Which figure should replace the question mark (?) if the following series were to be continued?

- (a)

- (b)

- (c)

- (d)

Answer
Why
Correct — D.
Rule: two different moves alternate, so the step from box 4 to the answer repeats the step from box 2 to box 3.
Box 2 to box 3: the bottom-right symbol went to the top-left, the top-left went to the bottom-centre, the bottom-centre went to the bottom-right, the two middle-row symbols swapped places, and the bottom-left symbol was replaced by a new one.
Box 4 is top-left T, middle row 8 and L, bottom row W, 2, X. Apply the move:
top-left takes X, bottom-centre takes T, bottom-right takes 2
middle row swaps to L, 8
bottom-left takes a fresh symbol, 9
That is option (d).
Why the others are wrong
- (a)Its top-left is 2. At this step the top-left cell takes the previous box's bottom-right symbol, and box 4's bottom-right is X, so the corner has to read X.
- (b)Its middle row reads L, T. The middle row only ever swaps the two symbols already sitting in it, so box 4's 8 and L must become L and 8 — a T cannot arrive there.
- (c)It keeps W, which is box 4's bottom-left symbol and therefore the one dropped at this step, exactly as K was dropped between box 2 and box 3.
Concept
Alternating figure series are common, and they look broken until you compare step 1 with step 3 and step 2 with step 4 rather than each step with the next.
Here the six symbols occupy the same six cells in every box: the top-left corner, the two right-hand cells of the middle row, and all three cells of the bottom row.
One transformation carries box 1 to box 2 and again carries box 3 to box 4. A different one carries box 2 to box 3, and that is the one still owed. The missing figure is that second transformation applied once more.
Boxes 1 and 2 hold the same six symbols, and so do boxes 3 and 4, so the substitution happens on the even step alone.
The new symbol at the bottom-left cannot be predicted from the series — 9 has not appeared before. That is why the question is settled by the five determined cells, and why two options can be eliminated on the dropped W alone.
Key facts
- In an alternating series the fifth figure repeats the move that produced the third.
- Boxes 1 and 2 carry the same six symbols, and boxes 3 and 4 carry the same six as each other.
- Box 2's bottom-left K is absent from box 3, which is what shows a symbol is dropped on the even step.
Study next
Common traps
- Comparing only consecutive boxes and abandoning the question when box 1 to box 2 does not match box 2 to box 3.
- Choosing an option that still carries a symbol the series has already dropped.
Four boxes then a question mark, with four candidate boxes below. Also asked 9 Sep 2024, 16:00, Reasoning Q.22 and 10 Sep 2024, 12:30, Reasoning Q.18.
Related PYQs
No directly related past PYQ was found.