Logical Reasoning and Analytical Ability for Engineers — ESE

Weightage: Engineering Aptitude, which the syllabus lists as logical reasoning and analytical ability, is a recurring block of ESE Prelims Paper I. Questions are short and, with 100 questions for 200 marks, worth about 2 marks each, so this block is where a prepared candidate buys time for the technical items.

1. Why this block is a time bank

Paper I has 100 questions in 2 hours, about 72 seconds each. Reasoning items that take 40 seconds give you minutes to spend elsewhere. Practise them to speed, not just to accuracy.

The 1/3 negative marking works for you here: because you can usually eliminate options by logic, your guesses are informed ones.

2. Number and letter series

Check in this order:

1. Constant difference (arithmetic).
2. Constant ratio (geometric).
3. Differences that themselves form a pattern (second differences, squares, cubes).
4. Alternating series made of two interleaved sequences.

Worked example. In 3, 7, 15, 31, 63 the differences are 4, 8, 16, 32, which double, so the next term is 63 + 64 = 127. Each term is also $2^n-1$ shifted: $2^2-1,2^3-1,2^4-1,\dots$.

For letters, convert to positions A=1 to Z=26 and apply the same tests. Remember that opposite letters pair to 27 (A with Z, B with Y).

3. Coding and decoding

Two shifts cover most items: a fixed shift (each letter moves by $k$) and a position-reversal (A becomes Z). Test the first letter, then confirm on the second before applying to the whole word. For number codes, check whether the code is a sum, product or position count.

4. Syllogisms and logical deduction

Draw a Venn diagram for every statement and test each conclusion against the diagram that is least favourable to it.

• "All A are B" puts A wholly inside B.
• "Some A are B" overlaps them, and does not say anything about the rest of A.
• "No A is B" separates them.

A conclusion follows only if it holds in every diagram that fits the statements. A conclusion that is merely possible does not follow.

Worked example. Statements: all pumps are machines; some machines are noisy. Conclusion: some pumps are noisy. The diagram can place the pump circle inside the machine circle away from the noisy part, so the conclusion does not follow.

5. Arrangements, directions and relations

For seating and ranking puzzles, draw the line or circle first and fix the most constrained person.

For directions, draw a coordinate sketch: north up, east right, and compute displacement with Pythagoras. A man who walks 5 km north, 12 km east, then returns by the straight line, travels 13 km back.

For blood relations, build a small family tree and label gender explicitly. "Pointing to a man, a woman says he is the son of my mother's only son" resolves to son, so the man is her nephew.

6. Data sufficiency and interpretation

In data-sufficiency items you decide whether the given statements are enough. Test each statement alone first, then together. A statement that fixes the answer to a single value is sufficient, even if you do not compute the value.

For tables and graphs, read units and axis labels before any arithmetic, and use percentage change against the correct base: $\frac{\text{new}-\text{old}}{\text{old}}\times 100$.

7. Arithmetic that appears with reasoning

Worked example. A pipe fills a tank in 10 hours and another empties it in 15. Together the net rate is $\frac{1}{10}-\frac{1}{15}=\frac{1}{30}$, so the tank fills in 30 hours.

8. A time budget

Spend 30 seconds on a first look. If you cannot see the method, mark it and move on. Return only after finishing the technical items you know. A reasoning puzzle that overruns two minutes costs more than a wrong guess.

Common traps

• Treating "some" as "some, but not all". Logic reads it as "at least one".
• Using a favourable diagram for a syllogism. Use the least favourable.
• Averaging speeds arithmetically. Over equal distances, use the harmonic mean.
• Reading a percentage against the wrong base. Always divide by the old value.
• Over-investing in one puzzle when two simpler items wait.

Memory aids

• "Difference, ratio, second difference, interleave": the series checklist.
• "Least favourable diagram": the syllogism test.
• "ab over a plus b": two workers together.

Summary

Reasoning questions are short and rule-driven. A fixed checklist for series, a Venn diagram for every syllogism, a sketch for every direction or relation puzzle, and four arithmetic rules cover nearly all of them.

The aim is speed. Done in about 40 seconds each, they free minutes for technical items.

Exam protocol

• Do reasoning items first, to bank time.
• Draw before you think, for arrangements, directions and syllogisms.
• Skip any item that passes two minutes.
• Guess only after removing two options.