Finding the Number Relationship in Sets

The problem asks us to identify the relationship between the numbers in the given sets and find an option that shares the same relationship. We are given two sets: (24, 12, 4) and (35, 5, 14). We must perform operations on the whole numbers themselves, not their individual digits.

Analyzing the Given Number Sets

Let's examine the first set: (24, 12, 4).

• We can see that 24 is twice 12 ($24 = 2 \times 12$).
• We can also see that 12 is three times 4 ($12 = 3 \times 4$).

Now let's examine the second set: (35, 5, 14).

• Here, 35 is seven times 5 ($35 = 7 \times 5$).
• 5 is not a simple multiple of 14, nor is 14 a simple multiple of 5.

The simple multiplier relationship between the first two numbers and the second and third numbers differs between the sets (2 vs 7, and 3 vs non-integer). We need to find a relationship that holds true for both sets.

Identifying the Consistent Relationship

Let's look for a connection involving all three numbers (First, Second, Third). Let the numbers in a set be A, B, and C.

Consider the first set (24, 12, 4). Let A=24, B=12, C=4.

• What if we divide the first number by the second number? $\frac{A}{B} = \frac{24}{12} = 2$.
• How does this relate to the third number, C=4? We can multiply this result by 2: $2 \times 2 = 4$. This matches C.

Let's test this pattern on the second set (35, 5, 14). Let A=35, B=5, C=14.

• Divide the first number by the second number: $\frac{A}{B} = \frac{35}{5} = 7$.
• How does this relate to the third number, C=14? We can multiply this result by 2: $7 \times 2 = 14$. This also matches C.

The relationship that holds for both sets is: The third number (C) is obtained by dividing the first number (A) by the second number (B) and then multiplying the result by 2.

Mathematically, the relationship is expressed as:

$\frac{\text{First Number}}{\text{Second Number}} \times 2 = \text{Third Number}$

Or, using A, B, and C: $\frac{A}{B} \times 2 = C$. This can also be written as $A \times 2 = B \times C$ or $2A = BC$.

Testing the Options Against the Relationship

We will now test each given option using the identified relationship $\frac{A}{B} \times 2 = C$.

Based on our testing, only Option 4 (36, 4, 18) satisfies the established relationship where the third number is equal to (the first number divided by the second number) multiplied by 2.

Conclusion

The set of numbers (36, 4, 18) shares the same relationship as the numbers in the given sets (24, 12, 4) and (35, 5, 14). The relationship is $\frac{A}{B} \times 2 = C$.

Revision Table: Checking the Number Relationship

This table summarizes the steps to verify the number relationship in a set (A, B, C).

Additional Information: Number Analogy and Reasoning

Number analogy problems, like finding the relationship in number sets, are a common type of question in logical and quantitative reasoning. They require identifying a pattern or rule that connects the numbers in a given set and then applying that rule to find a similar set from the options. The key is to look for consistent mathematical operations (addition, subtraction, multiplication, division, powers, roots, etc.) or relationships between the numbers.

Sometimes, the relationship might involve simple arithmetic, as in this case, while other times it might involve more complex operations or a combination of operations. It's important to systematically test potential relationships based on how the numbers in the initial sets are related.

The constraint about not breaking down numbers into constituent digits is crucial. For instance, if the number is 13, you can use 13 in operations like $13 \times 2$, $13+5$, etc., but you cannot separate 1 and 3 to perform operations like $1+3=4$ or $1 \times 3=3$ on the digits themselves to find the relationship between the whole numbers in the set.