Select the letter-cluster from among the given options that can replace the question mark (?) in the following series. C F J, H K O, M P T, ?

Correct — D.
Rule: +5 at every position from one cluster to the next.

First letters: C(3), H(8), M(13) → R(18).
Second letters: F(6), K(11), P(16) → U(21).
Third letters: J(10), O(15), T(20) → Y(25).

That gives RUY → option (d).

Why the others are wrong

• (a)
  RAS — RAS gets the first letter right and then breaks. The second letters run F, K, P in steps of 5, so the next is U, not A, and T + 5 is Y, not S.
• (b)
  RYS — RYS puts Y in the middle. P + 5 = U belongs there and Y belongs last; S(19) is not T + 5.
• (c)
  TSG — TSG fails at the first letter: M(13) + 5 = R(18), not T(20). S and G are off the +5 steps from P and T as well.

A letter-cluster series is three number series laid side by side. Convert letters to positions (A = 1 … Z = 26) and read one position at a time down the terms.

Here each position climbs by 5: C, H, M in the first place, F, K, P in the second, J, O, T in the third. Read that way, the next cluster is R, U, Y.

Key facts

• A = 1 through Z = 26 is the position code these series run on.
• Here every position steps +5 from one cluster to the next: C→H→M→R.
• Inside each given cluster the gaps are +3 then +4, as in C(3), F(6), J(10).

Common traps

• Reading each cluster as a word instead of converting letters to positions
• Checking only the first letter and stopping at R, which three of the four options share

No directly related past PYQ was found.