RBI Grade B Quantitative Aptitude and Data Interpretation Syllabus

What is the formula for average speed over two equal distances travelled at speeds x and y?

Average speed = 2xy/(x+y), the harmonic mean of the two speeds. (This applies only when the distances are equal.)

In time-and-work problems, how is one day's work used, and how do combined rates work?

If a person finishes a job in n days, their one day's work = 1/n. When several people work together, add their per-day rates; combined time = 1 ÷ (sum of rates).

How are time-and-work problems related to pipes-and-cisterns problems?

They use the same logic: an inlet pipe filling a tank in n hours does 1/n per hour (positive rate); an outlet/leak emptying it is a negative rate. Net rate = sum of inlet rates − sum of outlet rates.

What is the quadratic formula and what does the discriminant indicate?

For ax² + bx + c = 0, x = [−b ± √(b²−4ac)]/(2a). The discriminant D = b²−4ac: D>0 gives two distinct real roots, D=0 gives equal real roots, D<0 gives complex roots.

For a quadratic ax² + bx + c = 0, what are the sum and product of the roots?

Sum of roots = −b/a and product of roots = c/a.

How many solutions does a pair of linear equations a₁x+b₁y=c₁ and a₂x+b₂y=c₂ have, based on coefficient ratios?

Unique solution if a₁/a₂ ≠ b₁/b₂; infinitely many (consistent, dependent) if a₁/a₂ = b₁/b₂ = c₁/c₂; no solution (inconsistent) if a₁/a₂ = b₁/b₂ ≠ c₁/c₂.

What is the difference between a permutation and a combination?

A permutation is an arrangement where order matters; a combination is a selection where order does not matter. nPr = n!/(n−r)! and nCr = n!/[r!(n−r)!], so nPr = nCr × r!.

State the formula for the number of permutations of n objects when some are identical.

Number of distinct arrangements = n!/(p! × q! × ...), where p, q, ... are the counts of each set of identical objects.

What is the formula for circular permutations of n distinct objects?

For arrangements in a circle, the number of permutations = (n−1)!. If clockwise and anticlockwise arrangements are considered the same (e.g., a necklace), it is (n−1)!/2.

State the fundamental principle of counting (multiplication rule).

If one event can occur in m ways and a second independent event in n ways, then both can occur together in m × n ways. The rule extends to any number of successive independent choices.

What is the basic definition of the 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; P(certain) = 1, P(impossible) = 0.

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

P(A ∪ B) = P(A) + P(B) − P(A ∩ B). For mutually exclusive events, P(A ∩ B) = 0, so P(A ∪ B) = P(A) + P(B).

State the multiplication rule of probability and the condition for independence.

P(A ∩ B) = P(A) × P(B|A). If A and B are independent, P(B|A) = P(B), so P(A ∩ B) = P(A) × P(B).

What is the probability of the complement of an event, and how is it useful?

P(not E) = 1 − P(E). It is useful for 'at least one' problems: P(at least one) = 1 − P(none).

Write the formula for the nth term of an arithmetic progression (AP) and its sum.

nth term: aₙ = a + (n−1)d. Sum of first n terms: Sₙ = n/2 × [2a + (n−1)d] = n/2 × (first term + last term), where a is the first term and d the common difference.

Write the formula for the nth term of a geometric progression (GP) and the sum of n terms.

nth term: aₙ = a·r^(n−1). Sum: Sₙ = a(rⁿ−1)/(r−1) for r ≠ 1. The sum to infinity (|r|<1) is S∞ = a/(1−r).

What is the sum of the first n natural numbers, their squares, and their cubes?

Sum = n(n+1)/2; sum of squares = n(n+1)(2n+1)/6; sum of cubes = [n(n+1)/2]².

What is the relationship between arithmetic mean (AM), geometric mean (GM), and harmonic mean (HM) of two positive numbers?

AM ≥ GM ≥ HM, with equality only when the numbers are equal. Also GM² = AM × HM.

In tabular Data Interpretation, what is the recommended first step before attempting questions?

Read the table title, all row and column headings, and the units carefully; identify totals, what each cell represents, and any footnotes, before computing—so you interpret values correctly and avoid misreading units.

In graphical DI, what does a pie chart represent and how do you convert between percentage, degrees, and value?

A pie chart shows parts of a whole. Each sector's percentage = (value/total) × 100; its central angle (degrees) = percentage × 3.6, since 100% corresponds to 360°.

What is the difference between a line graph and a bar graph in DI?

A line graph shows trends or change of a variable over a continuous scale (usually time) and is best for trends; a bar graph compares discrete categories or quantities side by side and is best for comparisons of magnitude.

What is a caselet in Data Interpretation, and how does it differ from chart-based DI?

A caselet presents data in paragraph (text) form rather than a table or chart; the solver must extract and organize the data (often into a table or Venn diagram) before solving. Mixed DI combines two or more representations (e.g., table + chart) in one set.

What is the standard four-option answer convention for two-statement Data Sufficiency questions (statements I and II)?

Typically: (a) statement I alone is sufficient but II alone is not; (b) statement II alone is sufficient but I alone is not; (c) each alone is sufficient; (d) both together are needed; (e) even both together are not sufficient. The exact lettering can vary, so always read the instruction set.

In Data Sufficiency, why must you evaluate each statement independently before combining them?

Because the goal is to find the minimum information needed. Judging each statement alone first prevents 'carry-over' bias (using info from one statement while testing the other) and ensures you correctly identify whether one alone, the other alone, or only both together suffice.

What are the three common measures of central tendency, and which is most affected by extreme values?

Mean, median, and mode. The mean (arithmetic average) is most affected by extreme values/outliers; the median is resistant to outliers; the mode is the most frequently occurring value.

How do you find the median of a dataset for an odd and an even number of observations?

Arrange data in order. For an odd count n, median = the [(n+1)/2]th value. For an even count, median = the average of the (n/2)th and (n/2 + 1)th values.

What is the empirical relationship between mean, median, and mode?

Mode = 3 × Median − 2 × Mean (approximately, for moderately skewed distributions). Equivalently, Mean − Mode = 3 × (Mean − Median).

What are the main measures of dispersion, and which is the most commonly used?

Range, mean deviation, variance, standard deviation, and quartile deviation. Standard deviation (the square root of the variance) is the most widely used measure of dispersion.

Define variance and standard deviation, and state the formula for variance of a population.

Variance is the average of the squared deviations from the mean: σ² = Σ(xᵢ − x̄)²/n. Standard deviation σ = √variance. SD has the same units as the data; variance has squared units.

What is the coefficient of variation and what is it used for?

Coefficient of variation (CV) = (Standard Deviation/Mean) × 100%. It is a relative, unit-free measure of dispersion used to compare the variability of two or more datasets that have different means or units.

In quantity-comparison questions, what does the standard set of answer choices ask you to determine between Quantity I and Quantity II?

You must determine the relationship: Quantity I > Quantity II; Quantity I < Quantity II; Quantity I = Quantity II (or ≥ / ≤); or that the relationship cannot be determined from the given information. You usually solve each quantity, then compare.