Analytical Aptitude

Analytical Aptitude is the reasoning half of General Aptitude: logic, deduction and induction, analogy, numerical relations and constraint puzzles. It carries part of the 15 marks that every GATE paper allots to General Aptitude, and it is the part most amenable to method.

Every question in this area has the same underlying shape. You are given a set of constraints, and the answer is whatever survives all of them. Nothing is discovered by insight; things are eliminated by rules.

That reframing has a practical consequence. The difficulty of an analytical question is almost entirely a question of representation. A seating puzzle written out in sentences is hard; the same puzzle drawn as a circle with eight positions is easy. A blood-relation chain described in words is hard; drawn as a family tree with two symbols for gender it is trivial.

So the discipline is: choose the diagram before doing any reasoning, place the most restrictive constraint first, and let the remaining constraints eliminate.

The second principle is that validity is not plausibility. In a deduction question, a conclusion follows only if it must be true whenever the premises are true. Whether it is true in the world, or sensible, or what a reasonable person would do, is irrelevant and is exactly what the wrong options appeal to.

1. Deduction and Induction

GATE names both explicitly in its syllabus, and the distinction decides what counts as a correct answer.

Deduction moves from general to particular and preserves certainty. If all A are B and x is an A, then x is a B, with no room for doubt. A valid deduction cannot have true premises and a false conclusion.

Induction moves from particular to general and preserves only likelihood. Observing that every swan examined so far is white supports but does not establish that all swans are white.

The examinable consequence is that a deduction question asks what must follow, while an induction or inference question asks what is best supported. An option that is merely reasonable loses in the first case and can win in the second.

Validity and truth are independent. The argument "All birds can fly; a penguin is a bird; therefore a penguin can fly" is perfectly valid and has a false conclusion, because a premise is false. Questions exploit this by supplying premises that are obviously false in reality, and candidates reject valid conclusions for being untrue.

2. Syllogisms

Four statement forms cover the entire topic, and each permits exactly one conversion.

"All A are B" never gives "All B are A". This single confusion accounts for more errors here than everything else combined.

Two structural checks eliminate most questions before any diagram is drawn. Two negative premises yield no conclusion, because negatives only exclude and never establish that anything exists in a shared region. Two particular premises — both beginning with "some" — likewise yield nothing, since two separate overlaps need not touch each other.

When the premises do permit something, the reliable method is to hunt for the arrangement that breaks a candidate conclusion rather than one that supports it. Draw the premises as regions, then push the circles as far apart as the premises allow. A conclusion follows only if it survives every permitted arrangement, so a single counter-arrangement settles it.

Either-or conclusions are the one place two individually invalid conclusions combine into a valid pair. The pair is valid when the two options exhaust the possibilities and neither alone is certain — typically when the premises leave exactly two arrangements, one making the first conclusion true and the other the second.

3. Assumptions, Conclusions and Courses of Action

These three question types look similar and are decided by different tests.

An assumption is something the argument takes for granted and needs in order to work. The test is negation: if denying the candidate assumption destroys the argument, it is an assumption; if the argument survives, it is not.

A conclusion must be derivable from the statement alone. Additional information, however plausible, disqualifies it. This is the same discipline as comprehension: the passage is the universe.

A course of action is judged on whether it addresses the stated problem and is practically implementable. Options that are drastic, that address a different problem, or that assume authority nobody has, fail even when they would work.

A worked distinction makes the difference concrete. Given "The college has decided to install CCTV cameras in all laboratories":

• An assumption is that the cameras will deter or record the behaviour the college is worried about.
• A conclusion would be that the college has some concern about laboratory conduct.
• A course of action would be to also brief students on the policy.

4. Strengthen, Weaken and Flawed Reasoning

Critical-reasoning questions present a short argument and ask what supports or undermines it.

Locate the conclusion first, then the evidence, then the gap between them. Every strengthener closes that gap and every weakener widens it, so naming the gap explicitly makes the options sort themselves.

The commonest gaps repeat and are worth recognising by name.

An option that merely restates the conclusion does not strengthen it, and an option that attacks a premise's phrasing rather than the inference does not weaken it. Both are standard distractors.

For flawed-reasoning questions, the answer names the structural error rather than disputing the content. Circular reasoning, denying the antecedent, and affirming the consequent are the three that appear.

Affirming the consequent deserves a note because programmers meet it constantly. From "if the program compiles then the syntax is correct" and "the syntax is correct", nothing follows about compilation.

5. Arrangements and Ordering

Seating, ranking and scheduling puzzles are the most representation-sensitive questions in the section.

Draw the frame first. A row of six seats, a circle of eight, a table with two columns. Then place the most restrictive constraint, which is usually an absolute position or an adjacency, before any relative one.

Three conventions prevent the commonest errors.

In a circular arrangement facing the centre, left and right are reversed relative to how they look on the page. Facing outward, they read normally. Half of all circular-arrangement errors come from this alone, and the fix is to write the direction convention on the diagram before starting.

"Between" does not mean "immediately between" unless the question says so. Treat it as an ordering constraint, not an adjacency, unless the word immediately or exactly appears.

A constraint of the form "A is not adjacent to B" is often more powerful than a positive one, because it eliminates several arrangements at once. Applying negative constraints early rather than last saves substantial time.

For ordering by rank, height or marks, draw a single line and place items relative to each other. Note carefully whether the question counts from the top or the bottom, since "third from the top in a group of nine" is "seventh from the bottom", and the off-by-one is a standard trap.

6. Blood Relations

Draw a family tree with a fixed convention: males as squares, females as circles, a horizontal line for marriage, a vertical line for descent, and siblings on the same horizontal level.

Work strictly from the speaker outwards, one relation at a time. "The father of my son's mother" is resolved by finding my son, then his mother, then her father — three steps, no shortcuts.

Two traps recur. Gender is often unstated and unknowable, and a question whose answer requires knowing whether a person is male or female may be unanswerable by design. And "brother-in-law" and similar terms have several distinct meanings — a spouse's brother, a sister's husband, or a spouse's sister's husband — so a question using them usually admits more than one tree unless it says which.

Coded relation puzzles use symbols such as "A + B means A is the father of B". These are solved by substituting the code definitions into the expression from the innermost operation outwards, exactly as an expression is evaluated.

7. Directions and Distances

Fix north at the top of the page and draw each leg as a vector.

Left and right turns are relative to the direction currently faced, which is why the diagram must be drawn rather than tracked mentally. A person facing south who turns left is facing east, not west.

The final displacement is a straight line from start to finish, so net horizontal and net vertical displacements are computed separately and combined by Pythagoras.

Recognise the standard triples, since almost every such question is constructed around one: 3-4-5, 5-12-13, 8-15-17. If your legs come out as 9 and 12, the answer is 15.

A shadow-based direction question uses one fact: the sun rises in the east and sets in the west, so a morning shadow falls towards the west and an evening shadow towards the east. At noon the shadow is shortest and points north or south depending on hemisphere and season, which is why questions stay away from noon.

8. Coding, Decoding and Numerical Relations

Letter coding works on positional shifts. Knowing the alphabet's positions both forwards and backwards is what makes these fast.

The complement of a letter's position is 27 minus its position, so A pairs with Z, B with Y, and M with N. This "opposite letter" relation appears constantly.

The systematic approach is to write the plaintext and the code one above the other, compute the shift for each letter, and check whether the shift is constant, alternating, or increasing.

For number-and-symbol codes, treat the mapping as a function and test it on every given pair before applying it to the target. A rule that fits two examples and fails a third is not the rule, and testing all given pairs before answering prevents the commonest error in this area.

Numerical-relation questions in GATE frequently take the form of a defined operator: "a * b means a squared minus b". These are solved by direct substitution, working from the innermost bracket outwards, and the only difficulty is order of operations.

9. Clocks and Calendars

Both topics reduce to arithmetic on a fixed rate.

The minute hand gains 5.5 degrees per minute on the hour hand. The hour hand moves 0.5 degrees per minute and the minute hand 6 degrees per minute, so the angle between them at $h$ hours and $m$ minutes is

$\theta =|30h-5.5m|$

taking the smaller of $\theta$ and $360-\theta$.

The hands coincide 11 times in 12 hours, not 12, because between 11 o'clock and 1 o'clock they coincide only once, at 12. They are at right angles 22 times in 12 hours.

For calendars, work in odd days, the remainder when a day count is divided by 7. An ordinary year has 365 days and therefore 1 odd day; a leap year has 2.

A century has 5 odd days, and 400 years has 0, which is why the calendar repeats exactly every 400 years.

The leap-year rule is divisible by 4, except centuries, unless divisible by 400. So 1900 was not a leap year and 2000 was, and questions are constructed specifically around this exception.

10. Data Sufficiency

A data-sufficiency question gives a question and two statements, and asks whether each alone, both together, or neither suffices.

The task is to decide whether the answer is determined, not to compute it. Computing wastes time and, worse, tempts you to combine information from both statements while evaluating one.

The discipline is to evaluate statement I completely, then deliberately forget it before evaluating statement II. Carrying information across is the single commonest error, and it produces the wrong answer in exactly the cases the question was designed to test.

A statement is sufficient when it forces a unique answer, not when it produces a plausible one. If two different values are consistent with the statement, it is insufficient, and finding two such values is the fastest way to prove insufficiency.

11. Worked Examples

Example 1. Statements: All engineers are graduates. Some graduates are researchers. Conclusions: (I) Some engineers are researchers. (II) Some researchers are graduates. Which follows?

Take them separately.

Conclusion II is the valid conversion of "Some graduates are researchers", so it follows.

Conclusion I does not. Arrange the regions so that the researcher circle overlaps the graduate circle entirely outside the engineer region. Both premises remain satisfied and conclusion I is false, so it is not forced.

The answer is that only II follows.

The trap is that conclusion I is plausible — in the real world some engineers certainly are researchers — and plausibility is not what the question asks about.

Example 2. Six people A, B, C, D, E, F sit in a row facing north. C is at one end. B is immediately to the right of D. A is third from the left. E is not adjacent to A. Where does F sit?

Draw six positions numbered 1 to 6 from left to right.

A is at position 3. C is at an end, so position 1 or 6.

B is immediately right of D, so DB occupies consecutive positions: (1,2), (4,5) or (5,6).

If DB is at (1,2), then C must be at 6, leaving positions 4 and 5 for E and F. But E cannot be adjacent to A at position 3, so E cannot be at 4, giving E at 5 and F at 4.

Check the alternatives. If DB is at (4,5), then C is at 1 or 6 and E and F take the remaining two of 2 and 6. E cannot be at 2, since 2 is adjacent to 3. So E is at 6, which forces C to 1 and F to 2. This is also consistent.

Two consistent arrangements exist, so the puzzle as stated does not fix F uniquely — which is itself the point worth noticing. In an exam, a second consistent arrangement means a constraint has been misread, and the usual culprit is treating "between" as "immediately between" or forgetting that an end can be either end.

Example 3. Pointing to a photograph, a man says, "She is the daughter of the only son of my grandmother." How is she related to him?

Work outwards from the speaker, one step at a time.

"My grandmother" — the speaker's grandmother.

"The only son of my grandmother" — since she has only one son, and the speaker descends from her, that son is the speaker's father.

"The daughter of my father" — that is the speaker's sister.

She is his sister.

Note what the word "only" is doing: without it, the grandmother's son could be an uncle, and the woman would be a cousin. Removing a single word changes the answer, which is why these questions must be read literally.

Example 4. A man walks 10 km north, turns right and walks 6 km, turns right again and walks 4 km. How far is he from his starting point, and in which direction?

Draw north upward. The first leg is 10 km up.

Turning right while facing north means facing east, so the second leg is 6 km east.

Turning right again means facing south, so the third leg is 4 km south.

Net vertical displacement is 10 north minus 4 south, which is 6 km north. Net horizontal displacement is 6 km east.

The straight-line distance is the hypotenuse of a 6 by 6 triangle, which is $6\sqrt{2}$, approximately 8.49 km, and the direction is north-east.

The reason the diagram is not optional is the second turn. A person facing east who turns right faces south, and tracking that mentally while also tracking distances is where errors enter.

Example 5. At what time between 3 and 4 o'clock are the hands of a clock at right angles?

At exactly 3 o'clock the hour hand is at 90 degrees and the minute hand at 0.

Use the angle formula with $h=3$: the angle is $|90-5.5m|$, and we need this to equal 90.

Either $90-5.5m=90$, giving $m=0$, which is the trivial 3 o'clock position where the hands are already at right angles.

Or $5.5m-90=90$, giving $5.5m=180$ and $m=32\frac{8}{11}$.

So the hands are again at right angles at about 3:32:44.

Both answers are correct, and a question asking "at what time between 3 and 4" usually intends the second. This is worth checking against the options, since 3 o'clock itself is a boundary the question may or may not include.

Example 6. Data sufficiency. What is the value of the integer $n$? Statement I: $n$ is a multiple of 6. Statement II: $n$ is a two-digit number whose digits sum to 9 and which is even.

Evaluate statement I alone. Multiples of 6 include 6, 12, 18 and infinitely many others, so it is insufficient.

Now forget statement I entirely and evaluate statement II alone. Two-digit numbers with digit sum 9 are 18, 27, 36, 45, 54, 63, 72, 81 and 90. Keeping only the even ones leaves 18, 36, 54, 72 and 90. Five candidates remain, so statement II alone is insufficient.

Together: the numbers surviving statement II are 18, 36, 54, 72 and 90, and every one of them is already a multiple of 6, since 18 = 6 times 3, 36 = 6 times 6, 54 = 6 times 9, 72 = 6 times 12 and 90 = 6 times 15.

So statement I adds nothing, and even together the two statements leave five possibilities. The answer is that the data are insufficient even when combined.

The instructive part is that combining statements does not always narrow anything. A candidate who assumed that two constraints must be more restrictive than one would have chosen the wrong option without checking.

Summary

Every analytical question gives constraints and asks what survives all of them, so choose the representation before reasoning.

Deduction preserves certainty and asks what must follow; induction preserves likelihood and asks what is best supported. Validity and truth are independent.

"All A are B" converts only to "Some B are A". Two negative or two particular premises yield nothing. Find the arrangement that breaks a conclusion, not one that supports it.

An assumption is tested by negation, a conclusion must be derivable from the statement alone, and a course of action must address the stated problem practically.

In critical reasoning, name the gap between evidence and conclusion; strengtheners close it and weakeners widen it.

For arrangements, draw the frame, place the most restrictive constraint first, and write the facing convention down before using left and right in a circle.

For blood relations, draw the tree and work outward one step at a time, reading words like "only" literally.

For directions, draw each leg as a vector, remember that turns are relative to the current facing, and recognise the standard Pythagorean triples.

The clock-hand angle is $|30h-5.5m|$, and calendars reduce to odd days with 1 for an ordinary year and 2 for a leap year.

In data sufficiency, decide whether the answer is determined rather than computing it, and evaluate each statement in complete isolation.