Solving Number Set Relationship Problems

This question asks us to identify the logical relationship connecting the numbers within the given sets and then find an option set that follows the exact same rule. We are provided with two example sets: (6, 14, 40) and (10, 14, 48).

The key rule is that operations must be performed on the whole numbers themselves, not their individual digits.

Analyzing the Given Number Sets

Let's examine the first set: (6, 14, 40).

Let the numbers be represented as a, b, and c, where a = 6, b = 14, and c = 40. We need to find a relationship between a, b, and c.

Let's try common mathematical operations:

• Adding the first two numbers: $6 + 14 = 20$. How is 20 related to 40? $20 \times 2 = 40$.
• This suggests a possible rule: $(a + b) \times 2 = c$. Let's test this rule.
• For $(6, 14, 40)$: $(6 + 14) \times 2 = 20 \times 2 = 40$. This matches the third number, 40.

Now, let's test this potential rule on the second given set: (10, 14, 48).

Here, a = 10, b = 14, and c = 48.

• Using the rule $(a + b) \times 2 = c$: $(10 + 14) \times 2 = 24 \times 2 = 48$. This also matches the third number, 48.

Since the rule $(a + b) \times 2 = c$ works for both the given sets, it is highly likely to be the correct relationship.

Testing the Options

We will now apply the rule $(a + b) \times 2 = c$ to each of the provided options to see which one follows the same pattern.

Option 1: (11, 5, 87)

Here, a = 11, b = 5, c = 87.

Applying the rule: $(11 + 5) \times 2 = 16 \times 2 = 32$.

Since $32 \neq 87$, this option does not follow the rule.

Option 2: (5, 9, 28)

Here, a = 5, b = 9, c = 28.

Applying the rule: $(5 + 9) \times 2 = 14 \times 2 = 28$.

Since $28 = 28$, this option follows the rule.

Option 3: (5, 6, 45)

Here, a = 5, b = 6, c = 45.

Applying the rule: $(5 + 6) \times 2 = 11 \times 2 = 22$.

Since $22 \neq 45$, this option does not follow the rule.

Option 4: (10, 5, 91)

Here, a = 10, b = 5, c = 91.

Applying the rule: $(10 + 5) \times 2 = 15 \times 2 = 30$.

Since $30 \neq 91$, this option does not follow the rule.

Conclusion

Based on our analysis, only option (5, 9, 28) follows the same relationship $(a + b) \times 2 = c$ as the given sets (6, 14, 40) and (10, 14, 48).

Revision Table: Relationship Verification

Additional Information on Number Analogy

Number analogy questions are a common type in reasoning tests. They assess your ability to identify patterns and relationships between numbers in a set. The relationships can involve various arithmetic operations, squares, cubes, multiples, or combinations of these. Here are some strategies to find the relationship:

• Look for basic arithmetic operations: addition, subtraction, multiplication, division between the numbers.
• Check for relationships involving squares or cubes of the numbers.
• Consider relationships between the first and third numbers based on the second, or vice versa.
• Sometimes, the relationship involves the sum or difference of the first two numbers predicting the third (as seen in this problem).
• Always test your hypothesized rule on all the given example sets before applying it to the options.
• Remember the constraint: operations on whole numbers only, no breaking down digits.

Practicing different types of number analogy problems helps in quickly identifying common patterns and relationships.