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Number Reversal / Mirror Series

Introduction

In a Number Reversal or Mirror Series, each term is formed by reversing the digits of the previous number, or by applying a combination of reversal and simple arithmetic. These questions test your pattern recognition and ability to visualize digit operations or symmetry.

Example behaviours include pure digit reversal, reversal followed by addition/subtraction, or alternating reversal and arithmetic steps.

Pattern: Number Reversal / Mirror Series

Pattern: Number Reversal / Mirror Series

The key idea: terms are formed by reversing digits or by alternating between reversal and arithmetic operations.

Common forms include:

  • Pure reversal: 12, 21, 34, 43, 56, 65
  • Reversal + constant addition: 12, 21, 24, 42, 45, 54 (reverse, +3, reverse, +3 ...)
  • Alternating forward and reversed terms: 24, 42, 26, 62, 28, 82
  • Reversal combined with multiplication or halving in more complex patterns

Step-by-Step Example

Question

Find the next term in the series: 12, 21, 24, 42, 45, ?

Solution

  1. Step 1: Observe the first step (reversal)

    12 → reverse digits → 21.

  2. Step 2: Observe the second step (addition)

    21 → add 3 → 24.

  3. Step 3: Observe the third step (reversal)

    24 → reverse digits → 42.

  4. Step 4: Observe the fourth step (addition)

    42 → add 3 → 45.

  5. Step 5: Continue the rule

    The pattern alternates: reverse, +3, reverse, +3, … So after 45 we reverse → 54.

  6. Final Answer:

    54

  7. Quick Check:

    Sequence steps: 12 (reverse) → 21 (+3) → 24 (reverse) → 42 (+3) → 45 (reverse) → 54 ✅

Quick Variations

  • 1. Reverse digits alternately (e.g., 12, 21, 23, 32, 34, 43).
  • 2. Reverse and then add/subtract a constant that itself may change (e.g., +2, +3, +4).
  • 3. Reversal occurs only on even positions while odd positions follow an arithmetic rule.
  • 4. Combine reversal with multiplication for multi-digit manipulations in harder problems.

Trick to Always Use

  • Write the reversed number explicitly to avoid digit-position mistakes.
  • Check whether reversal happens every time or at fixed positions (every 2nd term, etc.).
  • Look for a small arithmetic step (+/- constant) applied before or after reversal.
  • Test the identified rule on every term to ensure consistency.

Summary

  • Number reversal series flip digit order or alternate reversal with arithmetic operations.
  • Confirm whether reversal is immediate or follows an addition/subtraction step.
  • Common exam patterns: reverse, reverse+add, reverse+multiply, or alternating rules.
  • Always verify the rule across at least 3-4 terms before finalizing the answer.

Example to remember:
12, 21, 24, 42, 45, 54 → pattern: reverse, +3, reverse, +3, ... → Next = 54

Practice

(1/5)
1. Find the next term in the series: 13, 31, 34, 43, ?
easy
A. 46
B. 48
C. 52
D. 53

Solution

  1. Step 1: Identify the alternating pattern

    13 → reverse → 31.

  2. Step 2: Apply the +3 step

    31 → +3 → 34.

  3. Step 3: Continue the alternation

    34 → reverse → 43, then 43 → +3 → 46.

  4. Final Answer:

    46 → Option A

  5. Quick Check:

    Alternate Reverse, +3 → 13, 31, 34, 43, 46 ✅
Hint: If reversal appears, check whether an arithmetic step (like +3) alternates with it.
Common Mistakes: Applying +3 at every step instead of alternating with reversal.
2. Find the missing term: 21, 12, 15, 51, ?
easy
A. 56
B. 55
C. 57
D. 54

Solution

  1. Step 1: Check first step (reversal)

    21 → reverse → 12.

  2. Step 2: Apply the arithmetic step

    12 → +3 → 15.

  3. Step 3: Continue alternation

    15 → reverse → 51 → then apply +3 → 51 + 3 = 54.

  4. Final Answer:

    54 → Option D

  5. Quick Check:

    Reverse, +3, Reverse, +3 → 21,12,15,51,54 ✅
Hint: When reversal and addition alternate, check if the added value is constant across repeats.
Common Mistakes: Assuming the added value increases unless evidence shows so.
3. Find the next number: 26, 62, 65, 56, ?
easy
A. 59
B. 58
C. 57
D. 55

Solution

  1. Step 1: Identify the alternating pattern

    26 → reverse → 62.

  2. Step 2: Apply the constant addition

    62 → +3 → 65.

  3. Step 3: Continue alternation

    65 → reverse → 56.

  4. Step 4: Repeat +3 step

    56 → +3 → 59.

  5. Final Answer:

    59 → Option A

  6. Quick Check:

    Reverse, +3, Reverse, +3 → 26,62,65,56,59
Hint: If the sequence alternates cleanly, first confirm the reversal step, then check for a fixed small addition.
Common Mistakes: Trying to increase the additive step without evidence; here it remains +3.
4. Find the next term in the series: 42, 24, 27, 72, ?
medium
A. 74
B. 75
C. 76
D. 77

Solution

  1. Step 1: Observe the alternation

    42 → reverse → 24.

  2. Step 2: Apply +3 step

    24 → +3 → 27.

  3. Step 3: Continue the pattern

    27 → reverse → 72 → then +3 → 72 + 3 = 75.

  4. Final Answer:

    75 → Option B

  5. Quick Check:

    Reverse, +3, Reverse, +3 → 42,24,27,72,75 ✅
Hint: Prefer the simplest repeating addition when reversal alternates consistently.
Common Mistakes: Overcomplicating by introducing increasing additions without clear evidence.
5. Find the next term in the sequence: 11, 22, 23, 32, 34, ?
medium
A. 43
B. 44
C. 45
D. 46

Solution

  1. Step 1: Note the initial seed and first operation

    Start with 11. The sequence first doubles: 11 × 2 = 22.

  2. Step 2: Observe the repeating block after the initial doubling

    After the initial ×2, the sequence alternates between an additive step and a digit-reversal step, where the additive amount increases by 1 each time: +1, reversal, +2, reversal, ...

  3. Step 3: Verify the pattern on given terms

    22 → +1 = 23 (matches third term). 23 → reverse = 32 (fourth term). 32 → +2 = 34 (fifth term).

  4. Step 4: Apply the next operation

    The next step is a reversal of 34 → reverse(34) = 43.

  5. Final Answer:

    43 → Option A

  6. Quick Check:

    Steps: 11 ×2 = 22, 22 +1 = 23, reverse(23)=32, 32 +2 = 34, reverse(34)=43 ✅
Hint: If a sequence starts with a seed operation (like ×2), check whether a small alternating block repeats afterwards (e.g., +n, reverse).
Common Mistakes: Expecting a single uniform operation for all steps instead of recognizing an initial seed operation followed by an alternating block.
Recommended

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10 questions~5 mineasy hard