Study Companion
Topic 03 | Verbal reasoning

Letter codes & sequences

Selective prep: continue letter sequences, decode letter shifts, and read alphabetical ciphers fast.

20-30 min Printable practice Answer key Challenge included
How to use this page

Read the explanation, work through the examples, then complete the core practice before printing.

Print practice Print answers
Study progress: Not started

What you will learn

Worked example 0 Continuing a letter sequence

Question: What comes next? A, C, E, G, ?   (a) H (b) I (c) J (d) K

Step 1. Convert to positions: A=1, C=3, E=5, G=7. Gap = +2 each time.

Step 2. Next position = 7 + 2 = 9. The 9th letter is I.

Step 3. Sanity check: the pattern is “every second letter starting from A”, so A, C, E, G, I. Answer: (b).

1. Constant-shift sequences

Every step uses the same shift. Compute the shift once, then apply it.

Worked example 1 Backwards shift

Z, W, T, Q, ? (a) M (b) N (c) O (d) P

Gap: Z to W is -3 (Z=26, W=23). W to T: 23 to 20 = -3. Confirmed. Q=17, so next = 17 - 3 = 14 = N. Answer: (b).

2. Increasing-gap sequences

The gap itself grows. Find the gap pattern first.

Worked example 2 Growing gaps

A, B, D, G, K, ? (a) O (b) P (c) Q (d) R

Gaps: A to B = +1, B to D = +2, D to G = +3, G to K = +4. Next gap = +5. K=11, so 11 + 5 = 16 = P. Answer: (b).

3. Interleaved (two patterns)

Two sequences take turns. Split into the odd positions and the even positions.

Worked example 3 Two interleaved sequences

A, Z, C, X, E, V, G, ? (a) S (b) T (c) U (d) V

Odd positions (1st, 3rd, 5th, 7th): A, C, E, G — gap +2 going forward. Even positions (2nd, 4th, 6th, ?): Z, X, V, ? — gap -2. Next even term = V - 2 = V=22, 22-2 = 20 = T. Answer: (b).

4. Caesar-shift ciphers

Every letter of the original word is moved the same number of places.

Worked example 4 Decoding a shift

“The code word for DOG is FQI. What is the code word for CAT?”

Step 1. Find the shift. D to F = +2. O to Q = +2. G to I = +2. Shift = +2.

Step 2. Apply to CAT: C + 2 = E, A + 2 = C, T + 2 = V. Code word = ECV.

Drill pack

10 minutes. Letters on fingers, counting from A=1. Trust the arithmetic, not the “feel” of the letters.

Drill timer
00:00
Target: 10:00
Previous attempts
  • No attempts yet.
Target: 10 minutes. Time yourself with a watch or phone timer — no pausing.
Fluency

Timed drill

    1. Next letter: B, D, F, H, ? (a) I (b) J (c) K (d) L
    2. Next letter: Z, Y, X, W, ? (a) T (b) U (c) V (d) S
    3. Next letter: C, F, I, L, ? (a) N (b) O (c) P (d) M
    4. Next letter: A, D, G, J, M, ? (a) O (b) P (c) Q (d) R
    5. Next letter: Y, V, S, P, ? (a) L (b) M (c) N (d) O
    6. Next letter: A, C, F, J, O, ? (a) T (b) U (c) S (d) V
    7. If CAT is coded as DBU, what is the code for DOG? (a) EPH (b) EPG (c) FPI (d) EOH
    8. If BAT is coded as EDW, what is the shift? (a) +2 (b) +3 (c) +4 (d) +5
    9. Next letter: M, J, G, D, ? (a) A (b) B (c) C (d) Z
    10. Next letter: A, Z, B, Y, C, ? (a) W (b) X (c) V (d) D
    11. Missing letter: P, ?, R, S (a) N (b) O (c) Q (d) T
    12. Next letter: D, H, L, P, ? (a) R (b) S (c) T (d) U
    13. If DOG = GRJ, decode FDW (shift the same way). (a) BAT (b) CAT (c) RAT (d) HAT
    14. Next pair: AB, CD, EF, GH, ? (a) IJ (b) JK (c) HI (d) KL
    15. Next letter: B, E, I, N, ? (a) S (b) T (c) U (d) R
    16. Pair sequence: AZ, BY, CX, DW, ? (a) EV (b) FV (c) EU (d) DV
    17. Next letter: T, Q, N, K, ? (a) H (b) I (c) J (d) G
    18. If ABC = ZYX (code by mirror), what is the code for DOG? (a) WLT (b) WLR (c) WLN (d) XLT
    19. Next letter: A, B, D, G, K, P, ? (a) T (b) U (c) V (d) W
    20. Missing middle: M, O, ?, S, U (a) P (b) Q (c) R (d) N

Challenge

Mixed shifts, mirrors, and two-letter groups.

Reasoning

Harder patterns

    1. Z, X, U, Q, L, ? (gaps -2, -3, -4, -5, -6) (a) F (b) G (c) E (d) H
    2. If MATH is coded NCWL (shifts +1, +2, +3, +4), decode PGRZ using shifts -1, -2, -3, -4. (a) OENV (b) OEOV (c) OEOW (d) PENV
    3. Next pair: AZ, CX, EV, GT, ? (a) IR (b) IS (c) JR (d) HS
    4. Next letter: B, C, E, H, L, Q, ? (gaps +1, +2, +3, +4, +5, +6) (a) V (b) W (c) X (d) U
    5. If the code uses the mirror rule (A->Z, B->Y, …), what is the plain text of ULLW? (a) ATOM (b) GOOD (c) FOOD (d) WOOD
    6. A, D, I, P, ? (differences follow odd numbers: +3, +5, +7, +9) (a) Y (b) Z (c) X (d) A (wrap)
    7. Next letter: C, D, F, I, M, R, ? (a) X (b) Y (c) W (d) V
    8. If Monday = NPOEBZ (shift +1), what day is GSJEBZ? (a) Friday (b) Saturday (c) Thursday (d) Sunday
Answers

Answer key

Attempt the practice first. When you're ready to check, expand the answers below.

Show the full answer key

Letters as numbers: A=1, B=2, C=3, … Z=26. Every answer gives the rule first, then the arithmetic.

Timed drill

    1. (b) J. Gap +2 each time: B, D, F, H, J.
    2. (c) V. Gap -1 each time: Z, Y, X, W, V.
    3. (b) O. Gap +3 each time: C(3), F(6), I(9), L(12), O(15).
    4. (b) P. Gap +3 each time: A, D, G, J, M, P.
    5. (b) M. Gap -3 each time: Y(25), V(22), S(19), P(16), M(13).
    6. (b) U. Gaps grow +2, +3, +4, +5, next +6. O(15) + 6 = 21 = U.
    7. (a) EPH. Shift +1: D+1=E, O+1=P, G+1=H.
    8. (b) +3. B+3=E, A+3=D, T+3=W.
    9. (a) A. Gap -3: M(13), J(10), G(7), D(4), A(1).
    10. (b) X. Two interleaved sequences: odd positions A, B, C (+1); even positions Z, Y, ? (-1). Next even = X.
    11. (c) Q. Gap +1: P, Q, R, S.
    12. (c) T. Gap +4: D(4), H(8), L(12), P(16), T(20).
    13. (b) CAT. The shift from DOG to GRJ is +3. Reverse (-3) on FDW: F-3=C, D-3=A, W-3=T.
    14. (a) IJ. Each pair steps +2 from the previous: AB, CD, EF, GH, IJ.
    15. (b) T. Gaps grow +3, +4, +5, next +6. N(14) + 6 = 20 = T.
    16. (a) EV. First letters A, B, C, D, E (+1); second letters Z, Y, X, W, V (-1).
    17. (a) H. Gap -3: T(20), Q(17), N(14), K(11), H(8).
    18. (a) WLT. Mirror: 27 - position. D(4) -> 23 = W; O(15) -> 12 = L; G(7) -> 20 = T.
    19. (c) V. Gaps +1, +2, +3, +4, +5, next +6. P(16) + 6 = 22 = V.
    20. (b) Q. Gap +2: M, O, Q, S, U.

Challenge

    1. (a) F. Gaps -2, -3, -4, -5, -6. L(12) - 6 = 6 = F.
    2. (b) OEOV. Applying shifts -1, -2, -3, -4: P-1=O, G-2=E, R-3=O, Z-4=V.
    3. (a) IR. First letters A, C, E, G, I (+2); second letters Z, X, V, T, R (-2).
    4. (b) W. Gaps +1, +2, +3, +4, +5, next +6. Q(17) + 6 = 23 = W.
    5. (c) FOOD. Mirror: 27 - position. U(21) -> 6 = F; L(12) -> 15 = O; L -> O; W(23) -> 4 = D.
    6. (a) Y. Gaps +3, +5, +7, next +9 (odd numbers). P(16) + 9 = 25 = Y.
    7. (a) X. Gaps +1, +2, +3, +4, +5, next +6. R(18) + 6 = 24 = X.
    8. (a) Friday. Shift is +1, so decode by -1: G-1=F, S-1=R, J-1=I, E-1=D, B-1=A, Z-1=Y. FRIDAY.

Prefer paper? Print the answer key as a separate booklet: open print view ->