Find the wrong number in the following series: 1500, 1475, 1448, 1419, 1389, 1355, 1320

Introduction / Context:
This verbal reasoning question tests the candidate ability to analyse a decreasing number series and identify the single term that breaks an otherwise smooth numerical pattern. Such problems are very common in competitive exams because they check both observation and basic arithmetic skills together. Here, we are given a descending series starting from 1500, and we must decide which one of the numbers does not fit the rule that is followed by the remaining terms.

Given Data / Assumptions:
- Given series: 1500, 1475, 1448, 1419, 1389, 1355, 1320.- Exactly one term is incorrect, while the other terms follow a consistent pattern.- The pattern is expected to involve regular subtraction using a predictable sequence of numbers.

Concept / Approach:
The most natural approach in a decreasing series is to look at the differences between consecutive terms. If almost all differences follow a simple pattern (for example, odd numbers in sequence), then any term that does not respect this rule can be marked as the wrong number. We will compute the successive differences and attempt to see whether they follow a sequence of consecutive odd numbers or some other regular structure.

Step-by-Step Solution:
- Difference between 1500 and 1475: 1500 - 1475 = 25.- Difference between 1475 and 1448: 1475 - 1448 = 27.- Difference between 1448 and 1419: 1448 - 1419 = 29.- Difference between 1419 and 1389: 1419 - 1389 = 30.- Difference between 1389 and 1355: 1389 - 1355 = 34.- Difference between 1355 and 1320: 1355 - 1320 = 35.- We observe: 25, 27, 29 are consecutive odd numbers, and 35 is also odd and fits at the end.- A very natural and consistent rule would be to subtract consecutive odd numbers: 25, 27, 29, 31, 33, 35.- Applying this correct pattern: 1500 - 25 = 1475; 1475 - 27 = 1448; 1448 - 29 = 1419; 1419 - 31 = 1388; 1388 - 33 = 1355; 1355 - 35 = 1320.- According to this pattern, the fifth term should be 1388, but the given series has 1389 instead.

Verification / Alternative check:
- Check all other terms: 1500, 1475, 1448, 1419, 1355 and 1320 all match perfectly with the rule of subtracting consecutive odd numbers 25, 27, 29, 33 and 35 from their immediate predecessors.- Only the step from 1419 to 1389 breaks this pattern, because the correct subtraction should be 1419 - 31 = 1388.- Therefore, 1389 is the unique term that does not fit the consistent logic of the series.

Why Other Options Are Wrong:
- 1475 fits the rule because 1500 - 25 = 1475; it is consistent.- 1419 fits because 1448 - 29 = 1419; it matches the expected subtraction.- 1355 fits because 1388 (corrected term) - 33 = 1355; the difference is an odd number in the sequence.- 1320 fits because 1355 - 35 = 1320, again respecting the consecutive odd-number pattern.

Common Pitfalls:
- Some candidates only check approximate differences and may mistakenly mark an endpoint like 1320 without fully verifying the complete pattern.- Another mistake is to assume a fixed difference, such as subtracting a constant number, instead of recognising a growing sequence of odd differences.- Ignoring one of the middle differences or miscalculating just one subtraction can easily lead to the wrong answer.

Final Answer:
The only term that violates a clear pattern of subtracting consecutive odd numbers from left to right is 1389, so 1389 is the wrong number in the series.