• Sequential operations on digits from left to right or right to left.
• Relationships based on squares, cubes, prime numbers, etc.
• Combining different pairs or groups of digits through addition, subtraction, multiplication, or division.

Identifying the type of pattern used is key to solving such logical reasoning questions efficiently. Practicing with various examples helps improve pattern recognition skills.