Number Set Relationship Analysis

The task is to find a consistent mathematical relationship between the numbers in the first two sets, (10, 5, 60) and (9, 6, 64), and then identify which of the given options exhibits the same relationship. Operations must be applied to the whole numbers, not their digits.

Analyzing Given Sets to Find the Pattern

Let's represent the numbers in each set as (A, B, C).

Set 1: (10, 5, 60)

Here, A = 10, B = 5, C = 60.

• First, calculate the product of A and B: \(A \times B = 10 \times 5 = 50\).
• Now, compare this product to C: \(C = 60\).
• The difference is \(C - (A \times B) = 60 - 50 = 10\).
• We notice that this difference (10) is equal to the first number, A. This suggests a potential pattern: \(A \times B + A = C\).
• Let's verify: \(10 \times 5 + 10 = 50 + 10 = 60\). This matches C for Set 1.

Set 2: (9, 6, 64)

Here, A = 9, B = 6, C = 64.

Let's test the potential pattern \(A \times B + A = C\) identified from Set 1.

• Calculate the product: \(A \times B = 9 \times 6 = 54\).
• Apply the pattern: \(54 + A = 54 + 9 = 63\).
• This result (63) does not match C (64). Therefore, the pattern \(A \times B + A = C\) is incorrect.

Revising the Pattern Search

Let's re-examine the relationship between the product \(A \times B\) and C across both sets.

• For Set 1 (10, 5, 60): \(A \times B = 50\). \(C = 60\). Difference: \(60 - 50 = 10\).
• For Set 2 (9, 6, 64): \(A \times B = 54\). \(C = 64\). Difference: \(64 - 54 = 10\).

In both cases, the difference between C and the product \(A \times B\) is consistently 10.

This reveals the correct pattern: \(A \times B + 10 = C\).

Verifying the Pattern with the Options

We now apply the pattern \(A \times B + 10 = C\) to each option to find the matching set.

Option 1: (17, 5, 85)

• A = 17, B = 5, C = 85.
• Test: \((17 \times 5) + 10 = 85 + 10 = 95\).
• Result: \(95 \neq 85\). This option does not match.

Option 2: (11, 6, 86)

• A = 11, B = 6, C = 86.
• Test: \((11 \times 6) + 10 = 66 + 10 = 76\).
• Result: \(76 \neq 86\). This option does not match.

Option 3: (12, 4, 58)

• A = 12, B = 4, C = 58.
• Test: \((12 \times 4) + 10 = 48 + 10 = 58\).
• Result: \(58 = 58\). This option matches the pattern.

Option 4: (8, 9, 62)

• A = 8, B = 9, C = 62.
• Test: \((8 \times 9) + 10 = 72 + 10 = 82\).
• Result: \(82 \neq 62\). This option does not match.

Conclusion

The set (12, 4, 58) adheres to the established relationship where the product of the first two numbers plus 10 equals the third number (\(A \times B + 10 = C\)).