NABARD Grade A Quantitative Aptitude Syllabus

What is the formula for Compound Interest (amount and interest) compounded annually?

Amount A = P(1 + R/100)ᵀ; Compound Interest = A − P, where P = principal, R = rate, T = time in years.

What is the difference between CI and SI for 2 years on the same principal and rate?

Difference = P(R/100)². This represents the interest earned on the first year's interest.

What is the relationship between discount, marked price, and selling price?

Discount = Marked Price − Selling Price; Discount% = (Discount / Marked Price) × 100; SP = MP × (100 − Discount%)/100.

What is the basic work-rate relationship in time and work problems?

Work = Rate × Time. If a person completes a job in n days, their one-day work (rate) = 1/n. Combined rate of multiple workers is the sum of individual rates.

If A can do a job in x days and B in y days, how long do they take working together?

Together they take xy/(x + y) days, since their combined rate is 1/x + 1/y.

What is the basic formula relating speed, distance, and time?

Speed = Distance / Time. Therefore Distance = Speed × Time and Time = Distance / Speed.

How do you convert speed from km/hr to m/s and vice versa?

km/hr to m/s: multiply by 5/18. m/s to km/hr: multiply by 18/5.

In relative speed, how do you handle two objects moving in the same versus opposite directions?

Opposite directions: relative speed = sum of speeds. Same direction: relative speed = difference of speeds.

How long does a train of length L take to cross a platform of length P at speed S?

Time = (L + P) / S. The train must cover its own length plus the platform length.

What is the formula for average speed when equal distances are covered at speeds x and y?

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

What is the formula for the average of a set of values?

Average = (Sum of all observations) / (Number of observations).

If the average of n numbers is A and a new number is added making the average A', how does the total change?

New total = (n + 1) × A'; the added number = (n + 1)A' − nA. The change in average × count reflects the new value's deviation.

A common problem type: how does the average age of a group change when a member is replaced?

Change in total age = (number of members) × (change in average). The new member's age = old member's age ± (n × change in average).

What is the alligation/mixture rule for finding the ratio of two ingredients?

(Quantity of cheaper)/(Quantity of dearer) = (Price of dearer − Mean price)/(Mean price − Price of cheaper). The mean lies between the two component values.

In a mixture problem, if x liters are removed from a container of milk and replaced with water n times, what fraction of milk remains?

Remaining milk fraction = (1 − x/V)ⁿ of the original, where V is the total volume and x is removed each time.

What is Data Interpretation (DI) and what is the first step in solving a DI set?

DI involves analyzing data presented in tables, bar/line/pie charts, or graphs to answer questions. The first step is to carefully read the data, units, headings, and what is asked before calculating.

In a pie chart DI, how do you convert a sector's degree measure into a percentage and value?

Percentage = (sector angle / 360) × 100; Value = (sector angle / 360) × total. Conversely, angle = (percentage/100) × 360°.

What does 'Caselet DI' refer to and how does it differ from tabular DI?

Caselet DI presents data in a paragraph/narrative form without a table or graph; the solver must extract and often tabulate the values themselves, unlike tabular DI where data is pre-organized.

In advanced/missing DI, what is the typical approach when some table values are not given?

Use the relationships, totals, percentages, or ratios provided in the question to compute the missing values step by step before answering the actual questions.

What is Data Sufficiency and how are the standard answer options structured?

Data Sufficiency asks whether given statements provide enough information to answer a question (not to find the actual answer). Typical options: (A) statement I alone sufficient, (B) II alone sufficient, (C) both together needed, (D) either alone sufficient, (E) neither sufficient.

In Data Sufficiency, why should you avoid actually computing the final numerical answer?

Because the goal is only to determine sufficiency, not the value. Fully solving wastes time; you only need to confirm a unique answer can (or cannot) be derived from each statement.

What is the standard form of a quadratic equation and the quadratic formula for its roots?

Standard form: ax² + bx + c = 0 (a ≠ 0). Roots: x = [−b ± √(b² − 4ac)] / 2a.

What does the discriminant of a quadratic equation tell you about its roots?

Discriminant D = b² − 4ac. If D > 0, two distinct real roots; if D = 0, two equal real roots; if D < 0, no real roots (complex roots).

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

Sum of roots = −b/a; Product of roots = c/a.

In comparison-type quadratic problems, after finding roots of two equations x and y, how do you state the relationship?

Compare each root of one equation with each root of the other. Possible conclusions: x > y, x < y, x ≥ y, x ≤ y, or relationship cannot be established (when ranges overlap).

What is the difference between a permutation and a combination?

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

What is the formula for the probability of an event?

Probability = (Number of favorable outcomes) / (Total number of possible outcomes), giving a value between 0 and 1.

What is the addition rule of probability for two 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).

State the formulas for area and perimeter/circumference of a circle.

Area = πr²; Circumference = 2πr, where r is the radius.

What are the formulas for the volume and total surface area of a cuboid and a cube?

Cuboid: Volume = l × b × h, TSA = 2(lb + bh + hl). Cube: Volume = a³, TSA = 6a², where a is the edge length.

What are the formulas for the volume and curved surface area of a cylinder?

Volume = πr²h; Curved Surface Area = 2πrh; Total Surface Area = 2πr(r + h), where r = radius and h = height.