Number series – alternating +1 and ×2 pattern: 2, 3, 6, 7, 14, 15, ?

Introduction / Context:
Alternating-operation series are a staple in reasoning tests. The sequence switches between two simple rules in turns, and identifying the alternation is the key to forecasting the next item.

Given Data / Assumptions:

• Series: 2, 3, 6, 7, 14, 15, ?
• Likely two-rule alternation due to the saw-tooth rise pattern.

Concept / Approach:
Check consecutive transitions to test a repeating pair of operations. Here, the transitions suggest adding 1 and then doubling, in strict alternation.

Step-by-Step Solution:
2 → 3: +13 → 6: ×26 → 7: +17 → 14: ×214 → 15: +1Therefore, the next step must be ×2: 15 × 2 = 30.

Verification / Alternative check:
Any proposal other than 30 would break the observed strict alternation of +1, ×2, +1, ×2, … across every step.

Why Other Options Are Wrong:
16/31/32: These correspond to +1 or ×2 applied in the wrong position (or an extra +1). Only 30 preserves the alternating structure.

Common Pitfalls:
Forgetting that the very last move was +1 (14 → 15), so the next must be ×2 rather than another +1.

Final Answer:
30