Analyzing Number Relations in Sets

The question asks us to find a set of numbers among the options that shares the same relationship between its elements as observed in the two given sets: (4, 13, 5) and (3, 12, 6). We need to identify the pattern or rule connecting the three numbers within each set, treating each number as a whole without breaking it into digits.

Identifying the Pattern in the Given Sets

Let's examine the numbers in the first set, (4, 13, 5). Let the numbers be A, B, and C respectively. So, A=4, B=13, and C=5.

We need to find a relationship between 4, 13, and 5. Let's try common arithmetic operations:

• Sum of A and C: $4 + 5 = 9$. This is not 13.
• Product of A and C: $4 \times 5 = 20$. This is not 13.
• Difference between B and A: $13 - 4 = 9$.
• Difference between B and C: $13 - 5 = 8$.

Let's try combining operations involving all three numbers. Consider if the middle number (B) is a result of an operation on the first (A) and third (C) numbers. We found that $4+5=9$. What if we involve A again? $9 + 4 = 13$. This looks promising. So, the relationship could be B = (A + C) + A, which simplifies to B = 2A + C.

Let's verify this rule with the second given set: (3, 12, 6). Here, A=3, B=12, and C=6.

Using the proposed rule $B = 2A + C$:

Substitute the values: $2 \times 3 + 6 = 6 + 6 = 12$.

This result matches the middle number (B = 12) in the second set. The rule $B = 2A + C$ holds for both given sets.

So, the established relationship between the three numbers (A, B, C) in the given sets is that the middle number (B) is equal to two times the first number (A) plus the third number (C), expressed as $B = 2A + C$.

Testing the Rule on the Options

Now, we will apply the rule $B = 2A + C$ to each of the given options to find the set that follows the same pattern.

Identifying the Correct Set

Based on the testing above, the set (5, 17, 7) is the only option where the numbers follow the rule $B = 2A + C$. For this set, A=5, B=17, and C=7. Calculating $2A + C$: $2 \times 5 + 7 = 10 + 7 = 17$, which is equal to B.

Therefore, the set (5, 17, 7) is related in the same way as the given sets.

Revision Table: Number Relation Summary

Additional Information: Solving Number Analogy Problems

Number analogy problems are common in logical reasoning and quantitative aptitude tests. They require you to identify the underlying mathematical relationship or pattern connecting the numbers in a given set or pair of sets and apply that same rule to find a missing number or a matching set.

Key strategies for solving these problems:

• Examine the relationship between the first and second numbers, second and third, or first and third.
• Look for common arithmetic operations: addition, subtraction, multiplication, division.
• Consider squares, cubes, square roots, or cube roots.
• Check for patterns involving multiples or factors.
• Sometimes, the relationship might involve a combination of operations, as seen in this problem ($B = 2A + C$).
• Always test the identified rule on all given examples (if more than one set is provided) to ensure consistency.
• Apply the confirmed rule systematically to each option.
• Remember the constraint about using whole numbers and not breaking down digits unless explicitly allowed.

Practice with various types of number analogies helps improve pattern recognition skills.