Series

Here is a detailed explanation of the Series.pdf content, along with solved examples and practice questions for each type of series covered in the PDF¹.

Introduction to Series (Alpha/Numeric/Figural)

Series reasoning involves identifying patterns or rules in sequences of letters, numbers, symbols, or figures and using these patterns to answer questions about missing elements, positions, or relationships.

Types of Series in Reasoning

1. Alphabet Series

• Definition: Arranging letters or groups of letters in a sequence or pattern.
• Key Concepts:
  • Vowels: A, E, I, O, U
  • Consonants: All other letters
  • Dictionary Order: Arranging words in alphabetical order
  • Interchanging Letters: Swapping first and last letters, etc.
• Example:
  • Given: DEW, BIG, RAW, FAN, DOG
  • Interchange first and last letters: WED, GIB, WAR, NAF, GOD
  • Arrange in dictionary order: GIB, GOD, NAF, WAR, WED
  • Last word: WED

Practice Question: If you swap the first and last letters of each word in the following list, how many meaningful words are formed? List: CAT, RAT, BAT, TAP Answer: CAT → TAC (not meaningful), RAT → TAR (meaningful), BAT → TAB (meaningful), TAP → PAT (meaningful) Total = 3

2. Number Series

• Definition: Sequences of numbers following a specific rule (e.g., addition, subtraction, multiplication, division, digit manipulation).
• Key Concepts:
  • Prime Numbers: 2, 3, 5, 7, 11, 13, …
  • Even/Odd Numbers: 0, 2, 4, 6, … / 1, 3, 5, 7, …
  • Digit Operations: Adding to digits, swapping digits, etc.
• Example:
  • Given: 567, 289, 376, 189, 852
  • Add 1 to the second digit of each number: 577, 299, 386, 199, 862
  • Interchange first and last digits: 775, 992, 683, 991, 268
  • Highest number: 992

Practice Question: If you arrange the digits of each number in increasing order, which number from the series 234, 541, 321, 654, 123 will be the lowest? Answer: 123 → 123 234 → 234 321 → 123 (but 123 is already present, so the correct unique lowest after rearrangement is 123 from 321 or 123 itself) But if you mean after arranging digits: 234 → 234 541 → 145 321 → 123 654 → 456 123 → 123 Lowest: 123 (from 321 or 123), but if only unique numbers after rearrangement, 145 (from 541) is not the lowest, so clarify the question. If you mean after rearranging digits, the lowest number formed is 123 (from both 123 and 321).

3. Mixed Series

• Definition: Sequences containing a mix of letters, numbers, and symbols.
• Key Concepts:
  • Position-based questions: Find the nth element from the left/right, or relative positions.
  • Operation-based series: Apply rules like swapping vowels, replacing symbols, etc.
• Example:
  • Given: A B 6 P 7 2 Z @ X ? V T W # & N S L %
  • Which element is 6th to the left of the 12th element from the left?
    • 12th from left: X
    • 6th to the left of X: 2 (count back 6 positions from X)
  • Which element is 4th to the right of the 11th element from the left?
    • 11th from left: ?
    • 4th to the right of ?: & (count forward 4 positions from ?)

Practice Question: In the series: 6 R 0 T 4 A 8 % B F 1 E # W @ 9 H I $ M N * 3 2 V $ 5 G P 7 Q How many consonants are immediately preceded by a consonant and immediately followed by a number? Answer: Look for the pattern: consonant-consonant-number B F 1 and G P 7 Total = 2

4. Operation-based Series

• Definition: Apply specific operations step-by-step to the series.
• Example:
  • Step 1: Exchange vowels with their next letter (A→B, E→F, etc.)
  • Step 2: Replace symbols with 8
  • Step 3: Increase numbers by 1
  • Input: NPLB S% &1E4G4$TG2I0UK@17VA
  • After Step 1: NPLB S% &1F4G4$TG2J0VK@17VB
  • After Step 2: NPLB S88 1F4G48TG2J0VK817VB
  • After Step 3: NPLB S88 2F5G59TG3J1VK928VB

Practice Question: If all symbols are removed from the series 6 R 0 T 4 A 8 % B F 1 E # W @ 9 H I $ M N * 3 2 V $ 5 G P 7 Q, which element is 5th to the right of the 10th from the right end? Answer:

• Remove symbols: 6 R 0 T 4 A 8 B F 1 E W 9 H I M N 3 2 V 5 G P 7 Q
• 10th from right: 2
• 5th to the right of 2: 5

5. Figural Series

• Definition: Sequences of figures where each figure changes in a specific way (rotation, shading, adding elements, etc.).
• Key Concepts:
  • Clockwise/Anticlockwise Rotation: Figures rotate by 45°, 90°, 135°, etc.
  • Shading/Unshading: Parts of the figure change shading in each step.
  • Adding/Removing Elements: New elements are added or removed in each step.
• Example:
  • Problem: A series of figures where a pin is inverted in each step.
  • Answer: The figure with the next pin inverted continues the series.

Practice Question: If a series of squares shows a shaded region moving one step clockwise in each figure, which figure comes next? Answer: The figure with the shaded region in the next clockwise position.

Solved Examples and Practice Questions

Alphabet Series Practice

Q1: Arrange the following words in dictionary order after swapping the first and last letters: Words: CAT, DOG, RAT, BAT Answer: CAT → TAC DOG → GOD RAT → TAR BAT → TAB Dictionary order: GOD, TAB, TAC, TAR First word: GOD

Number Series Practice

Q2: Find the missing number: 2, 7, 14, 23, ?, 47 Solution: Differences: 5, 7, 9, 11, 13 Missing number: 23 + 11 = 34²

Q3: Find the next number: 4, 6, 9, 13.5, ? Solution: Multiply by 1.5 each time Next number: 13.5 × 1.5 = 20.25²

Mixed Series Practice

Q4: In the series: 6 R 0 T 4 A 8 % B F 1 E # W @ 9 H I $ M N * 3 2 V $ 5 G P 7 Q How many vowels are immediately preceded by a letter but not immediately followed by a symbol? Answer: Look for: letter-vowel-letter/number R 0 T (O is not a vowel in English, but if A is considered, check for A, E, I, etc.) Assuming A is a vowel: A is preceded by 4 (number), not a letter. E is preceded by 1 (number), not a letter. I is preceded by H (letter), followed by $ (symbol, so not counted if the question says “not followed by symbol”). If the question is about vowels immediately preceded by a letter and not followed by a symbol: Only possible if a vowel is after a letter and before a letter/number. In the given series, no such case exists for standard vowels A, E, I. Clarification needed for the exact question, but based on the PDF example, the answer is 1 (R-O-T, but O is not a vowel in English; likely a typo or misprint).

Figural Series Practice

Q5: In a series of figures, a square rotates 90° clockwise in each step. If the first figure is a square with a dot at the top, what will the next figure look like? Answer: Square with the dot on the right side.

Summary Table

Additional Tips

• Identify the pattern or rule in the series.
• For number series, check for arithmetic, geometric, or digit-based patterns.
• For alphabet series, consider dictionary order, letter positions, or word operations.
• For mixed series, pay attention to the type and position of each element.
• For figural series, note the direction and type of change in each step.

This comprehensive guide, with explanations, examples, and practice questions, will help you master series reasoning for any competitive exam¹²³.