How Aptitude Tests Work and How to Prepare

Almost every campus placement process starts with an online aptitude test. It is a filter: it cuts a large applicant pool to a manageable one, usually before any human reads your resume. The questions are not hard, but the time pressure is. This chapter explains the typical structure, the topics, the scoring habits that matter, and a preparation plan, then sets up the conventions used in the rest of the track.

1. What a typical test looks like

Formats vary by company and year, so always check the current pattern in the official hiring announcement or on the company's careers page. The usual building blocks are:

Many tests are adaptive in time, not in difficulty: each section has its own timer, and you cannot return to a finished section. Some use negative marking (often one third or one quarter of a mark for a wrong answer); others have none. Read the instructions before you start, because the right strategy depends on it.

2. The scoring logic

Let $n$ be the number of options, $m$ the marks per correct answer and $p$ the penalty for a wrong one. If you can eliminate no options, guessing has expected value

$E=\frac{m}{n}-\frac{(n-1)p}{n}$

With four options, one mark for a correct answer and a quarter-mark penalty, a blind guess has expected value $0.25-0.1875=+0.0625$: slightly positive. With a one-third penalty it is exactly zero. If you can eliminate one option confidently, guessing becomes clearly worthwhile in both cases.

def guess_value(options, correct_marks, penalty):
    return correct_marks / options - penalty * (options - 1) / options

assert abs(guess_value(4, 1, 0.25) - 0.0625) < 1e-12
assert abs(guess_value(4, 1, 1 / 3)) < 1e-12            # a one-third penalty makes a blind guess worth exactly nothing
assert abs(guess_value(3, 1, 1 / 3) - 1 / 9) < 1e-12     # after eliminating one option, a guess is worth about +0.11 per attempt
assert guess_value(2, 1, 1 / 3) > guess_value(3, 1, 1 / 3) > guess_value(4, 1, 1 / 3)     # every option you remove raises the value of guessing

3. Time management

Time per question is the real constraint. A test with 30 questions in 30 minutes leaves 60 seconds each, including reading.

1. Do a quick first pass. Spend at most 10 to 15 seconds deciding whether a question is "easy now", "doable but long" or "skip".
2. Answer the easy ones first. Marks per minute is what matters.
3. Set a hard cap (about 1.5 times the average time) after which you move on.
4. Use elimination. Often two options can be discarded by estimating the size or the last digit of the answer.
5. Leave the last few minutes for flagged questions, never for new heavy ones.
6. Do not get stuck at the start of a section. You can lose ten minutes on one problem and not recover.

def seconds_per_question(minutes, questions, reading_overhead=5):
    return (minutes * 60) / questions - reading_overhead

assert seconds_per_question(30, 30) == 55.0              # 60 s on the clock, 5 s spent reading
assert seconds_per_question(25, 25, reading_overhead=0) == 60.0

4. How to prepare: a plan

The method that works: learn the concept, solve untimed, then solve timed, then review mistakes. Keep an error log with three columns: the question type, why you missed it (concept gap, calculation slip, misread, time), and the fix. Revisit it weekly; the same few mistakes usually cost most of your marks.

5. Speed comes from calculation fluency

Much of the "difficulty" is arithmetic speed. Memorise:

• Squares to 30, cubes to 15, primes to 100.
• Fraction and percentage equivalents: $\frac{1}{2}=50\%$, $\frac{1}{3}=33.33\%$, $\frac{1}{4}=25\%$, $\frac{1}{5}=20\%$, $\frac{1}{6}=16.67\%$, $\frac{1}{7}\approx 14.29\%$, $\frac{1}{8}=12.5\%$, $\frac{1}{9}\approx 11.11\%$, $\frac{1}{10}=10\%$, $\frac{1}{11}\approx 9.09\%$, $\frac{1}{12}\approx 8.33\%$.
• Multiplication tables to 20 and the square-near-a-base trick below.
• Divisibility rules (see the number system chapter).

from fractions import Fraction

table = {2: 50, 3: 100 / 3, 4: 25, 5: 20, 6: 100 / 6, 8: 12.5, 10: 10}
assert all(abs(100 / d - p) < 1e-9 for d, p in table.items())
assert round(100 / 7, 2) == 14.29 and round(100 / 9, 2) == 11.11 and round(100 / 11, 2) == 9.09 and round(100 / 12, 2) == 8.33
assert Fraction(3, 8) * 100 == Fraction(75, 2)           # 3/8 = 37.5 %, useful in profit and discount questions

Quick squares and products

For a number near a base such as 50 or 100:

• $a^2$ near 50: $(50+d{)}^2=2500+100d+d^2$. So $47^2=2500-300+9=2209$.
• Numbers ending in 5: $(10a+5{)}^2=a(a+1)$ followed by 25. So $35^2=3\times 4=12$, then 25: 1225.
• $(a+b)(a-b)=a^2-b^2$: $48\times 52=50^2-2^2=2496$.
• Multiplying by 11: add adjacent digits; $63\times 11=6(6+3)3=693$.

assert 47 ** 2 == 2500 - 100 * 3 + 9 == 2209
assert all((10 * a + 5) ** 2 == int(f"{a * (a + 1)}25") for a in range(1, 20))
assert 48 * 52 == 50 ** 2 - 2 ** 2 == 2496
assert 63 * 11 == 693 and 78 * 11 == 858                  # 7+8 = 15: carry the 1 into the hundreds place

6. Estimation and elimination

Many options differ in size or last digit. Before computing exactly:

• Round and estimate; discard options that are far off.
• Check the last digit of the product or sum.
• Check divisibility (the answer to "how many people" must be a whole number).
• Substitute the options back into the question when they are simple numbers.
• Use unit sanity: a percentage cannot exceed 100 in a "percentage of" question about a part.

# last-digit elimination: 47 * 38 ends in 6 (7 * 8 = 56), so among 1782, 1786, 1790 and 1795 only 1786 can be right
options = [1782, 1786, 1790, 1795]
assert [o for o in options if o % 10 == (47 * 38) % 10] == [1786]
assert 47 * 38 == 1786

7. Common reasons people lose marks

• Misreading ("not", "at least", "except", "per cent of what").
• Unit slips: minutes versus hours, km/h versus m/s.
• Spending too long on one question.
• Fatigue and panic after a bad start; take one breath and reset.
• Silly arithmetic: carry mistakes; write intermediate steps for anything non-trivial.
• Skipping the instructions about negative marking and navigation.
• Not practising on the actual interface (calculator rules, rough work policy, on-screen keyboard).

8. Conventions in this track

• Each chapter gives the concepts and formulas, then worked examples with a clear method, shortcuts, common traps and a practice set with verified answers.
• Worked answers were checked by computation. If you ever disagree with an answer, re-read the wording of the question first, since small wording changes alter the result.
• Money is in rupees (₹ written as Rs). Percentages are written with the percent sign.
• Where a company's actual pattern matters, treat the examples as representative practice, not as leaked or exact questions.

9. Practice questions

1. A test has 4 options, +1 for correct and -1/3 for wrong. What is the expected value of a blind guess? What if you can eliminate one option?
2. You have 40 questions in 35 minutes. What average time per question is available?
3. Compute $65^2$, $48\times 52$ and $73\times 11$ without a calculator.
4. Convert $\frac{5}{8}$, $\frac{7}{12}$ and $\frac{2}{7}$ to percentages.

assert abs(guess_value(4, 1, 1 / 3)) < 1e-12 and guess_value(3, 1, 1 / 3) > 0
assert round(35 * 60 / 40, 2) == 52.5                               # 52.5 seconds each
assert 65 ** 2 == 4225 and 48 * 52 == 2496 and 73 * 11 == 803
assert (62.5, round(58.333333, 2), round(28.571428, 2)) == (5 / 8 * 100, round(7 / 12 * 100, 2), round(2 / 7 * 100, 2))

Answers: 0 for a blind guess, and about $+0.11$ after eliminating one; 52.5 seconds; 4225, 2496, 803; 62.5%, 58.33%, 28.57%.