Letter and Symbol Series: MDCAT Logical Reasoning notes
Letter and Symbol Series MDCAT notes: spotting differences, ratios and alternating patterns in number and letter series, letter positions, worked examples.
How series questions work
A series follows a hidden rule. Your task is to find the rule and apply it to get the next or missing term. Most MDCAT series use one of a few standard patterns, so test them in order.
Step-by-step method
- Differences: subtract each term from the next. Are the differences constant, or do they themselves form a pattern (+1, +2, +3 or -14, -12...)?
- Ratios: divide consecutive terms. Doubling, halving and tripling are common (geometric series).
- Combined rule: e.g. multiply by 2 then add 1.
- Alternating series: if nothing fits, look at the 1st, 3rd, 5th terms and the 2nd, 4th, 6th terms separately.
- Squares and cubes: 1, 4, 9, 16 or 1, 8, 27, 64, or these plus/minus 1.
Number series patterns
| Pattern | Example | Next term |
|---|---|---|
| Constant difference | 3, 7, 11, 15 | 19 (+4) |
| Growing difference | 2, 3, 5, 8, 12 | 17 (+1, +2, +3, +4, +5) |
| Geometric (ratio) | 3, 9, 27, 81 | 243 (×3) |
| ×2 + 1 | 2, 5, 11, 23 | 47 |
| Alternating | 10, 1, 11, 2, 12, 3 | 13 |
| Squares | 1, 4, 9, 16, 25 | 36 |
For a geometric series with first term $a$ and ratio $r$, the $n$th term is $T_n=ar^{\,n-1}$. Example: 81, 27, 9, ... has $r=\tfrac13$, so $T_6=81\times(\tfrac13)^5=\tfrac13$.
Real-life versions: a population doubling daily (5, 10, 20, 40 gives 80 next), or a drug dose halving every day (200 mg, 100, 50, 25 on day 4).
Letter series
Convert letters to their positions in the alphabet and treat them like numbers.
| A | B | C | D | E | F | G | H | I | J | K | L | M |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
| N 14 | O 15 | P 16 | Q 17 | R 18 | S 19 | T 20 | U 21 | V 22 | W 23 | X 24 | Y 25 | Z 26 |
Tip: remember EJOTY = 5, 10, 15, 20, 25 to locate letters quickly.
Worked examples
- B, E, H, K, ? Positions 2, 5, 8, 11 (+3). Next: 14 = N.
- AZ, BY, CX, ? First letters move forward, second letters move back: DW.
- Symmetric blocks: MMMMM, MMLMM, MLKLM, LKJKL, ? Each step, every letter moves one place back and the middle drops one further: KJIJK.
- Numbers: 50, 45, 41, 38, ? Differences -5, -4, -3, so next -2: 36.
- Paired series: 2, 7, 3, 8, 4, 9, ? Odd positions 2, 3, 4; even positions 7, 8, 9. Next: 5.
Common MDCAT traps
- Differences that change steadily (-14, -12, -10) are easy to misread as constant.
- Alternating series look random until you split them.
- For the $n$th term of a halving series, the power is $n-1$, not $n$.
- Count alphabet positions carefully; an off-by-one error is the commonest mistake.
Quick revision
- Try differences, then ratios, then alternation.
- Doubling: ×2; halving: ÷2.
- $T_n=ar^{n-1}$ for geometric series.
- EJOTY: E5, J10, O15, T20, Y25.
- Symmetric letter blocks: track the outer and middle letters separately.