Select the option that can replace the question mark (?) in the following series. NW17, PY19, RA21, TC23, ?

Correct — C.

Rule: all three tracks move +2 — first letter, second letter and number alike.

First letters: N, P, R, T, V
Second letters: W, Y, A, C, E, the alphabet treated as a loop
Numbers: 17, 19, 21, 23, 25

Y is the 25th letter, so Y + 2 runs past Z and returns to A, which is where the second track's A and C come from.

Putting the three tracks back together gives VE25 — option (c).

Why the others are wrong

• (a)
  XD24 — XD24 moves the first letter four places, T to X, and the second only one, C to D. The number also steps by one instead of two.
• (b)
  WF23 — WF23 repeats 23 instead of stepping to 25, and W and F sit three places past T and C rather than two.
• (d)
  WD24 — WD24 mixes its steps: W is three places past T, D is one past C, and 24 is one past 23. Every track in this series moves by the same two.

Alphanumeric series split into independent tracks. Read the first letters as one series, the second letters as another and the numbers as a third, then solve each on its own.

Here all three tracks happen to move by the same amount, +2, which makes the alphabet wrap the only place to slip.

Treat the alphabet as a ring of 26: after Z comes A again. W to Y is ordinary, Y to A is the wrap, and A to C is ordinary again.

Each track is confirmed on three transitions before the fourth is applied, which is as much evidence as a four-term series can give.

Key facts

• N, P, R, T advance two letters at a time, so the next is V.
• W, Y, A, C advance two letters with the alphabet treated as a loop, so the next is E.
• 17, 19, 21, 23 advance by two, so the next is 25.
• Y is the 25th letter, so Y + 2 wraps round to A.

Common traps

• Stopping the letter track at Z instead of wrapping round to A
• Assuming all three tracks share one step size without checking each
• Reading the number as a code for a letter rather than as its own track

No directly related past PYQ was found.