Quantitative Reasoning: Concepts and Tips | 3 Months Preparation for CAT PDF Download

What is Arithmetic Reasoning?

Arithmetic Reasoning entails the capacity to comprehend and address mathematical challenges through fundamental arithmetic operations like addition, subtraction, multiplication, and division. This aptitude requires the utilization of logic, critical thinking, and problem-solving methods to execute calculations and scrutinize numerical connections. Integral to mathematics education, it plays a pivotal role in everyday responsibilities and extends to more intricate endeavors like financial management, engineering, and scientific research. Proficiency in arithmetic reasoning encompasses not only the skill to carry out calculations but also a grasp of the underlying principles, the ability to discern patterns, and the aptitude to make informed decisions grounded in numerical data.

Arithmetic Reasoning assesses a candidate's mathematical proficiency, typically featuring numerical questions that often involve calculations. Individuals with an aversion to mathematics may find this section challenging, but with a solid understanding of concepts and regular practice, they can excel in this area. The topics within arithmetic reasoning encompass Puzzle, Analogy, Series, Venn Diagram, Cube and Dice, Inequality, and more.

This article delves into essential Arithmetic Reasoning concepts, exploring various types, providing solved examples, presenting practice questions, and offering tips and tricks for solving related problems. A thorough reading of this article will help dispel any uncertainties regarding this subject.

Examples

Q1: In a class of 40 students, 12 students are girls. What percentage of the class is made up of girls?
Sol: Percentage of girls = (Number of girls / Total students) * 100 Percentage of girls = (12 / 40) * 100 Percentage of girls = 30%

Q2: 5, 11, 24.2, 53.24, ?, 257.6816
Sol: The solution of the series is as follows.
5 x 2.2 = 11
11 x 2.2 = 24.2
24.2 x 2.2 = 53.24
53.24 x 2.2 = 117.128
117.128 x 2.2 = 257.6816
Hence, the correct answer is 117.128.

Q3: 49, 121, 169, ?, 361
Sol: The solution of the series is as follows.
7² = 49
11² = 121
13² = 169
17² = 289
19² = 361
Hence, the correct answer is 289.

Q4: The position of how many digit(s) in the number 381576 will remain the same after the number is arranged in the ascending order?
Sol: 
Original number form is: 3 8 1 5 7 6
Ascending order form is: 1 3 5 6 7 8
If we check the number/s whose position will remain the same in both forms then we will see that the position of only number remains same or unchanged which is the number 7.
Hence, the correct answer is One.

Q5: A car travels 360 miles in 6 hours. What is its average speed?
Sol: Average speed = Total distance / Total time Average speed = 360 miles / 6 hours Average speed = 60 miles per hour

Q6: What is 35% of 120?
Sol: 35% of 120 = (35/100) * 120 = 42

Q7: If the area of a rectangle is 180 square units and its length is 12 units, what is its width?
Sol: Area of a rectangle = length * width 180 = 12 * width width = 180 / 12 width = 15 units

Q8: Solve for y: 4y + 5 = 3y + 12
Sol: 4y + 5 = 3y + 12 4y - 3y = 12 - 5 y = 7

Q9: 67 : 76 :: 42: ?
Sol:
67 + 9 = 76
Similarly, 42 + 9 = 51,
Hence, 51 will replace the question mark.

Q10: 3, 6, 11, 18, 27, ?, 51
Sol: The solution of the series is as follows.
3 + 3 = 6
6 + 5 = 11
11 + 7 = 18
18 + 9 = 27
27 +11 = 38
38 + 13 = 51
Hence, the correct answer is 38.

Q11: A fruit seller sold 120 kg of apples at $4 per kg and 80 kg of oranges at $5 per kg. How much money did he earn in total?
Sol: Money from apples = 120 kg * $4 = $480 Money from oranges = 80 kg * $5 = $400 Total money earned = $480 + $400 = $880

Q12: A store is offering a 25% discount on a jacket that originally costs $80. What is the sale price of the jacket?
Sol: Discount amount = 25% of $80 = (25/100) * $80 = $20 Sale price = Original price - Discount amount Sale price = $80 - $20 = $60

Q13: If 3x - 7 = 20, what is the value of x?
Sol: 3x - 7 = 20 3x = 20 + 7 3x = 27 x = 27 / 3 x = 9

Q14: If a train travels at 75 miles per hour for 2 hours and 45 minutes, how far does it travel?
Sol: Time in hours: 2 hours + (45 minutes / 60 minutes) = 2.75 hours Distance = Speed * Time Distance = 75 miles/hour * 2.75 hours = 206.25 miles

Q15: 71 : 42 :: 98 : ?
Sol:
71 – 29 = 42
Similar, 98 – 29 = 69
Hence, 69 will replace the question mark.

Q16: What is the average of the numbers 18, 24, and 30?
Sol: Average = (Sum of numbers) / (Number of numbers) Average = (18 + 24 + 30) / 3 Average = 72 / 3 = 24

Q17: A rectangular garden has a perimeter of 60 meters, and its width is 10 meters. What is its length?
Sol: Perimeter of a rectangle = 2 * (length + width) 60 = 2 * (length + 10) 30 = length + 10 Length = 20 meters

Q18: What is the smallest positive integer that is divisible by both 6 and 8?
Sol: Find the least common multiple (LCM) of 6 and 8. Prime factors of 6 = 2 * 3 Prime factors of 8 = 2^3 LCM = 2³ * 3 = 24 The smallest positive integer is 24.

Q19: Solve the following equation: 5(x - 3) = 4(x + 2)
Sol: 5(x - 3) = 4(x + 2) 5x - 15 = 4x + 8 5x - 4x = 15 + 8 x = 23

Q20: A car rental company charges $20 per day plus an additional $0.15 per mile driven. How much would it cost to rent a car for 3 days and drive 200 miles?
Sol: Cost for 3 days = 3 * $20 = $60 Cost for 200 miles = 200 * $0.15 = $30 Total cost = $60 + $30 = $90

Q21: If 9 books weigh 36 pounds, how much would 15 books weigh?
Sol: Weight of 1 book = 36 pounds / 9 books = 4 pounds/book Weight of 15 books = 15 books * 4 pounds/book = 60 pounds

Q22: A person invests $1000 in a savings account with an annual interest rate of 4% compounded annually. What is the balance in the account after 2 years?
Sol: A = P(1 + r/n)^(nt) Where A is the final amount, P is the principal, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.
A = P(1 + r/n)^(nt) Where A is the final amount, P is the principal, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. A = 1000(1 + 0.04/1)^(1*2) A = 1000(1 + 0.04)² A = 1000(1.04)² A = 1000 * 1.0816 A = 1081.60
The balance in the account after 2 years is $1081.60.

Q23: What is the sum of the first ten positive odd numbers?
Sol: The first ten positive odd numbers are: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 Sum = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100

Q24: If a square has a side length of 8 units, what is the length of its diagonal?
Sol: Diagonal length = Side length * √2 Diagonal length = 8 * √2 = 8√2 units

Q25: A store sells packs of 6 pens for $4.50 per pack. How much would 3 packs cost?
Sol: Cost of 3 packs = 3 * $4.50 = $13.50

Q26: If the sum of three consecutive even numbers is 78, what is the largest number?
Sol: Let the numbers be x, x+2, and x+4. x + (x+2) + (x+4) = 78 3x + 6 = 78 3x = 72 x = 24 The largest number is x + 4 = 24 + 4 = 28