In the following number series, select the missing number that will correctly complete the pattern: 63, 56, 50, 43, 37, 30, ?

Introduction / Context:
This is a decreasing number series where the differences between consecutive terms alternate between two fixed values. The question evaluates your ability to observe repeating patterns in differences, which is a crucial skill for solving many verbal reasoning and quantitative aptitude problems efficiently.

Given Data / Assumptions:
Given series: 63, 56, 50, 43, 37, 30, ?The last term is missing after 30.We assume that the pattern in the differences continues consistently to the missing term.

Concept / Approach:
Instead of trying to guess the rule from the numbers themselves, we compute the stepwise differences. When these differences alternate between two specific numbers, we can extend that alternation to find the next difference and thus the missing term. This approach is systematic and less error-prone than intuitive guessing.

Step-by-Step Solution:
Step 1: Compute 63 - 56 = 7.Step 2: Compute 56 - 50 = 6.Step 3: Compute 50 - 43 = 7.Step 4: Compute 43 - 37 = 6.Step 5: Compute 37 - 30 = 7.Step 6: The pattern is an alternating sequence of -7, -6, -7, -6, -7, so the next step should be -6.Step 7: Let the missing term be x. Then x = 30 - 6 = 24.

Verification / Alternative check:
Insert the candidate value into the series: 63, 56, 50, 43, 37, 30, 24. Now compute all differences: 63 - 56 = 7, 56 - 50 = 6, 50 - 43 = 7, 43 - 37 = 6, 37 - 30 = 7, 30 - 24 = 6. The alternating pattern of 7, 6, 7, 6, 7, 6 is perfectly maintained, confirming that 24 is the correct missing number.

Why Other Options Are Wrong:
Option 23 would give a final difference of 7 from 30 to 23, resulting in two consecutive differences of 7 at the end, which breaks the alternation.Option 29 would produce a difference of 1 from 30 to 29, which does not match either 7 or 6 and disrupts the pattern entirely.Option 21 would yield a difference of 9, which is again incompatible with the alternating differences of 7 and 6 observed earlier.

Common Pitfalls:
Some learners focus only on the first few terms and overlook the full sequence of differences, which can lead to incorrect patterns. Others may compute differences incorrectly or assume that the differences must steadily increase or decrease rather than alternate. Careful and complete calculation of each step is the best way to avoid these mistakes.

Final Answer:
The missing number that fits the alternating difference pattern is 24.