FIA Recruitment Test Mathematics and Reasoning Syllabus

What is the formula for simple interest (SI)?

SI = (P × R × T) / 100, where P = principal, R = rate% per annum, T = time in years.

What is the formula for the amount under compound interest (compounded annually)?

A = P(1 + R/100)^T, where A is the final amount. Compound interest CI = A − P.

What is the key difference between simple and compound interest?

Simple interest is calculated only on the original principal each period. Compound interest is calculated on the principal plus accumulated interest, so interest earns interest.

For the same principal, rate, and time of 2 years, what is the difference between CI and SI?

Difference (CI − SI) for 2 years = P × (R/100)². This equals the interest on the first year's interest.

What is a linear equation in one variable, and what does its solution represent?

An equation of the form ax + b = 0 (a ≠ 0), where the variable has power 1. Its solution is x = −b/a, the single value satisfying the equation.

What is the standard form of a linear equation in two variables, and what does its graph look like?

ax + by + c = 0 (a, b not both zero). Its graph is a straight line in the coordinate plane.

Name two algebraic methods for solving a pair of simultaneous linear equations.

Substitution method (solve one equation for a variable and substitute) and elimination method (add/subtract equations to remove a variable). (Cross-multiplication is a third.)

How many solutions does a pair of linear equations have when the lines are parallel versus identical?

Parallel lines: no solution (inconsistent). Identical/coincident lines: infinitely many solutions (dependent). Intersecting lines: exactly one solution.

What is the HCF (Highest Common Factor) of two numbers?

The largest number that divides both numbers exactly (without remainder). Also called the Greatest Common Divisor (GCD).

What is the LCM (Least Common Multiple) of two numbers?

The smallest number that is exactly divisible by both numbers (the smallest common multiple).

What is the relationship between the HCF and LCM of two numbers a and b?

HCF × LCM = a × b. The product of two numbers equals the product of their HCF and LCM.

How do you find the HCF and LCM using prime factorization?

HCF = product of common prime factors with the lowest powers. LCM = product of all prime factors with the highest powers.

In a number series, what defines an arithmetic progression (AP) and how do you find its nth term?

An AP has a constant common difference d between consecutive terms. nth term = a + (n − 1)d, where a is the first term.

In a geometric progression (GP), what is constant, and what is the formula for the nth term?

A GP has a constant common ratio r (each term = previous × r). nth term = a × r^(n−1), where a is the first term.

What is the sum of the first n terms of an arithmetic progression?

Sₙ = (n/2)[2a + (n − 1)d], or equivalently Sₙ = (n/2)(first term + last term).

How do you identify the pattern in a number series problem?

Check the differences between consecutive terms (arithmetic), the ratios (geometric), or look for squares, cubes, primes, alternating patterns, or combined operations to find the rule.

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

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

How do you convert a speed from km/h to m/s and from m/s to km/h?

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

For two objects moving toward each other or in the same direction, how do you compute relative speed?

Opposite directions (approaching): add the speeds. Same direction: subtract the speeds. Relative speed is used for meeting/overtaking problems.

What is the average speed for a round trip of equal distances at speeds x and y?

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

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

Crossing a pole: time = L / S. Crossing a platform: time = (L + P) / S (it must cover its own length plus the platform).

If a person can complete a piece of work in n days, what fraction of the work do they do in one day?

They complete 1/n of the work per day.

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

Combined time = xy / (x + y) days. (Their combined one-day work is 1/x + 1/y.)

In time-and-work problems, what is the relationship between number of workers and time taken (for a fixed job)?

They are inversely proportional: more workers take less time. M₁ × D₁ = M₂ × D₂ (men × days are constant for the same work).

What is the standard work-equation linking men (M), days (D), hours/day (H), and work (W)?

(M₁ × D₁ × H₁) / W₁ = (M₂ × D₂ × H₂) / W₂. Used to compare two work scenarios.

In a logical letter/number sequence, what does coding-decoding test, and what is the first step to solve it?

It tests the rule mapping letters/numbers to a code. First step: determine the shift or pattern (e.g. +1 letter, reverse order, positional value) by comparing the original and coded forms.

In an alphabet-position sequence, what are the position numbers of A, M, N, and Z?

A = 1, M = 13, N = 14, Z = 26. (Knowing these reference points helps solve coding and series problems quickly.)

What is an analogy (A is to B as C is to ?) type of logical reasoning question?

It asks you to identify the relationship between the first pair and apply the same relationship to complete the second pair.

In a 'find the odd one out' (classification) question, what are you looking for?

The item that does not share the common property or pattern with the others in the group; all others belong to one category and the odd one breaks it.

In logical sequences using mirror/reverse alphabet, what letter corresponds to a letter at position n from the start?

It corresponds to the letter at position (27 − n), i.e. position n from the end. For example A↔Z, B↔Y, C↔X (since their positions sum to 27).