Quick Summary
Numerical ability questions are essential to competitive exams and selection processes in India. For banking exams or looking for a job through the SSC, management entrance, or campus placement, a solid understanding of numerical ability will help you differentiate yourself from other candidates. In the Year 2025, employers and examiners will look for candidates who can solve problems correctly and quickly and display reasoning skills.
This book focuses on quantitative aptitude questions, with worked solutions and expert tips. You will learn about key areas, including arithmetic, algebra, data interpretation, and so much more, with many illustrations to build your confidence and score. With relevant examples and practical tips, we hope you will improve your preparation for any quantitative section you face. So let’s get started and improve your quantitative aptitude skills for your upcoming exams!
Quantitative Aptitude is a fundamental component of many competitive examinations and job interviews, especially for freshers joining the job market. You may find yourself asking, What is Quantitative Aptitude? In summary, it measures your ability to quickly solve quantitative problems accurately. It can be considered your skill in solving issues related to arithmetic, algebra, geometry, and fundamental approaches. Therefore, it tests your understanding of each of these concepts. Strong quantitative aptitude for competitive examinations is essential for performing well and standing out in the selection process.
College students or graduating students who do well in Quantitative Aptitude could give themselves a huge advantage over their competitors during their job search. Companies commonly use quantitative aptitude tests to screen candidates through an understanding of their analytical skills and problem-solving skills; therefore, seeking understanding, practice, and performance will put a candidate in a good place to start their career.
The abstract reasoning test is a type of quantitative aptitude that assesses the mental ability to generate unique, real-time ideas, understand changes in shapes, and create sketches. It also tests the ability to derive logical connections between sets of data.
Numerical tests assess your ability to work with numbers and make decisions based on statistical data. These tests often include questions on fractions, graphs, and other numerical information. They help employers gauge how well you handle quantitative information, solve numerical problems, and interpret data accurately. Practicing numerical tests can improve your confidence and performance in such assessments, ensuring you’re well-prepared to demonstrate your numerical aptitude and analytical skills during job applications or academic evaluations.
A verbal reasoning test is helpful to test comprehension and communication skills. The candidate is asked to read a passage thoroughly, retain all the information, and then answer MCQ-based questions based on the passage. An individual’s complete presence of mind is checked during these tests.
The general aptitude test provides a set of relevant subject questions and analyzes a student’s strong and weak learning areas, thereby determining how well they are prepared for their exams.
Logical reasoning tests evaluate the ability to draw sensible conclusions from statements and information, they test students on their creative and logical thinking capability. This trait even helps to navigate through daily life without any obstructions for further.
Here’s a concise description of each numerical aptitude topic:
The quantitative aptitude syllabus includes various components, some of which are listed here.
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Coordinate Geometry | Points, Lines, and Planes |
Points, Lines and Planes |
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Mensuration |
Ratio, Proportion & Variation |
Geometric Progression |
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LCM & HCF |
Compound Interest |
Graphical Division Geometry |
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Factorials |
Relatives Speed |
Properties of Ratio |
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Remainder Concepts |
Quantitative Aptitude Questions |
Complex Numbers |
Quantitative aptitude boosts your mental alertness. Complex challenges are a part of the routine in the business world. Hence, a person with great quantitative skills will have a sharp mind. Practicing aptitude questions and answers regularly can further enhance these skills, sharpening problem-solving abilities and logical thinking. A person with a good quantitative aptitude can handle problems in a better way as he/she has a knack for finding solutions to problems.
Numbers play an important role in businesses and commerce. Balance sheets, investment analysis, profit and loss calculations, etc., require the individual to be comfortable with numbers. A person with a good level of quantitative aptitude will be better at the analysis and interpretation of data given.
Answer: Rate of interest(r):
r= (Y-X)*100/X
Y = Rs. 9500
X = 9050
On substituting values, r = 5%
Answer: Let the age of the son = X years
∴age of the mother would be = 2X
As per the question 20 years ago;
10 (X -20) = 2X – 20
10X – 200 = 2X – 20
10X – 2X= – 20 + 200
8X = 180
X= 22.5 years
∴Age of mother = 22.5 * 2 = 45 years
Answer: Let the two numbers be 5x and 4x.
(5x – 12) ÷ (4x – 12) = 4 ÷ 3
3(5x – 12) = 4(4x – 12)
15x – 36 = 16x – 48
x = 12
The smaller number is 48.
Answer: The sample space when you roll a die is:
S = (1, 2, 3, 4, 5, 6)
The probability when you roll a die is:
Total number of favorable outcomes ÷ Total number of outcomes
Probability = 2/6 = 1/3
Answer: Find the distance travelled by the train in 7 seconds by applying the following formula:
Distance Speed x Time
Speed is given in Km/hr, so we will convert it into m/s as answers are given in meters.
Speed=90* 5/18= 25 m/s
Time = 7 seconds
Distance = 25 * 7= 175 meters
Answer: 3
Answer: r = 3 cm and h = 4 cm.
using 1/3(pir² h), we get 12pi cm³ as the volume
Answer: (360*6)/12 = 180 degrees
Answer: They are at 22 right angles in 12 hours.
In 24 hours, they are at right angles 44 times.
Answer: 24
Answer: Saturday
Answer: C = (5/10) * 1260
money which C gets = 630
Answer: value of the share = Rs. 100
Dividend per share = 9
An income of Rs. 9 is obtained from an investment of Rs. = (4000/180)*9 = 200
market price of the share = Rs. 200
Answer: 60 ÷ 3 = 20
The chef completes 20 pastas in 30 minutes.
In 2 hours or 120 minutes, the chef can cook four batches.
4 x 20 = 80 pastas
Money notes, cheques, debit cards, coins, letters
Answer: letters
Answer: Let the number of working hours per day be x.
Fewer days, More working hours per day
4 x 1 x x = 3 x 2 x 8
x = 12.
Answer:
When we combine 3 consonants and 2 vowels out of 7 consonants and 4 vowels, using combinations
7C3 * 4C2 = = 210
Every group consists of 5 words, hence the possible arrangement of the letters is 5!
Or, 5! = 120 ways.
The required number of words = 210*120 = 25200.
Answer: let cost of apple = x, kiwi = y, papaya = z
according to the question
10x + 8y + 12z = 240
8x + 6y + 10z = 180
Solve these equations
x + y + z = 30
thus the cost of one apple, one kiwi, and one papaya is 30.
Answer:
When the vowels EAI are always together, they can form one letter.
now we have to arrange the letters LNDG apart from (EAI).
5 i.e. (4 + 1 = 5) letters can be arranged in 5! = 120 ways.
The vowels (EAI) can be arranged in 3! = 6 ways.
hence required number of ways for our required arrangement = (120 x 6) = 720.
Answer: 87 because the other numbers are prime numbers, but 87 has other factors.
Answer:
Suppose the speed of the stream is X km/hr
The speed of the boat is 5 km/hr
Speed upstream is given to be 3km/hr
Speed upstream = speed of the boat – speed of the stream
3 = 5 – X
X = 5 – 3 = 2 km/hr
Answer:
51/4 x (125)0.25
51/4 × (53 )1/4= 5
Answer:
Required number of permutations =
Or, = 180
180 words can be formed.
Answer:
A number is divisible by 5 only if it ends with 0 or 5, since we don’t have 0 in the given digits that means 5 should come at the unit place.
The remaining 5 digits (2, 3, 4, 6, and 7) can come at the tens place.
In the same way, fill the hundreds place with one of the remaining 4 digits.
The thousands place can be filled by one of the remaining 3 digits.
Therefore, the required number of the numbers = 1*5*4*3 = 60.
A fair six-sided die is rolled once. What is the probability of getting a number greater than 4?
Solution:
Possible outcomes = {1, 2, 3, 4, 5, 6}
Numbers greater than 4 = {5, 6} → 2 outcomes
Total outcomes = 6
Probability = Favorable outcomes / Total outcomes = 2 / 6 = 1 / 3
Answer: 1/3
A card is drawn randomly from a standard deck of 52 cards. What is the probability of drawing a heart?
Solution:
There are 4 suits: Hearts, Diamonds, Clubs, Spades
Each suit has 13 cards.
Probability = Favorable / Total = 13 / 52 = 1 / 4
Answer: 1/4
Two fair coins are tossed. What is the probability of getting at least one head?
Solution:
Possible outcomes = {HH, HT, TH, TT}
Outcomes with at least one head = {HH, HT, TH} → 3 outcomes
Total outcomes = 4
Probability = 3 / 4
Answer: 3/4
A bag contains 3 red, 4 blue, and 5 green marbles. One marble is drawn at random. What is the probability it is green?
Solution:
Total marbles = 3 + 4 + 5 = 12
Green marbles = 5
Probability = 5 / 12
Answer: 5/12
Two fair six-sided dice are rolled. What is the probability that the sum is equal to 7?
Solution:
Total outcomes when rolling two dice = 6 × 6 = 36
Favorable outcomes for sum = 7:
Probability = 6 / 36 = 1 / 6
Answer: 1/6
Find sin(30°).
Answer: 0.5 (Standard trigonometric value)
Find cos(60°)
Answer: 0.5 (Standard trigonometric value)
Find tan(45°)
Answer: 1 (Standard trigonometric value)
The 5th term of an AP is 18 and the 10th term is 33. Find the first term and common difference.
Answer:
Let a be the first term, d the common difference.
a+4d=18a + 4d = 18a+4d=18
a+9d=33a + 9d = 33a+9d=33
⇒ d=3d = 3d=3, a=6a = 6a=6
a = 6, d = 3
Find the sum of the first 20 terms of the AP: 7, 10, 13, …
Answer:
a=7,d=3,n=20 Sn=n2[2a+n−1)d]=10[14+57]=710S_n = \frac{n}{2}[2a + (n – 1)d] = 10[14 + 57] = 710 Sn=2n[2a+(n−1)d]=10[14+57]=710
Sum = 710
In a GP, the second term is 6, and the fifth term is 48. Find the first term and common ratio.
Answer:
Let ar=6ar = 6ar=6, ar4=48ar^4 = 48ar4=48
⇒ r=2r = 2r=2, a=3a = 3a=3
ans = a = 3, r = 2
Q: A person walks 5 km north, then 3 km east, then 5 km south. How far is he from the starting point?
Answer:
Net movement north-south = 5 km north − 5 km south = 0
East movement = 3 km
Distance from start = 3 km
Q: Pointing to a man, a woman said, “He is the son of my grandfather’s only son.” How is the woman related to the man?
Answer:
The man is the son of the woman’s father (grandfather’s only son = father).
So, the woman is the sister of the man.
Q: What comes next in the series: A, C, F, J, O, ?
Answer:
Difference between positions:
C (3) – A (1) = 2
F (6) – C (3) = 3
J (10) – F (6) = 4
O (15) – J (10) = 5
Next difference = 6
Next letter = 15 + 6 = 21 (U)
Concepts are the core of mathematics, and to ace your quantitative aptitude exam it is important to understand the concepts to improve your score. The main step is to practice a lot of mathematical questions, and once your grasp is strong on it, you can easily ace any question.
In the process of test preparation for Quantitative Aptitude exams, an essential skill is the ability to recognize both strengths and weaknesses. This fundamental skill significantly enhances the preparation journey. Once students gain a clear understanding of where they need to concentrate more, they can tailor their preparation accordingly. Given that quantitative aptitude revolves around solving mathematical problems, adopting a strategic and intelligent approach is the key to success.
Always make notes and summarise all formulas so that they can be revised frequently, and they are of utmost importance, especially on the night before the exam. Remember that grasping solutions or rote learning is not as crucial as understanding concepts, as only better concepts will lead to better quantitative aptitude abilities.
Employers expect candidates to complete quantitative aptitude tests in a fixed time frame. So, while solving quantitative aptitude questions see the time frame and manage accordingly to answer as many questions as you can.
Keep a record of your timing and note the number of quantitative aptitude questions that you were able to answer correctly, as this will keep you motivated to improve the accuracy and reduce the time, thus charting your success to keep your morale up.
Quantitative aptitude questions for interviews are nothing but a play on English grammar. In such a situation, having impeccable English skills would only be an advantage for you; hence, remember to brush up on your grammar.
There are books and study materials both online and offline as well as thousands of websites offering training materials for improving quantitative aptitude skills, you can join a series of online tests for better results. Not only these, but many educational institutions provide training opportunities to candidates preparing for the quantitative aptitude exams.
Recommended Read:
Preparing thoroughly for the quantitative aptitude test is crucial for success in entrance examinations. This test assesses problem-solving abilities, including cognitive skills like reasoning and decision-making, as well as tasks such as error spotting and pattern recognition. Candidates benefit greatly from practising various types of numerical and quantitative aptitude problems and familiarizing themselves with the test format. By doing so, they can build confidence in their abilities and improve their readiness to tackle the challenges presented. Diligent preparation enhances their performance during the test and boosts their overall chances of achieving a competitive score necessary for admission or employment opportunities.
Explore more information and the latest resources in our Interview Tips section.
Building my quantitative aptitude skills for any competitive exam or job placement is essential. I must practice daily to hone speed, accuracy, and problem-solving skills. Practice is vital because it supplements your foundation in a given subject area by introducing core concepts, shortcut methods, and effective detailed solutions. It is also essential to familiarize yourself with current exam trends and expose yourself to new types of problems to challenge your problem-solving approach.
However, once you develop a consistent daily practice plan and implement innovative methods to prepare for exams, your confidence level and ability to perform on quantitative aptitude exams will elevate significantly, one practice session at a time. Start preparing now to prepare yourself for your session in 2025 and beyond.
Quantitative aptitude is the ability to solve numerical and logical problems. This skill is often tested in competitive exams, job interviews, and academic assessments.
Example: Solving profit and loss questions in a banking entrance exam.
Tip: Practice mental math daily to speed up your calculations.
Regular practice, solving mock tests, and learning shortcut methods are the best ways to improve.
Example: Students solve 20 aptitude questions for placement daily to prepare for campus recruitment.
Tip: Time yourself while solving questions to build speed and accuracy.
Key topics include arithmetic, algebra, geometry, number systems, probability, data interpretation, and logical reasoning.
Example: In CAT exams, data interpretation and probability are critical.
Tip: Focus on high-weight topics that matter for the exam you are studying for.
It is assessed through multiple-choice questions, problem-solving tasks, and case studies in exams such as CAT, GRE, SSC, and banking tests.
For example, SSC exams evaluate arithmetic skills, while CAT emphasizes logical reasoning and data interpretation.
Tip: Check previous years’ papers to understand the exam pattern.
It shows problem-solving skills, logical thinking, and analytical reasoning, especially in finance, consulting, and IT jobs.
Example: In an IT interview, a candidate solves a puzzle about number patterns to show analytical skills.
Tip: Before technical or HR interview rounds, brush up on basic math concepts.
Blend traditional practice with AI-driven learning tools, adaptive quizzes, and personalized feedback systems.
Example: A candidate uses AI-based prep apps, highlighting weak areas after each test.
Tip: Track your progress weekly and adjust your study plan.
Authored by, Mansi Rawat
Career Guidance Expert
Mansi crafts content that makes learning engaging and accessible. For her, writing is more than just a profession—it’s a way to transform complex ideas into meaningful, relatable stories. She has written extensively on topics such as education, online teaching tools, and productivity. Whether she’s reading, observing, or striking up a conversation while waiting in line, she’s constantly discovering new narratives hidden in everyday moments.
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Chegg India does not ask for money to offer any opportunity with the company. We request you to be vigilant before sharing your personal and financial information with any third party. Beware of fraudulent activities claiming affiliation with our company and promising monetary rewards or benefits. Chegg India shall not be responsible for any losses resulting from such activities.
