Verbal and Numerical Ability
Mental-ability tests measure how quickly you can recognise patterns under time pressure. Two of the most heavily-tested families are verbal ability (word relationships) and numerical ability (number patterns and quick calculation).
1. Verbal analogies
The format: A : B :: C : ?
Your job is to identify the relationship between A and B, then apply the same relationship to C.
Common relationships:
- Synonym — Brave : Courageous
- Antonym — Hot : Cold
- Tool–User — Brush : Painter
- Part–Whole — Petal : Flower
- Cause–Effect — Rain : Flood
- Function — Pen : Write
- Degree — Warm : Hot
Worked Example 1
Doctor : Hospital :: Teacher : ? (a) Pupil (b) School (c) Book (d) Knowledge
The doctor's place of work is a hospital. Apply the same relation: a teacher works at a school. Answer: (b).
Before looking at options, state the relationship in a full sentence: "A doctor works in a hospital." Then test which option fits the same sentence: "A teacher works in a ___ ." This blocks plausible but wrong distractors.
2. Odd-one-out
Identify the property four of the five share, and isolate the one that doesn't.
Worked Example 2
Find the odd one: Lion, Tiger, Leopard, Elephant, Cheetah
Four are big cats (Felidae). Elephant is not a cat. Answer: Elephant.
3. Coding–decoding
A code maps letters or numbers to other letters or numbers. Crack the rule, then apply it.
Worked Example 3
If CAT is coded as DBU, then DOG is coded as:
Each letter is shifted +1 in the alphabet (C→D, A→B, T→U). Apply to DOG: D→E, O→P, G→H. Code = EPH.
Worked Example 4 — Positional code
If MONDAY is coded as 132541, then DAY is coded as:
We can read off: M=1, O=3, N=2, D=5, A=4, Y=1. So DAY = 541.
4. Number series
A sequence of numbers follows a hidden rule. Find the next term.
Common patterns
| Pattern | Example | Rule |
|---|---|---|
| Arithmetic progression | 2, 5, 8, 11, … | +3 each time |
| Geometric progression | 3, 6, 12, 24, … | ×2 each time |
| Differences-of-differences | 2, 6, 12, 20, 30, … | gaps 4, 6, 8, 10 |
| Squares | 1, 4, 9, 16, 25, … | n² |
| Cubes | 1, 8, 27, 64, 125, … | n³ |
| Fibonacci-like | 1, 1, 2, 3, 5, 8, … | each = sum of previous two |
| Alternating | 2, 7, 4, 9, 6, 11, … | two interleaved series |
Worked Example 5
Find the next term: 3, 7, 15, 31, 63, ?
Differences: 4, 8, 16, 32 — each double. So next difference is 64; next term is 63 + 64 = 127.
Alternatively, each term = 2×(previous) + 1. 2×63 + 1 = 127. ✓
5. BODMAS / order of operations
When a single expression mixes operations, evaluate in order:
Brackets → Orders (powers, roots) → Division and Multiplication (left to right) → Addition and Subtraction (left to right).
Worked Example 6
Simplify: 24 ÷ 6 × 2 + 3² − 4
Step 1 — Orders: 3² = 9. So: 24 ÷ 6 × 2 + 9 − 4. Step 2 — Division and multiplication, left to right: 24 ÷ 6 = 4; 4 × 2 = 8. So: 8 + 9 − 4. Step 3 — Addition and subtraction, left to right: 8 + 9 = 17; 17 − 4 = 13.
- Division and multiplication have equal priority — go left to right. So does addition and subtraction.
- Negative numbers and signs are a frequent source of errors. Use brackets liberally on scratch paper.
- For number series, first list the differences; if those don't form a pattern, list the ratios; if those don't, try alternating series.
- For analogies, always articulate the relationship in words before picking an option.
Quick estimation tricks
- Multiplying by 5: multiply by 10 and halve. 84 × 5 = 840 / 2 = 420.
- Squaring numbers ending in 5: a5 squared = a(a+1) followed by 25. So 35² = 3 × 4 = 12 → 1225.
- Percent of a number: 12% of 50 = 50% of 12 = 6 (swap the operands).