Maths for Competitive Exams

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Maths for Competitive Exams

While preparing for a competitive exam like GRE, GMAT or SAT, it is common to feel panicked about the mathematical section which is a complex one to crack. The main purpose of adding the category of Quantitative Aptitude to a competitive exam is to test your ability to solve basic mathematical problems logically. For this, a good grasp of quantitative concepts with sufficient practice is needed. If you are planning to appear for a competitive test, you have come to the right place. In this blog, we will elaborate on the key concepts of Maths for competitive exams along with helpful tips, tricks and math books for competitive exams you can employ to score better.

Take This Simple Maths Quiz to Test Your Maths Skills for Competitive Exams

Syllabus: Maths for Competitive Exams

Here is a recap of the topics which are commonly found in the quantitative aptitude section of Maths for Competitive Exams :

Also Read: Success Mantra for Competitive Exams

Maths Tricks & Tips for Competitive Exams

Here is a compilation of few tricks and examples which you can follow to score well in Maths for Competitive Exams :

1. Substitute variable with 0 or 1

Substituting variables with simple numbers like 0 or 1 can assist you in solving algebra questions in the section of Maths for competitive exams.

Quantity A = 8x + 2
Quantity B = 8(x+2)

a) Quantity B > A
b) Both quantities are equal
c) The relationship cannot be determined
d) Quantity A>B

Trick: Substitute variable “x” with 0

The answer is option b 

2. Plugging-in numbers

Plugging-in numbers is a common trick that you should know while practising Maths for competitive exams. The basic idea behind this strategy is to substitute variable with easy and manageable numbers like 1, 2, -1 etc. and find the answer. Let us understand using an example.

x is an even integer. Which of the following is the sum of two even integers greater than 4x+2?

a) x+8
b) 8x+6
c) 8x+4
d) 8x+2

Trick: Follow these steps:
Step 1: Choose a number. In this case, let us take x=2 (as it says “even integer”)
Step 2: Substitute this value in the above equation. This gives us 9
Step 3: Look for even integers greater than 9. Which brings us to 10 and 12
Step 4: Since the question says, “sum of two even integers greater than 4x+2” therefore, add the integers i.e. 10 + 12 = 22


The correct answer lies where the sum equals to 22, i.e. option b

3. Speed Problems

Always remember that if two objects with speed x and y respectively are moving in the same direction, then their relative speed will be x-y.

However, if the same two objects move in the opposite direction then, their relative speed will be x+y.

4. Back Substitution

Back Substitution is a helpful trick that can help you in acing Maths for competitive exams. This technique can be used when you are not sure about which formulas or methods to use to solve the question. 

What can be the possible value of y so that |(2-|y-2|)| = 7

a) -4
b) -7
c) 3
d) 11
e) 5

Let us start with the first option. On substituting y= -4, we get the final answer as 8
Let us now substitute y=-7. This gives 7 on both sides.
Thus, if you are not familiar with any technique to solve the question, you can simply start substituting values into the equation. 

Answer of the example is option a

Here are some Number Series questions for you!

Tips to Improve Maths for Competitive Exams

Let’s impart you with the key tips you can follow to nail your preparation for the section of Maths for Competitive Exams.

Always Keep a List of Important Formulas on Your Desk
Maths without formulas is like Pizza without cheese. Instead of cramming up the formulas at the last moment, it is better to go through them as many times as you can. Also, try to memorise only few important formulas and not the entire list. 

Master Important Topics First
Study smart, not hard. Almost all the topics in Maths for competitive exams are important but there are a few concepts that are commonly asked. Identify those areas and practise them thoroughly. 

Break the Shapes
In the section of Maths for competitive exams, you are bound to get confused in questions with complex and intertwined shapes. Simply redraw the shapes separately on a rough sheet and then answer the question.

Memorize the Right Stuff
Remember multiplication tables at least up to 30 and learn the square as well as cube roots for numbers till 40. These hacks can help you save time from difficult calculations.

Follow the Mantra of Practice
When you take competitive tests that are set in a specific time frame, it improves your speed and helps you identify the areas where you still lag. So, keep practising the key concepts until you feel confident enough to crack them.

Practice Questions Maths for Competitive Exams

Now that you are equipped with all the insights of competitive Maths questions that appear in competitive exams, it’s time to brush up your Mathematics skills with the help of some practice questions. We have compiled some questions from all popular topics to ensure all-around learning. Here you go:

Percentage

Q1: Express 40 metres as a percentage of 6 miles.
Q2: A’s income is 50% more than B. By how much percentage is B’s income less than A’s?
Q3: Arvind spends 75% of his income. His income increased by 20% while his expenditure increased by 10%. By what percentage did his savings increase?

Decimals 

Q1: Convert 45 3/11 into decimals.
Q2: A man spends 414.68$ on clothes. Each shirt costs 23.44$. He decides to purchase 5 shirts and spend the rest of the money on pants. How much does he spend on pants?
Q3: A car travels 34.56 miles per hour. It has to complete a journey of 400 miles in total. How much time would it take to complete the journey?

Factors and Multiples

Q1: Write down all the factors of 3280.
Q2: Give a list of 5 consecutive numbers which are not prime.
Q3: Give the first five common multiples of 48 and 57. 

Ratios

Q1: What is the ratio of the radius of a circle to its circumference?
Q2: Divide 360$ among A, B and C in such a way that As share is twice that of B, and Bs share is twice that of C.
Q3: The ratio of two digits is 1:3. What is their maximum sum if the first digit is a prime number? 

Geometry 

Q1: If one angle of a triangle is equal to 80 degrees, what is the smallest possible angle in the triangle?
Q2: The sum of interior angles of a regular polygon is equal to 900 degrees. What is the shape of the polygon?
Q3: What is the maximum number of circles of diameter 6 cm which can be drawn in a square of area 144 sq cm.?

Integers

Q1: The sum of three consecutive integers is 87. What is the biggest number among them?
Q2: If the difference between an integer and its negative value is 68, what is the integer?
Q3: There are 12 students in the classroom. The teacher adds twice the number of students to the class sheet and half the new students are absent. What is the present strength of the class?

Check out: Short Tricks used in Maths for Competitive Exams

Number System

Q1. What are the five rational numbers between 1 and 2?
Q2. Show that 0.3333… = 0 3, can be expressed in the form of rational numbers, i.e. p/q.
Q3. How many whole numbers are there between 244 and 332 which are exactly divisible by 7?

 Simplification

Q1. 136÷5÷0.4 =? – 24×3.5
Q2. 53457 + 19743 – 49850 =?
Q3.13% of 1100 + 17% of 2100 =? + 26% of 350

HCF and LCM

Q1. Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. What is the sum of the digits in N?
Q2. The greatest number of four digits which is divisible by 15, 25,40 and 75?
Q3. Find the lowest common multiple of 24, 36 and 40?

Ratio and Proportion

Q1.A sum of Rs.312 was divided among 100 boys and girls in such a way that the boy gets Rs.3.60 and each girl Rs. 2.40 the number of girls is?
Q2. The salaries of A, B, and C are in the ratio of 1: 2 : 3. The salary of B and C together is Rs. 6000. By what per cent is the salary of C more than that of A?
Q3. Seats for Mathematics, Physics and Biology in a school are in the ratio 5:7:8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?

Problems on Age

Q1. One year ago, the ratio of Rahul and Ram ages was 2: 3 respectively. After five years from now, this ratio becomes 4: 5. How old is Ram now?
Q2. Ten years ago, the age of a mother was three times the age of her son. After ten years, the mother’s age will be twice that of his son. Find the ratio of their present ages.
Q3. The ratio of the present ages of Pranav and Qureshi is 4:5. Five years ago, the ratio of their ages was 7:9. Find their present ages? (In years)

Partnership

Q1. Shakeel started a software business by investing Rs. 20,000. After six months, Neel joined him with a capital of Rs. 30,000. After 3 years, they earned a profit of Rs. 13,950. What was Shakeel’s share in the profit?
Q2. In business, Anuj and Chirag invested amounts in the ratio 4:2, whereas the ratio between amounts invested by Anuj and Bimal was 6:4, If Rs 314600 was their profit, how much amount did Bimal receive?
Q3. Rs.1400 is divided among Amla, Bimla and Simla so that Amla receives half as much as Bimla and Bimla half as much as Simla. Then Simla’s share is?

Must Read: Solve Different Types of Maths & Reasoning Questions for Competitive Exams

BODMAS

Q1. Solve this question using the BODMAS rule: 2 [2 + 2 {39 -2 (17 + 2)}] 
Q2. 25- 1/25 {5+ 4 – (3+ 2- 1 + 3)}
Q3. Determine the correct answer for- (1/4 + 7/4) – 2  

Average

Q1. The average marks of a Suresh in 10 papers are 80. If the highest and the lowest scores are not considered, the average is 81. If his highest score is 92, find the lowest?
Q2. Suraj has a certain average of runs for 12 innings. In the 13th innings, he scores 96 runs thereby increasing his average by 5 runs. What is his average after the 13th innings?
Q3. The average weight of 8 sailors in a boat is increased by 1 kg if one of them weighing 56 kg is replaced by a new sailor. The weight of the new sailor is?

Profit and Loss

Q1. A man bought a cycle for Rs. 250. For how much should he sell it so as to gain 10%?
Q2. If a man purchases 11 oranges for Rs. 10 and sells 10 oranges for Rs. 11. How much profit or loss does he make?
Q3. A dishonest dealer professes to sell his goods at a profit of 20% and also weighs 800 gm in place of a kg. Find his actual gain percentage?

Simple and Compound Interest

Q1.How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
Q2. What will be the ratio of simple interest earned by a certain amount at the same rate of interest for 6 years and that for 9 years?
Q3. What should be the least number of years in which the simple interest on Rs.2600 at 6⅔%  will be an exact number of rupees?

Mensuration

Q1. What will be the cost of building a fence around a square plot with an area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?
Q2. A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangle, whose length and breadth are in the ratio of 6: 5. What is the area of the rectangle?
Q3. The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions?

Time and Work

Q1. A, B, and C can do a piece of work in 8 days. B and C together do it in 24 days. B alone can do it in 40 days. In what time will it be done by C working alone?
Q2. Daku and Tamatar can do a piece of work in 70 and 60 days respectively. They began the work together, but Daku left after some days and Tamatar finished the remaining work in 47 days. After how many days did Daku leave?
Q3. Kim can do a work in 3 days while David can do the same work in 2 days. Both of them finish the work together and get Rs. 150. What is the share of Kim?

Check out: Learn Statistics Formulas for Maths Section in Competitive Exams

Time and Distance

Q1. If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
Q2. Nikita takes as much time in running 18 meters as a car takes in covering 48 meters. What will be the distance covered by Nikita during the time the car covers 1.6 km? 
Q3. What distance will be covered by a bus moving at 72 kmph in 30 seconds?

Square Root

Q1. Calculate the square root of 0.036?
Q2.  Determine the final value of the number 151 
Q3. There are 8 odd numbers. Describe how the sum of these 8 numbers is 64. 

Trigonometry

Q1. In triangle, ABC, ∠B = 90 degrees, tan A = 6/5, Find other trigonometric ratios of Angle A
Q2. In an triangle ABC, right-angled at B, AB = 7 and ∠ACB = 30 degrees. Find the lengths of sides BC and AC.
Q3. If tan(A+B)= √3 and tan(A–B)= 1/√3 ;0°<A+B≤90° ; A>B, find A and B. 

Approximation

Q1. 40.01² – 23.98² – ? = 31.97²
Q2. 17.1% of 725 + 12.8% of 643 =? 
Q3. 4433.764 – 2211.993 – 1133.667 + 3377.442

Mixture & Alligation

Q1. How many kilograms of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per Kg so that there may be a gain of 10 % by selling the mixture at Rs. 9.24 per Kg?
Q2. A can contains a mixture of two liquids A and B in the ratio of 7: 5. When 9 litres of the mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7: 9. How many litres of liquid A was contained by the can initially?
Q3.  A sum of Rs.118 was divided among 50 boys and girls such that each boy received Rs.2.60 and each girl Rs.1.80. Find the number of boys and girls?

Permutation and Combination

Q1. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
Q2. In how many ways can the letters of the word ‘LEADER’ be arranged?
Q3. In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

Boats and Streams

Q1. A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
Q2. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?
Q3. A man rows to a place 48 km distant and comes back in 14 hours. He finds that he can row 4 km with the stream at the same time as 3 km against the stream. The rate of the stream is

Surds and Indices

Q1. If 5a = 3125, then the value of 5(a – 3) is:
Q2. If 3(xy) = 27 and 3(x + y) = 243, then x is equal to:
Q3. (256)0.16 x (256)0.09 = ?

Pipes and Cisterns

Q1. Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:
Q2. A tank is filled in 5 hours by three pipes A, B and C. Pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
Q3. A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tanker from an empty state if B is used for half the time and A and B fill it together for the other half?

Maths Books for Competitive Exams

Maths is the trickiest section in every competitive exam and solving maths questions for competitive exam is overwhelming and frightening for some people. This is why we have created a list of math books for competitive exams that will make maths easy and fun! These books are ideally used for banking exams, management exams and  UPSC. All candidates should refer to these books because they contain practise questions, tricks and tips on how to ace your math and quantitative section in upcoming competitive exams!

  • Fast Track Objective Arithmetic by Rajesh Verma
  • Handbook for Mathematics by Arihant Experts
  • For Competitive Exams Vedic Mathematics by Ramnandan Shastri
  • Quantitative Aptitude for Competitive Examinations by R S Aggarwal 
  • Mathematics for All Competitive Exams SSC (Pre./Mains) by Ramniwas Mathuriya 
  • Arithmetic Subjective and Objective for Competitive Examination by R S Aggarwal
  • Objective Arithmetic (SSC & Railway Exam Special) by R.S Aggarwal
  • Shortcuts in Quantitative Aptitude for Competitive Exams by Disha Publication
  • Teach Yourself Quantitative Aptitude by Arun Sharma
  • The Pearson Guide To Quantitative Aptitude For Competitive Examination by Dinesh Khattar
  • Quantitative Aptitude for all Competitive Exam by Abhijit Gupta
  • NCERT Math Books for 10th,11th and 12th

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FAQs: Maths for Competitive Exams

How can I improve my maths in competitive exams?

Regular practice and memorising important tables and formulas are the best way to improve your maths for competitive exams.

Which maths book is best for competitive exams?

Here are some of the best math books for competitive exams-
Fast Track Objective Arithmetic by Rajesh Verma
Handbook for Mathematics by Arihant Experts
For Competitive Exams Vedic Mathematics by Ramnandan Shastri
Quantitative Aptitude for Competitive Examinations by R S Aggarwal 
Mathematics for All Competitive Exams SSC (Pre./Mains) by Ramniwas Mathuriya 
Arithmetic Subjective and Objective for Competitive Examination by R S Aggarwal
Objective Arithmetic (SSC & Railway Exam Special) by R.S Aggarwal

What is the syllabus for maths competitive exams?

Maths section in competitive exams is the toughest portion and includes a wide range of topics such as Time & Distance, Trignometry, Number System, Approximation, Mixture and Alligation, Permutation and Combination, Boats and Streams, Surds and Indices, Pipes and Cisterns etc

What competitive exams include Maths section?

Many competitive exams include Maths as a section in the exam such as CAT, MAT, UPSC, BPSC, Bank exams, Railway exams.

Also Read: Logical Reasoning for Competitive Exams

We hope that now solving Maths for competitive exams will no longer be a nightmare for you after reading this blog. If you require any further guidance on how to score well in competitive exams, get in touch with our Leverage Edu experts and we will give you the right guidance and preparation mantras to nail any competitive test with high scores.

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