Mastering Quantitative Aptitude Your Ultimate Guide
Are you feeling overwhelmed by the math section in your upcoming competitive exams? You are definitely not alone. Quantitative Aptitude is often considered the most challenging hurdle for students aiming to crack bank exams, management entrance tests, or corporate campus placements. The trick to scoring 100% in quant lies in understanding core arithmetic concepts and mastering shortcut tricks that allow you to solve complex puzzles in under 30 seconds.
Percentages form the absolute bedrock of arithmetic calculation, representing fractions as a part of 100. Mastery of this core chapter is crucial because it acts as the foundation for solving problems in profit and loss, simple interest, and data interpretation.
Sample Problem 1
If the price of an item increases by 20%, by what percentage must a householder reduce their consumption so that the overall expenditure remains exactly the same?
Solution
Let original price = 100, consumption = 100 units → initial cost = 10,000. New price = 120. New consumption to keep cost at 10,000 = 10,000 ÷ 120 = 83.33 units. Reduction = 100 − 83.33 = 16.67%.
Sample Problem 2
A student must secure 40% marks to pass. Rahul gets 185 marks and fails by 15 marks. What are the maximum total marks?
Solution
Minimum passing marks = 185 + 15 = 200. Since 200 = 40% of Total → Total = 200 ÷ 0.40 = 500.
Ratio and Proportion deals with comparing the relative sizes of two or more values, showing how many times one number contains another. It is widely used to split quantities, scale values, and simplify complex word problems.
Sample Problem 1
Divide a total sum of 1200 between A and B in the ratio 3:5. What is the exact share that B receives?
Solution
Total parts = 3 + 5 = 8. B's share = (5/8) × 1200 = 750.
Sample Problem 2
The weekly incomes of two individuals are in the ratio 9:7 and their expenses are in the ratio 4:3. Each saves 200 per week. Find the weekly income of the first person.
Solution
Let incomes = 9x and 7x; expenses = 4y and 3y. From savings: 9x − 4y = 200 and 7x − 3y = 200. Solving: x = 200. First person's income = 9 × 200 = 1800.
This subtopic covers commercial business mathematics involving cost price, selling price, profit/loss margins, and the strategic distribution of profits among business partners based on their individual investment ratios and timelines.
Sample Problem 1
A retailer buys an electronic gadget for 400 and sells it to a customer for 480. Find his net profit percentage.
Averages help find a central, balanced value within a dataset. Mixtures and Alligations provide an elegant, visual rule to quickly determine the exact proportion in which two or more distinct ingredients are mixed to achieve a specific target price or concentration level.
Sample Problem 1
In what ratio must a grocer mix tea worth 60 per kg with tea worth 65 per kg so that the blend is worth 62 per kg?
Solution
By the rule of alligation: (Dearer − Mean) : (Mean − Cheaper) = (65 − 62) : (62 − 60) = 3 : 2.
Sample Problem 2
The average weight of a class of 24 students is 35 kg. Including the teacher, the average increases by 0.4 kg. What is the teacher's weight?
Solution
New people = 25. Total weight increase = 25 × 0.4 = 10 kg. Teacher's weight = 35 + 10 = 45 kg.
This high-frequency topic measures the operational efficiency of individuals or groups working together or separately to complete a task, including real-world scenarios related to leaking pipes and water cisterns.
Sample Problem 1
Worker A can finish a project in 10 days; Worker B in 15 days. How long will they take working together?
This module explores the core kinetic relationship between the speed of an object, the total distance covered, and the time taken. It covers specialized conceptual problems on moving trains, boats navigating streams, and relative velocity.
Sample Problem 1
A delivery vehicle travels at 54 km/h. Express its speed in m/s.
Solution
Speed = 54 × (5/18) = 15 m/s.
Sample Problem 2
A train 150 m long passes a telegraph pole in 9 seconds. Find its speed in km/h.
Solution
Speed = 150/9 m/s = 16.67 m/s. Convert: 16.67 × (18/5) = 60 km/h.
This area focuses on practical financial mathematics. Simple interest is calculated purely on the initial principal amount invested, whereas compound interest calculates "interest on interest" accumulating over given compounding periods.
Sample Problem 1
Find the compound interest on 10,000 for 2 years at 10% per annum compounded annually.
Solution
A = 10,000 × (1 + 10/100)² = 10,000 × 1.21 = 12,100. CI = 12,100 − 10,000 = 2,100.
Sample Problem 2
A sum triples itself in 5 years at simple interest. In how many years will it become 5 times?
The absolute structural foundation of mathematics, the Number System deals with classifications of numbers (primes, integers, rationals), properties of divisibility, remainders, and finding unit digits in massive expressions.
Sample Problem 1
What is the least positive number that must be added to 1056 so that it is completely divisible by 23?
Solution
1056 ÷ 23 → remainder 21. Number to add = 23 − 21 = 2.
Sample Problem 2
Find the unit digit in the product: 213 × 781 × 527 × 329.
Solution
Unit digits: 3 × 1 × 7 × 9 = 21 × 9 → unit digit = 9.
Number Series tests your logical pattern-recognition skills by presenting an ordered sequence of numbers following a hidden mathematical rule (such as geometric progressions, squares, or alternating prime differences) to identify a missing term.
Sample Problem 1
Find the next number in: 2, 4, 8, 16, 32, ___.
Solution
Geometric progression × 2 each time. Next term = 32 × 2 = 64.
Sample Problem 2
Identify the missing number: 5, 11, 23, 47, 95, ___.
Simplification checks your basic arithmetic parsing speed by requiring you to evaluate complex mathematical expressions quickly using the standard BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction).
Algebra introduces variable notations, linear equations, quadratic equations, and standard polynomial identities to solve for unknown mathematical values hidden within balanced algebraic structures.
A highly popular subset of linear algebraic equations, this topic uses worded relationships to determine past, present, or future ages of individuals based on changing ratios and timelines.
Sample Problem 1
A father is 4 times as old as his son today. In 20 years, he will be twice as old as his son. Find the son's present age.
Solution
Let son = x, father = 4x. In 20 years: 4x + 20 = 2(x + 20) → 2x = 20 → x = 10 years.
Sample Problem 2
The ratio of ages of A and B is 3:4, and their sum is 28 years. Find their age ratio after 4 years.
Solution
A = 12, B = 16. After 4 years: A = 16, B = 20. Ratio = 16:20 = 4:5.
This topic handles fundamental counting principles. Permutations focus specifically on the total number of unique ways to arrange items where order matters, while Combinations handle selecting items where order does not matter.
Sample Problem 1
In how many distinct ways can a committee of 3 members be selected from a total group of 5 people?
Solution
⁵C₃ = (5 × 4 × 3) / (3 × 2 × 1) = 10 unique ways.
Sample Problem 2
How many 3-letter words can be formed using the letters of "SMART" without repetition?
Probability evaluates the exact mathematical likelihood or chance of a specific event occurring out of all possible outcomes, heavily utilizing sample spaces and combination formulas.
Sample Problem 1
What is the probability of getting a sum of exactly 7 when rolling two fair dice?
Solution
Total outcomes = 36. Favorable: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6. Probability = 6/36 = 1/6.
Sample Problem 2
A bag contains 3 red and 5 blue balls. What is the probability of drawing a blue ball?
Mensuration calculates the geometric, spatial properties of 2D shapes (area, perimeter, circumference) and 3D geometric objects (volume, total surface area, curved surface area) like cylinders, spheres, cones, and cubes.
Sample Problem 1
Find the volume of a solid cylinder with base radius 7 cm and height 10 cm. (π = 22/7)
Solution
V = πr²h = (22/7) × 7 × 7 × 10 = 1540 cm³.
Sample Problem 2
Find the perimeter of a rectangular field with length 20 m and width 15 m.
Data Interpretation evaluates your data-literacy skills, specifically your ability to extract, organize, analyze, and manipulate structured statistical information presented visually through bar graphs, pie charts, line charts, and tables.
Sample Problem 1
A pie chart shows 25% of a budget of 100,000 is spent on marketing. What is the exact marketing spend?
Solution
25% of 100,000 = (25/100) × 100,000 = 25,000.
Sample Problem 2
Factory production increases from 500 to 650 units. Find the percentage increase.
Statistics covers the collection, organization, and mathematical analysis of raw datasets, primarily focusing on calculating measures of central tendency (mean, median, mode) and dispersion (range, variance, standard deviation).
Trigonometry explores the geometric relationships between the sides and angles of right-angled triangles, utilizing trigonometric ratios (sine, cosine, tangent) and standard geometric identities.
Sample Problem 1
If sin θ = 3/5, find the value of tan θ.
Solution
Base = √(5² − 3²) = 4. tan θ = Perpendicular / Base = 3/4.
Sample Problem 2
Evaluate: sin²30° + cos²30°.
Solution
By the fundamental identity sin²θ + cos²θ = 1. → Answer = 1.
This topic involves solving relationships where sides are not perfectly equal, comparing expressions using greater than, less than, or equal to conditions, common in quadratic and linear comparison formats.
Sample Problem 1
Solve the inequality: 5x − 3 > 12.
Solution
5x > 15 → x > 3.
Sample Problem 2
Find the range of x: −3x + 4 ≤ 10.
Solution
−3x ≤ 6 → x ≥ −2 (inequality flips when dividing by negative).
You have studied the theory. Now put your skills to the test. Take a full Quantitative Aptitude test, earn your ShaSang Score, and showcase your mathematical prowess to the world.
