What are the Mathematical Tricks Used in Aptitude Tests: A Guide for Efficiently Solving MCQs
Mathematics used in aptitude tests often involves various types of tricks and techniques that candidates can employ to solve problems quickly and accurately. These techniques can be particularly useful in multiple-choice questions (MCQs) which are common in aptitude tests, including those for the Joint Entrance Examination (JEE) Mains and Advanced. Understanding these tricks can significantly enhance your performance in such tests.
Patterns and Sequences
Identifying and extrapolating numeric, geometric, or alphanumeric patterns is a fundamental skill in aptitude tests. This involves finding the next number, shape, or letter in a sequence. For example, if the sequence is 3, 6, 12, 24, ?, a candidate should recognize the pattern as a sequence where each number is doubled. The next number would be 48.
Logical Reasoning
Aptitude questions may present logical scenarios and ask the test-taker to deduce the next step or conclusion based on the given information. Analytical thinking and the ability to draw inferences are crucial here. For example, if a question states that 'A is more intelligent than B, and B is more intelligent than C', one must logically deduce that 'A is the most intelligent among A, B, and C'.
Number Manipulation
Questions often involve performing quick calculations, estimating answers, or using properties of numbers such as divisibility rules, square roots, and percentages. For instance, if a question asks about the percentage increase of a value, using the property that a 20% increase from 50 is 60 can be much faster than performing the full calculation.
Using Options for MCQs
The most efficient method for solving MCQs is often to leverage the provided answer options. Here are some strategies:
Reverse Substitution: Use this method for geometry or complex functions. If a question asks for the intersection of two curves, try substituting the options into the equations. For example, if the equation of a curve is Y x^2 5, and the options are points, substitute each point to find the one that fits both equations. Trigonometric Simplification: For trigonometric equations, pick a random angle, such as 30 degrees, calculate the value, and then substitute this value into each option to find the correct one. This is particularly useful when options are the simplified forms of complex equations. Calculus Integration: For integration problems, differentiate each option and check if it matches the function you are integrating. This method can save time and provide accurate results.Attention to Detail and Confirmation
While the reverse substitution method can be highly effective, it's crucial to maintain a high level of scrutiny, especially in high-stakes exams like JEE Advanced. If an answer seems too easy, double-check your work. A simple oversight can lead to incorrect conclusions, and JEE Advanced does not forgive such errors.
Conclusion
Mastering these mathematical tricks and techniques can significantly improve your performance in aptitude tests and MCQs like those in the JEE. Developing a strong foundation in mathematics and practicing these techniques will help you tackle complex problems with confidence and accuracy.