Identify the figure given in the options which when put in place of ? will logically complete the series.

Correct — B. Two patterns run together, one on the lines and one on the numbers.

Rule: each square is the one before it turned 90° clockwise.

Square 1 has a diagonal rising from bottom-left to top-right, with a spur from that diagonal's midpoint to the bottom-right corner. Each quarter-turn gives the next square, and four turns close the circle — so square 5 repeats square 1's layout.

Option (d) draws square 3's instead, spur to the top-left, so it goes on the lines alone.

Rule: each square's lower number is the upper number of the square before it, running 4, 6, 3. Square 5 carries 8 below, which removes option (a) and its 2.

That leaves (b) and (c), and only the number above the 8 separates them. In the rising-diagonal squares the pair has added to 5, then 9, and option (b)'s 5 is the one that keeps that run going.

Why the others are wrong

• (a)
  Option (a) draws the right layout but puts 2 below. The lower number is handed down by the square before, and square 4 carries 8 upstairs, so 8 is what has to appear.
• (c)
  Option (c) puts 3 above the 8. That pair adds to 11 and does not continue the 5, then 9 of the earlier rising-diagonal squares — the only test left once the lines and the carried 8 are settled.
• (d)
  Option (d) fails on the figure before its numbers matter. Its spur runs from the diagonal's midpoint to the top-left corner, which is square 3's layout, whereas four clockwise turns put square 5 back on square 1's.

A number-in-figure series carries two independent patterns and both have to be read. The lines usually rotate or reflect on a fixed step, and the numbers usually run as an arithmetic series threaded through the figures.

Settle the lines first. It is the cheaper test and it often kills options outright — here the quarter-turn rule fixes square 5's layout exactly and eliminates one option before any arithmetic starts.

Then read the numbers in a fixed order, upper first and lower second, and look for a value that repeats across the boundary between two figures. A number that reappears is a chain, and a chain hands you one of the two missing values for free.

Key facts

• Each square is the previous one rotated 90° clockwise, so the layout repeats every fourth square.
• The lower number of each square is the upper number of the square before it, running 4, 6, 3, 8.
• In the 1st and 3rd squares — the ones with the rising diagonal — the two numbers add to 5 and to 9.
• Square 5 therefore repeats square 1's lines and carries the keyed 5 above the 8.

Common traps

• Choosing on the numbers alone and missing that one option draws the wrong spur.
• Turning the figure anticlockwise, which lands square 5 on square 3's layout.
• Reading the two numbers in a different order in different squares, which breaks the chain.

No directly related past PYQ was found.