General Aptitude

Percentages, mixtures, work rates, speeds and scale factors are all the same idea in different clothing. Once a question is set up as a proportion, the arithmetic is trivial; nearly all the errors happen before that, in deciding what the base quantity is.

That result is worth remembering as a caution: a rise followed by an equal fall does not return to the start, because the second change acts on a different base.

Alligation handles mixtures in one line. To find the ratio in which two components at concentrations c and d must be mixed to give a mean C:

Ratios also handle proportional division, partnership profits and scale problems. If a quantity is divided in the ratio 3 : 4 : 5, the parts are 3/12, 4/12 and 5/12 of the whole — write the denominator as the sum of the parts and there is nothing left to get wrong.

Work. Convert everyone to a rate per unit time, then add the rates. Never average the times.

For questions with people joining and leaving, work in fractions of the job completed rather than in days — it keeps the bookkeeping straight, as in worked example 1.

Speed. Average speed is total distance over total time, always. Which mean that reduces to depends on what is held equal:

Relative speed. Add when closing, subtract when moving the same way. For trains or objects with length, the distance covered is the sum of the lengths when passing each other, or one length when passing a fixed point.

Boats and streams are the same idea: downstream speed is boat plus current, upstream is boat minus current, and the two together let you solve for either unknown.

The first decision is always whether order matters. If it does, permutations; if not, combinations.

Then look for a restriction, because that is where the question actually lives. Three techniques cover most of them:

• Complement. "At least one" is nearly always faster as 1 − P(none).
• Glue. If two items must sit together, treat them as one item and multiply by the number of internal arrangements.
• Gap method. If two items must not sit together, arrange the others first and place the restricted items in the gaps between them.

Keep two distinctions clear. Mutually exclusive is not independent — mutually exclusive events cannot both happen, so knowing one occurred tells you a great deal about the other. And with replacement versus without changes whether the probabilities stay constant between draws.

A chart or table with three or four questions attached. The marks are quick, and they are lost to carelessness rather than difficulty.

Read the axes and the units before reading the question — figures given in lakhs, in percentages of a total that itself changes, or on a logarithmic scale are all standard misdirections. Then check whether the question asks for an absolute value or a change, and whether that change is in absolute terms or as a percentage.

The most common trap is the percentage of a moving base: a segment whose share falls from 40 % to 35 % may still have grown in absolute terms, if the total grew faster. Whenever a question mixes shares and totals, convert to absolute numbers first.

Estimate before computing. Most data interpretation options are far enough apart that a rough figure identifies the answer, and the exact calculation is only needed when two options are close.

Roughly half the aptitude section, and the part engineering candidates most often leave to chance.

Reading comprehension and inference. The correct option is the one that cannot be false given the passage. Anything requiring an extra assumption, however reasonable, is wrong. Options that are true in the world but not supported by the passage are the standard distractor.

Word usage. Learn confusable pairs rather than long vocabulary lists — principal and principle, affect and effect, comprise and compose, complement and compliment, discreet and discrete, imply and infer. These recur far more than obscure words do.

Grammar. The recurring items are subject–verb agreement across an intervening phrase, misplaced modifiers, parallel structure in lists, and tense consistency. Read the sentence aloud in your head — most errors are audible.

Critical reasoning. Identify the conclusion first, then the evidence offered for it, then ask what the argument assumes to get from one to the other. A question asking to strengthen or weaken an argument is asking about that assumption, not about the conclusion.

The aptitude section is worth 15 of 100 marks — as much as several core chapters together — and it is the most predictable part of the paper.

• Do it early, while your reading is sharp and before time pressure builds. Candidates who leave it for the last twenty minutes lose marks they could have taken in ten.
• Respect the negative marking. Aptitude MCQs carry the same penalty as subject questions. Eliminate rather than guess blindly: two options gone makes a guess worth taking, none gone does not.
• Numerical answer type questions carry no penalty. Attempt every one of them, whatever your confidence.
• Watch the units. Lakhs and crores, km/h and m/s, percentage points and percentages — the arithmetic is easy and the units are where the marks go.

Three problems in the style GATE sets, each with the wrong answer the question is designed to attract.