Find the next number in the series: 5, 8, 16, 19, 57, 60, ....

Introduction / Context:
This number series question asks you to determine the next term by identifying the rule that transforms each number into the next. Many competitive exams use such patterns where operations alternate between addition and multiplication. Recognizing that structure quickly is the key to solving the problem efficiently.

Given Data / Assumptions:

• The sequence is: 5, 8, 16, 19, 57, 60, ?
• Exactly one next term is to be found.
• A single consistent rule, possibly alternating operations, generates the series.

Concept / Approach:
When the jumps between numbers vary widely, it often indicates alternating operations such as add then multiply, or multiply then add. Examining the differences and ratios between consecutive terms helps reveal this pattern. Here, the values sometimes increase slightly and sometimes jump sharply, which strongly suggests an add then multiply structure.

Step-by-Step Solution:
Step 1: Compare 5 and 8. We see 5 + 3 = 8. Step 2: Compare 8 and 16. We see 8 × 2 = 16. Step 3: Compare 16 and 19. We see 16 + 3 = 19. Step 4: Compare 19 and 57. We see 19 × 3 = 57. Step 5: Compare 57 and 60. We see 57 + 3 = 60. Step 6: The pattern is now clear: +3, ×2, +3, ×3, +3, ×4, and so on, with the multiplier increasing by 1 each time. Step 7: To obtain the missing term, follow the pattern after the last visible step. From 60, we must multiply by 4. Step 8: Compute 60 × 4 = 240.

Verification / Alternative check:
Write the operations explicitly under the series: 5 (+3) 8 (×2) 16 (+3) 19 (×3) 57 (+3) 60 (×4) 240. We see a stable structure: addition of 3 every second step, and multiplication by 2, then 3, then 4. This is a very standard pattern in reasoning questions, so the value 240 fits perfectly and there is no contradiction at any step.

Why Other Options Are Wrong:
Values such as 188, 256, and 180 do not satisfy a simple, consistent sequence of alternating operations starting from 5. If we plug in any of these alternatives and try to work backward, the multiply steps or add steps would become irregular or fractional, which is unlikely for a well constructed exam series. Only 240 preserves the neat +3, ×2, +3, ×3, +3, ×4 pattern.

Common Pitfalls:
Students sometimes look only at first differences, which here are 3, 8, 3, 38, 3, ... and appear confusing. The correct strategy is to also consider multiplication, especially when some jumps are very large compared to others. Another pitfall is forcing a complicated high level formula, while exam setters usually prefer very simple alternating patterns that can be spotted by careful inspection.

Final Answer:
Following the alternating pattern of adding 3 and multiplying by increasing integers, the next term in the series is 240.