IRDAI Assistant Manager Quantitative Aptitude and Data Interpretation Syllabus

State the fundamental relation between speed, distance and time, and the units conversion between km/h and m/s.

Speed = Distance / Time, so Distance = Speed x Time and Time = Distance / Speed. To convert km/h to m/s multiply by 5/18; to convert m/s to km/h multiply by 18/5.

How do you compute the time for a train of length L to pass a stationary pole versus a platform of length P?

To pass a pole, the train covers its own length L: time = L / speed. To pass a platform, it covers L + P: time = (L + P) / speed.

How do you find relative speed for two trains moving in the same direction and in opposite directions?

Same direction: relative speed = difference of speeds (s1 - s2). Opposite directions: relative speed = sum of speeds (s1 + s2). Time to cross = combined length / relative speed.

What is the average speed for a journey covering equal distances at speeds x and y?

Average speed = 2xy / (x + y), the harmonic mean. This is not the simple arithmetic average of the two speeds.

If A can do a work in 'a' days and B in 'b' days, how long do they take working together?

Combined time = ab / (a + b) days, because together they do (1/a + 1/b) of the work per day.

In pipes and cisterns, how do you handle an inlet pipe and an outlet (leak) pipe acting together?

Treat filling as positive work and emptying as negative. Net rate per hour = (1/inlet time) - (1/outlet time); the tank fills if this is positive, and time = 1 / net rate.

State the alligation rule for mixing two ingredients of prices (or concentrations) c (cheaper) and d (dearer) to get mean m.

Quantity of cheaper : Quantity of dearer = (d - m) : (m - c). The mean value lies between the two ingredient values, and the ratio is the cross-difference.

A vessel of milk has x litres removed and replaced by water, repeated n times; what fraction of milk remains?

Milk remaining = Initial x (1 - x/V)^n, where V is the vessel's total capacity. The replacement formula applies each time the same volume is drawn and refilled.

If the ratio of present ages of A and B is given, how do you set up an ages problem and use it later?

Let the ages be common multiples (e.g. 5x and 3x). Add or subtract the given number of years to each, then form an equation from the second condition and solve for x.

How is the average of a set of numbers defined, and how does it change when one value is added or removed?

Average = Sum of values / Number of values. New average after adding a value = (old sum + new value) / (old count + 1); removing works similarly by subtracting the value and reducing the count.

In partnership, how are profits shared when partners invest different amounts for different periods?

Profit is shared in the ratio of each partner's capital x time invested. E.g. A invests Rs P1 for t1 months, B invests P2 for t2 months; ratio = P1 x t1 : P2 x t2.

State the formulas for the number of permutations and combinations of n objects taken r at a time.

Permutations nPr = n! / (n - r)! (order matters). Combinations nCr = n! / [r!(n - r)!] (order does not matter). Relation: nPr = nCr x r!.

What is the classical (theoretical) definition of probability of an event?

Probability P(E) = (Number of favourable outcomes) / (Total number of equally likely outcomes). It always lies between 0 and 1 inclusive, where 0 is impossible and 1 is certain.

State the addition rule of probability for events A and B.

P(A or B) = P(A) + P(B) - P(A and B). For mutually exclusive events, P(A and B) = 0, so P(A or B) = P(A) + P(B).

For independent events A and B, what is the probability that both occur?

P(A and B) = P(A) x P(B) when A and B are independent (the occurrence of one does not affect the other).

State the area and perimeter/circumference formulas for a rectangle, triangle, and circle.

Rectangle: area = length x breadth, perimeter = 2(l + b). Triangle: area = 1/2 x base x height. Circle: area = pi r^2, circumference = 2 pi r.

State the volume and total surface area of a cube and a cuboid.

Cube (side a): volume = a^3, total surface area = 6a^2. Cuboid (l x b x h): volume = lbh, total surface area = 2(lb + bh + hl).

State the volume, curved surface area and total surface area of a cylinder.

Cylinder (radius r, height h): volume = pi r^2 h, curved surface area = 2 pi r h, total surface area = 2 pi r (r + h).

State the volume and surface area of a sphere of radius r.

Sphere: volume = (4/3) pi r^3, surface area = 4 pi r^2. A hemisphere has volume (2/3) pi r^3 and total surface area 3 pi r^2.

State the quadratic formula and what the discriminant tells you about the roots.

For ax^2 + bx + c = 0, x = [-b +/- sqrt(b^2 - 4ac)] / 2a. Discriminant D = b^2 - 4ac: D > 0 gives two real distinct roots, D = 0 gives equal real roots, D < 0 gives no real (complex) roots.

For ax^2 + bx + c = 0, what are the sum and product of the roots?

Sum of roots = -b/a and product of roots = c/a. These let you build or analyse a quadratic without solving it directly.

In comparing two quantities in banking exams (e.g. x from one equation, y from another), what are the possible inequality conclusions?

After solving both equations, compare: x > y, x < y, x >= y, x <= y, or 'relationship cannot be established / x = y'. You must check all root combinations before concluding.

What is the general formula for the nth term and sum of an arithmetic progression (AP)?

nth term: a_n = a + (n - 1)d. Sum of n terms: S_n = n/2 [2a + (n - 1)d] = n/2 (first term + last term), where a = first term and d = common difference.

What is the general formula for the nth term and sum of a geometric progression (GP)?

nth term: a_n = a r^(n-1). Sum of n terms: S_n = a(r^n - 1)/(r - 1) for r not equal to 1. Sum to infinity (|r| < 1) = a / (1 - r).

In a Tabular DI set, what is the standard first step before attempting the questions?

Read the table headings, units, and row/column labels carefully to understand what each cell represents, and note any totals or footnotes. Misreading units (e.g. lakhs vs thousands) is the most common error.

In a Line Graph DI, how do you read the percentage increase or decrease between two years?

Percentage change = (later value - earlier value) / earlier value x 100. A rising line means increase, a falling line means decrease; the steepness shows the rate of change, not the actual values.

In a Bar Graph DI comparing two categories per period, what does the difference in bar heights represent?

It represents the absolute difference between the two categories for that period. To find percentage difference, divide that difference by the base category's value and multiply by 100.

In a Pie Chart DI, how do you convert a sector to a value and a degree to a percentage?

Each sector's percentage of the whole = its central angle / 360 x 100. Its value = (sector percentage) x total. Conversely, degrees = (percentage/100) x 360.

What characterises a Caselet (paragraph-based) DI, and how should you approach it?

A Caselet presents data in a paragraph of text rather than a chart, often requiring you to extract figures and build your own table or Venn diagram. The key step is to organise the scattered numerical data into a structured form before solving.

What is a Missing/Comparative DI, and what skill does it test?

In Missing DI some values are blank and must be derived from totals, ratios, or given relationships before answering. Comparative DI asks you to compare data across two or more datasets/charts. Both test data interpretation plus deriving values from interlinked clues.

In Data Sufficiency, what do the standard answer options mean and how do you evaluate the statements?

You judge whether each statement alone, or both together, suffice to answer; you do NOT compute the final value. Typical options: (A) Statement I alone sufficient, (B) Statement II alone sufficient, (C) both together sufficient but neither alone, (D) each alone sufficient, (E) both together not sufficient. Evaluate each statement independently first, then combined.