Logical and analytical reasoning
Reasoning questions test how carefully you can follow a rule, a chain or a set of conditions. There is rarely any heavy arithmetic, but there is always exactly one right answer. The habit to build is to write each fact down as you read it, then check the final answer against every condition.
Formulas and when they apply
- Letter positions: A = 1, B = 2, … Z = 26. Position from the other end = 27 − position.Applies when: Uses the 26-letter English alphabet.
- Position from the other end = total + 1 − position from this endApplies when: Counting the person or object itself in both counts.
- People between two persons = total − (position of A from one end + position of B from the other end)Applies when: A and B are counted from opposite ends and do not overlap, so the two positions add to less than the total.
- Distance from the start = √(east-west displacement² + north-south displacement²)Applies when: All turns are right angles. Opposite directions are subtracted.
- Each right-angle turn is 90°. Direction angle measured clockwise from north: N 0°, E 90°, S 180°, W 270°.
- A syllogism conclusion follows only if it is true in every possible diagram of the statements.Applies when: Take the statements as true, even if they differ from known facts.
- Series: check the gaps, then the gaps of the gaps, then the ratios, then the odd and even places separately.
Worked examples
Example 1. Find the next number: 7, 9, 13, 21, 37, ?
Solution. The gaps are 2, 4, 8, 16, doubling each time. The next gap is 32, so the next number is 37 + 32 = 69.
Example 2. A cyclist rides 9 km north and then 12 km east. How far is she from the start in a straight line?
Solution. The two legs are at right angles, so distance = √(9² + 12²) = √(81 + 144) = √225 = 15 km.
Example 3. In a row of 35 children, Ravi is 9th from the left and Sana is 14th from the right. How many children are between them?
Solution. Sana is 35 − 14 + 1 = 22nd from the left. The children between are 22 − 9 − 1 = 12. Check with the shortcut: 35 − 9 − 14 = 12.
Shortcuts and their limits
- Between two people counted from opposite ends: total − (sum of their two positions).Does not apply when: Fails if the two positions add up to more than the total, which means they overlap in the count.
- In letter series and coding, convert letters to numbers first and look at the gaps.Does not apply when: Does not help when the rule depends on the meaning of the words, not their spelling.
- If a series jumps up and down, split it into odd places and even places.Does not apply when: Fails when each term depends on the term just before it.
- For syllogisms, draw the case that breaks the conclusion. If you can draw one, the conclusion does not follow.Does not apply when: Make sure the diagram you draw still obeys every statement.
Common mistakes
- Settling on the first rule that fits one or two terms. Test it against every term before using it.
- Mixing up left and right turns, or clockwise and anticlockwise, in direction questions. Sketch each step.
- Counting the person twice, or not at all, when finding positions from the left and right ends.
- Treating 'some A are B' as if it meant 'all A are B' or 'some A are not B'.
- Stopping at the first arrangement that satisfies the early conditions. A valid answer must satisfy all of them.
Independent practice made by EduVistaHQ with original questions. It is not an official examination paper, it is not affiliated with or endorsed by any examination body or company, and a practice score does not predict a real result.