What number should replace the question mark in the series: 1050, 420, 168, 67.2, ?

Introduction / Context:
This question checks understanding of number series based on repeated multiplication by a constant factor. Reasoning questions of this type are extremely common in aptitude tests because they require candidates to recognise patterns involving fractions and decimal multipliers, not just simple addition or subtraction. Here, we must decide which number should replace the question mark to continue the series logically.

Given Data / Assumptions:
- Given series: 1050, 420, 168, 67.2, ?- Exactly one value is missing, represented by a question mark.- All terms are real numbers and can include decimals.- We expect a single consistent rule operating between consecutive terms.

Concept / Approach:
The natural approach is to check the ratio between each pair of consecutive terms. If the ratios are approximately equal, the series is multiplicative. The presence of decimal values like 67.2 suggests a fractional multiplier such as 0.4 or 2.5. Once we discover the common ratio, we can apply it to the last known term to find the missing value.

Step-by-Step Solution:
- Compute the ratio from 1050 to 420: 420 / 1050 = 0.4.- Compute the ratio from 420 to 168: 168 / 420 = 0.4.- Compute the ratio from 168 to 67.2: 67.2 / 168 = 0.4.- The common ratio between all consecutive terms is therefore 0.4.- To obtain the missing term, multiply the last known term by the same factor: 67.2 * 0.4.- Calculation: 67.2 * 0.4 = 26.88.- Thus, the missing number that continues the series is 26.88.

Verification / Alternative check:
- We can rewrite the complete series using the discovered rule: 1050, 1050 * 0.4 = 420, 420 * 0.4 = 168, 168 * 0.4 = 67.2, and 67.2 * 0.4 = 26.88.- The factor 0.4 is equal to 2 / 5, so the series is equivalent to repeatedly taking two fifths of the previous term.- There is no inconsistency once we include 26.88 as the fifth term, confirming that it is the correct answer.

Why Other Options Are Wrong:
- 19.11, 14.25, 10.752 and 8.64 do not equal 67.2 multiplied by 0.4 and would break the constant-ratio pattern.- Using any of these values would make the series ratios unequal, which contradicts the clear multiplicative structure from the first three transitions.

Common Pitfalls:
- Some candidates look for differences instead of ratios and may attempt to treat this as an additive series, which quickly leads to confusion because the differences are not constant.- Rounding errors while computing decimal ratios can cause incorrect guesses when the exact factor 0.4 is not recognised.- Ignoring the clear pattern in the first three transitions and only attempting to fit the given options can also be misleading.

Final Answer:
The only value that maintains a constant multiplicative factor of 0.4 between all consecutive terms is 26.88, so 26.88 is the correct number to replace the question mark.