Maths tricks and shortcuts are the easiest and fastest ways in which you can solve mathematical problems in the upcoming Government exams. The quantitative aptitude or the numerical ability section are most commonly a part of all major tests and if a candidate can get shortcut tricks to solve this section quickly he or she may be able to score more overall in the examination.
1. Quadratic Equations
Given below are two examples of quadratic equations solved with easy tricks to find the answer quickly:
Example: x² – 18x + 45 = 0
Step 1: Multiply the coefficient of x² and the constant in the equation. In this case, 1×45 = 45
Step 2: Multiply “-1” with the coefficient of x. In this case, -1× (-18) = 18
Step 3: Hence, the value of x will be 15 and 3 (3+15=18 & 3×15=45). Remember, for signs, if the answer obtained in both step 1 & 2 is positive, then both values of x will be positive. If even one is negative, then values of x will be negative.
Here, the value obtained in step 1 & 2 is positive hence the value of x will be positive. So, the answer is x = 15, 3
Example: x²-5x-6 = 0
Step 1: Multiply the coefficient of x² and the constant in the equation. In this case, 1×(-6) = (-6)
Step 2: Multiply “-1” with the coefficient of x. In this case, (-1)× (-5) = 5
Step 3: Hence, the value of x will be 6 and 1 (6-1=5 & 6×1=6). Remember, for signs, if the answer obtained in both step 1 & 2 is positive, then both values of x will be positive. If even one is negative, then one of the values of x will be negative.
Step 4: Here the answer in step 1 is negative. Thus, one value of x will be negative. If the answer in step 1 is negative, the smaller value of x will be negative. If the answer in step 2 is negative, the larger value will be negative.
So, x= 6, -1.
2. Number Series
If a candidate is confused about the system followed in a number series, the easiest way to find the difference between two numbers in the series.
Example: 46 62 87 123 ? 236
Solution:
Step 1: Start with finding the difference between two numbers
Step 2: Once you find the difference, you will notice that the pattern with the square of numbers has been followed.
42 = 16
52 = 25
62 = 36
72 = 49
82 = 64
For any other question asked in number series format and the candidate faces any kind of confusion in following the pattern, they can directly find the difference between two numbers in the series, it shall make solving it easier.
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