Arithmetical Reasoning | CSAT Preparation - UPSC PDF Download

What is Arithmetic Reasoning?

Arithmetic Reasoning Formulas

Arithmetic reasoning often involves using basic formulas to solve problems. Here's a list of some common arithmetic formulas that can be helpful:

• Addition: a + b = c
• Subtraction: a - b = c
• Multiplication: a * b = c
• Division: a / b = c
• Average: (a + b + c + ... + n) / n
• Percentage: (part/whole) * 100
• Ratio: a: b
• Proportion: a / b = c / d
• Distance: Speed * Time
• Speed: Distance / Time
• Time: Distance / Speed
• Simple Interest: I = P * R * T / 100 (where I = interest, P = principal, R = rate, and T = time)
• Compound Interest: A = P(1 + r/n)^(nt) (where A = amount, P = principal, r = annual interest rate, n = number of times interest is compounded per year, and t = time in years)
• Profit or Loss: Profit = Selling Price - Cost Price (Loss = Cost Price - Selling Price)
• Percent Increase or Decrease: (New Value - Old Value) / Old Value * 100
• Fractions:
  • Addition: a/b + c/d = (ad + bc) / bd
  • Subtraction: a/b - c/d = (ad - bc) / bd
  • Multiplication: (a/b) * (c/d) = (a * c) / (b * d)
  • Division: (a/b) ÷ (c/d) = (a * d) / (b * c)
• Decimal to Fraction: To convert a decimal to a fraction, write the decimal as the numerator and the denominator as a power of 10 based on the number of decimal places. Then, simplify the fraction.
• Fraction to Decimal: Divide the numerator by the denominator.
• Fraction to Percentage: (Fraction) * 100
• Percentage to Fraction: (Percentage) / 100
• Percentage to Decimal: (Percentage) / 100
• Decimal to Percentage: (Decimal) * 100
• Weighted Average: (w1 * x1 + w2 * x2 + ... + wn * xn) / (w1 + w2 + ... + wn)
• Least Common Multiple (LCM): The smallest multiple that is exactly divisible by each of the numbers.
• Greatest Common Divisor (GCD): The largest number that divides two or more numbers without leaving a remainder.
• Prime Numbers: A number greater than 1 that has only two factors: 1 and itself.
• Factors: The numbers that can be multiplied together to get the original number.
• Square of a Number: a² = a * a
• Cube of a Number: a³ = a * a * a
• Square Root: √a is the number that, when multiplied by itself, equals a.
• Cube Root: ∛a is the number that, when multiplied by itself three times, equals a.
• Permutations: nPr = n! / (n - r)!, where n is the total number of elements and r is the number of elements chosen.
• Combinations: nCr = n! / [r!(n - r)!], where n is the total number of elements and r is the number of elements chosen.

These arithmetic formulas cover the basic concepts and can be applied to various problem-solving situations. However, keep in mind that more advanced arithmetic problems might require additional formulas or a combination of these basic formulas.

Types of Arithmetic Reasoning 

Let us see the various types of arithmetic reasoning questions that may come in your upcoming competitive exams. 

1. Puzzle 
In these type of arithmetic reasoning questions, candidates need to analyze the given piece of information, pick the information that is important, and leave out the information that is not required in solving the given set of questions.

2. Analogy
In these type of arithmetic reasoning questions, candidates will need to find a word or paid words analogous to those given in the question.

3. Series 
In these type of arithmetic reasoning questions, Candidates need to find the missing or wrong number in the provided series. There may be some questions where one of the terms in the given series will be incorrect, and candidates need to find out that term of the series by identifying the pattern involved in the formation of the series. 

4. Inequality 
In these type of arithmetic reasoning questions, candidates must know about various signs, which are used in such types of questions. The same is given below:

5. Venn Diagram
A Venn Diagram is a representation method for all possible relations that can exist between a given group of elements in a single figure. A venn diagram is the easiest way to express the relationship between sets.

6. Cube & Dice
In these type of arithmetic reasoning questions, problems based on single or multiple cube and dice will be asked and candidates need to give the correct answer by analyzing.

Arithmetic Reasoning Tips and Tricks

Solving arithmetic reasoning questions can be made easier by following a step-by-step approach. Here are some arithmetic reasoning tricks and tips to help you tackle these problems more effectively:

• Read the question carefully: Make sure you thoroughly understand the problem statement of the arithmetic reasoning question and identify the information given, as well as what you need to find out.
• Break down the problem: Simplify complex arithmetic problems by breaking them into smaller, more manageable parts. Identify the underlying concepts and relationships between the given data.
• Choose the right formula or method: Based on the information and relationships identified, select the appropriate arithmetic formula or method to solve the problem.
• Organize the data: Arrange the given data and any additional information you've deduced in a structured way. This can be in the form of a table, diagram, or equation.
• Perform calculations: Apply the chosen arithmetic formula or method and carry out the necessary calculations. Keep track of units, if applicable, and ensure the accuracy of your calculations.
• Check your work: Verify the accuracy of your calculations and ensure that your answer makes logical sense in the context of the problem. If necessary, retrace your steps and identify any errors.
• Simplify the answer: If required, simplify your answer by expressing it in the most appropriate format, such as a fraction, decimal, or percentage.
• Review the question: Go back to the problem statement and ensure your answer addresses what was asked. If the question has multiple parts, make sure you've addressed all aspects.

Solved Arithmetic Reasoning Questions

Q1: A store sells packs of 6 pens for $4.50 per pack. How much would 3 packs cost?
Ans: Cost of 3 packs = 3 * $4.50 = $13.50

Q2: 3, 6, 11, 18, 27, ?, 51
Ans: 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.

Q3: 71 : 42 :: 98 : ?
Ans: 71 – 29 = 42
Similar, 98 – 29 = 69
Hence, 69 will replace the question mark.

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?
Ans: 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?
Ans: Average speed = Total distance / Total time Average speed = 360 miles / 6 hours Average speed = 60 miles per hour 

Q6: If the area of a rectangle is 180 square units and its length is 12 units, what is its width?
Ans: Area of a rectangle = length * width 180 = 12 * width width = 180 / 12 width = 15 units

Q7: In a class of 40 students, 12 students are girls. What percentage of the class is made up of girls?
Ans: Percentage of girls = (Number of girls / Total students) * 100 Percentage of girls = (12 / 40) * 100 Percentage of girls = 30%