Identifying the Number Series Pattern

This question requires identifying a consistent set of mathematical operations applied across two given number sequences. The goal is to find the option that uses the same operations.

Analyzing Number Set Patterns

Let's break down the operations in the provided sets:

Set 1: 7 - 21 - 31 - 62

• From 7 to 21: The operation is multiplication. Calculation: $7 \times 3 = 21$.
• From 21 to 31: The operation is addition. Calculation: $21 + 10 = 31$.
• From 31 to 62: The operation is multiplication. Calculation: $31 \times 2 = 62$.

Set 2: 9 - 27 - 37 - 74

• From 9 to 27: The operation is multiplication. Calculation: $9 \times 3 = 27$.
• From 27 to 37: The operation is addition. Calculation: $27 + 10 = 37$.
• From 37 to 74: The operation is multiplication. Calculation: $37 \times 2 = 74$.

Determining the Consistent Operations

Both sets demonstrate a clear pattern comprising three sequential operations:

1. Multiply the number by 3.
2. Add 10 to the result.
3. Multiply the result by 2.

Checking Options Against the Pattern

We will now apply this pattern (x3, +10, x2) to each option:

Option 1: 11-33-43-86

• Step 1: $11 \times 3 = 33$. (Correct)
• Step 2: $33 + 10 = 43$. (Correct)
• Step 3: $43 \times 2 = 86$. (Correct)

This sequence perfectly matches the identified operations.

Checking Other Options

• Option 2 (12-36-46-82): $12 \times 3 = 36$; $36 + 10 = 46$; $46 \times 2 = 92$. The last number (92) does not match 82.
• Option 3 (8-32-42-84): $8 \times 3 = 24$. The second number (24) does not match 32.
• Option 4 (6-18-28-76): $6 \times 3 = 18$; $18 + 10 = 28$; $28 \times 2 = 56$. The last number (56) does not match 76.

Therefore, Option 1 is the only sequence that follows the established mathematical operations.