CAT Questions based on simplification and approximation - Practice Questions & MCQ

Introduction to simplification and approximation

Simplification and approximation are important concepts in quantitative aptitude as they help in solving complex mathematical problems quickly and efficiently. These concepts are frequently tested in management entrance exams, such as CAT, MAT, XAT, and SNAP.

Importance of simplification and approximation

Simplification and approximation techniques are crucial to save time during the exam. By simplifying complex calculations and making reasonable approximations, candidates can solve complicated equations and arrive at the answer quickly.

Tips for simplification and approximation

- Break down complex expressions into simpler ones, keeping track of operations. - Focusing on the order of operations (BODMAS/BIDMAS) helps solve expressions step by step. - Apply approximation techniques to simplify complicated calculations. - Round off longer digits in the given numbers to make calculations easier. - Avoid unnecessary steps in calculations and practise mental math techniques to save time. - Memorise common ratios, squares, cubes, and fractions to speed up calculations.

Types of questions asked in management entrance exams

Questions on simplification and approximation can cover various topics, such as percentage, fractions, decimals, ratio and proportion, square roots, and logarithms. These questions test the candidate's ability to apply the concepts effectively to arrive at an accurate answer within the given time frame.

Sample question:

Question: Simplify the expression: 

Solution: 

Step 1: Simplify the exponent:

Step 2: Add the simplified exponent to 121: 343 + 121 = 464 

Step 3: Divide the sum by 11: 464 / 11 = 42.18 (rounded off to two decimal places) 

Answer: 42.18

Example question:

Question: Simplify the expression:

Solution: 

Step 1: Simplify the square:  

Step 2: Multiply the simplified numbers: 2.5 * 8.9 * 225 = 5628.75 

Step 3: Divide the product by 4.5: 5628.75 / 4.5 = 1250.833 (rounded off to three decimal places) 

Answer: 1250.833

Tips and tricks:

- Look for common factors or ratios that can be simplified. 

- Practice estimation techniques, such as rounding off numbers to the nearest whole or tenth, to quickly gauge the approximate answer. 

- Familiarise yourself with the logarithmic rules to simplify complex calculations involving exponents. 

- Develop a strong understanding of percentages and their relationships with fractions, decimals, and ratios.

More solved example:

Question: In an entrance test, a candidate who answers 70% of the questions correctly fails by 18 marks. However, another candidate who answers 75% of the questions correctly scores 12 marks more than the passing marks. Find the number of questions in the test. 

Solution: Let the total number of questions be x. 70% of x (0.70x) - 75% of x (0.75x) = 18 + 12 0.05x = 30 x = 30 / 0.05 = 600 

Answer: The total number of questions in the test is 600.

Summary

Simplification and approximation are important concepts in quantitative aptitude, particularly in management entrance exams. These concepts help in solving complex calculations quickly and efficiently. By practising various types of questions and applying tips and tricks, candidates can improve their problem-solving skills and boost their score in this area. Practice is key to gaining proficiency in simplification and approximation, so make sure to solve previous year's questions and time yourself to enhance your speed.