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Which shape comes next in the sequence?

Mathematics

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Answer

A\text{A}

To solve this abstract reasoning question, we need to identify the pattern in the sequence of shapes. Let's analyze the shapes in each of the four given boxes. Each box contains a 2x2 grid with four positions: Top-Left (TL), Top-Right (TR), Bottom-Left (BL), and Bottom-Right (BR).

Sequence Analysis:

Box 1:

  • TL: Empty Up Triangle
  • TR: Filled Square
  • BL: Empty Square
  • BR: Filled Down Triangle

Box 2:

  • TL: Empty Square
  • TR: Empty Circle
  • BL: Empty Up Triangle
  • BR: Filled Right Triangle

Box 3:

  • TL: Empty Up Triangle
  • TR: Filled Square
  • BL: Empty Square
  • BR: Filled Down Triangle

Box 4:

  • TL: Empty Up Triangle
  • TR: Empty Circle
  • BL: Empty Square
  • BR: Filled Right Triangle

Identifying the Pattern:

  1. Alternating Patterns: We can observe that Box 1 and Box 3 are identical. This suggests an alternating pattern. Let's call this "Pattern A".

    • Pattern A: (TL: Empty Up Triangle, TR: Filled Square, BL: Empty Square, BR: Filled Down Triangle)
  2. Variations in the Second Pattern: Box 2 and Box 4 are similar but not identical. Let's call this "Pattern B".

    • Box 2 (Pattern B - Version 1): (TL: Empty Square, TR: Empty Circle, BL: Empty Up Triangle, BR: Filled Right Triangle)
    • Box 4 (Pattern B - Version 2): (TL: Empty Up Triangle, TR: Empty Circle, BL: Empty Square, BR: Filled Right Triangle)

    Comparing Box 2 and Box 4, we see that the shapes in the Top-Left (TL) and Bottom-Left (BL) positions have swapped.

    • In Box 2: TL has an Empty Square, BL has an Empty Up Triangle.
    • In Box 4: TL has an Empty Up Triangle, BL has an Empty Square. The TR and BR positions remain the same in both versions of Pattern B.

Predicting the Next Shape:

The sequence follows this order:

  1. Pattern A (Box 1)
  2. Pattern B - Version 1 (Box 2)
  3. Pattern A (Box 3)
  4. Pattern B - Version 2 (Box 4)

Following this alternating sequence, the next shape (Box 5) should be Pattern A.

Pattern A is:

  • TL: Empty Up Triangle
  • TR: Filled Square
  • BL: Empty Square
  • BR: Filled Down Triangle

Now, let's compare this with the given options:

  • Option A:

    • TL: Empty Up Triangle
    • TR: Filled Square
    • BL: Empty Square
    • BR: Filled Down Triangle This matches Pattern A exactly.
  • Option B: TR is an Empty Square (should be Filled Square).

  • Option C: Many differences.

  • Option D: BR is a Filled Square (should be Filled Down Triangle).

Therefore, Option A is the correct shape that comes next in the sequence.

The final answer is A\text{A}.

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