Question

Find the term which doesn't fit into the series given below:
H4Q, K10N, N20K, Q43H, T90E

• A. H4Q
• B. K10N
• C. Q43H
• D. T90E

Hint:

In a series with multiple components (letters, numbers), analyze each component's pattern separately. For number series, check for arithmetic progression, geometric progression, or a mixed pattern like \(y = ax+b\). If a single term breaks an otherwise perfect pattern, it's the outlier.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This is a mixed series problem with three components in each term: a letter, a number, and another letter. We need to find the pattern for each component separately to identify the outlier.
Step 2: Key Formula or Approach:
1. Analyze the pattern of the first letter of each term.
2. Analyze the pattern of the last letter of each term.
3. Analyze the pattern of the number in each term.
Step 3: Detailed Explanation:
The series is: H4Q, K10N, N20K, Q43H, T90E.
Pattern of the first letter:
H (8th letter) \(\xrightarrow{+3}\) K (11th) \(\xrightarrow{+3}\) N (14th) \(\xrightarrow{+3}\) Q (17th) \(\xrightarrow{+3}\) T (20th).
This pattern is consistent throughout the series.
Pattern of the last letter:
Q (17th letter) \(\xrightarrow{-3}\) N (14th) \(\xrightarrow{-3}\) K (11th) \(\xrightarrow{-3}\) H (8th) \(\xrightarrow{-3}\) E (5th).
This pattern is also consistent throughout the series.
Pattern of the number:
The numbers are 4, 10, 20, 43, 90.
Let's look for a recursive pattern, where each number is derived from the previous one. A common pattern is of the form \(a_n = k \cdot a_{n-1} + c\). Let's try k=2.
Let's assume there is a consistent rule that one term breaks. Let's test the rule \(a_n = 2 \times a_{n-1} + (n-1)\) starting from the first term.
Term 1 number = 4.
Term 2 number should be: \(2 \times 4 + (2-1) = 8 + 1 = 9\). The series has 10. This suggests K10N is the incorrect term.
Let's check if this pattern holds for the rest of the series, assuming the second number was 9.
Term 3 number should be: \(2 \times 9 + (3-1) = 18 + 2 = 20\). This matches the number in N20K.
Term 4 number should be: \(2 \times 20 + (4-1) = 40 + 3 = 43\). This matches the number in Q43H.
Term 5 number should be: \(2 \times 43 + (5-1) = 86 + 4 = 90\). This matches the number in T90E.
The pattern \(a_n = 2a_{n-1} + n-1\) works perfectly for all terms except the second one.
Step 4: Final Answer:
The term K10N doesn't fit the series; its number should be 9, not 10, to maintain the pattern.